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Merge pull request #17683 from ivashmak:homography

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[GSoC] New RANSAC. Homography part

* change enum and squash commits

* add small improvements

* change function to static, update magsac

* remove path from samples, remove license, small updates

* update pnp solver, small improvements

* fix warnings

* add tutorial, comments

* fix markdown warnings

* fix markdown warnings

* fix markdown warnings
pull/18116/head
Maksym Ivashechkin 4 years ago committed by GitHub
parent b45273eccb
commit a66f61748f
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  1. 307
      doc/tutorials/calib3d/usac.markdown
  2. 1
      modules/calib3d/CMakeLists.txt
  3. 62
      modules/calib3d/include/opencv2/calib3d.hpp
  4. 20
      modules/calib3d/src/five-point.cpp
  5. 36
      modules/calib3d/src/fundam.cpp
  6. 19
      modules/calib3d/src/ptsetreg.cpp
  7. 29
      modules/calib3d/src/solvepnp.cpp
  8. 800
      modules/calib3d/src/usac.hpp
  9. 336
      modules/calib3d/src/usac/degeneracy.cpp
  10. 877
      modules/calib3d/src/usac/dls_solver.cpp
  11. 273
      modules/calib3d/src/usac/essential_solver.cpp
  12. 625
      modules/calib3d/src/usac/estimator.cpp
  13. 335
      modules/calib3d/src/usac/fundamental_solver.cpp
  14. 237
      modules/calib3d/src/usac/gamma_values.hpp
  15. 445
      modules/calib3d/src/usac/homography_solver.cpp
  16. 676
      modules/calib3d/src/usac/local_optimization.cpp
  17. 377
      modules/calib3d/src/usac/pnp_solver.cpp
  18. 581
      modules/calib3d/src/usac/quality.cpp
  19. 977
      modules/calib3d/src/usac/ransac_solvers.cpp
  20. 548
      modules/calib3d/src/usac/sampler.cpp
  21. 378
      modules/calib3d/src/usac/termination.cpp
  22. 526
      modules/calib3d/src/usac/utils.cpp
  23. 408
      modules/calib3d/test/test_usac.cpp
  24. 106
      samples/cpp/epipolar_lines.cpp
  25. 342
      samples/cpp/essential_mat_reconstr.cpp
  26. 5
      samples/data/essential_mat_data.txt
  27. BIN
      samples/data/leuvenA.jpg
  28. BIN
      samples/data/leuvenB.jpg
  29. 137
      samples/python/essential_mat_reconstr.py

307
doc/tutorials/calib3d/usac.markdown
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@ -0,0 +1,307 @@
---
author:
- Maksym Ivashechkin
bibliography: 'bibs.bib'
csl: 'acm-sigchi-proceedings.csl'
date: August 2020
title: 'Google Summer of Code: Improvement of Random Sample Consensus in OpenCV'
...
Contribution
============
The integrated part to OpenCV `calib3d` module is RANSAC-based universal
framework USAC (`namespace usac`) written in C++. The framework includes
different state-of-the-arts methods for sampling, verification or local
optimization. The main advantage of the framework is its independence to
any estimation problem and modular structure. Therefore, new solvers or
methods can be added/removed easily. So far it includes the following
components:
1. Sampling method:
1. Uniform – standard RANSAC sampling proposed in \[8\] which draw
minimal subset independently uniformly at random. *The default
option in proposed framework*.
2. PROSAC – method \[4\] that assumes input data points sorted by
quality so sampling can start from the most promising points.
Correspondences for this method can be sorted e.g., by ratio of
descriptor distances of the best to second match obtained from
SIFT detector. *This is method is recommended to use because it
can find good model and terminate much earlier*.
3. NAPSAC – sampling method \[10\] which takes initial point
uniformly at random and the rest of points for minimal sample in
the neighborhood of initial point. This is method can be
potentially useful when models are localized. For example, for
plane fitting. However, in practise struggles from degenerate
issues and defining optimal neighborhood size.
4. Progressive-NAPSAC – sampler \[2\] which is similar to NAPSAC,
although it starts from local and gradually converges to
global sampling. This method can be quite useful if local models
are expected but distribution of data can be arbitrary. The
implemented version assumes data points to be sorted by quality
as in PROSAC.
2. Score Method. USAC as well as standard RANSAC finds model which
minimizes total loss. Loss can be represented by following
functions:
1. RANSAC – binary 0 / 1 loss. 1 for outlier, 0 for inlier. *Good
option if the goal is to find as many inliers as possible.*
2. MSAC – truncated squared error distance of point to model. *The
default option in framework*. The model might not have as many
inliers as using RANSAC score, however will be more accurate.
3. MAGSAC – threshold-free method \[3\] to compute score. Using,
although, maximum sigma (standard deviation of noise) level to
marginalize residual of point over sigma. Score of the point
represents likelihood of point being inlier. *Recommended option
when image noise is unknown since method does not require
threshold*. However, it is still recommended to provide at least
approximated threshold, because termination itself is based on
number of points which error is less than threshold. By giving 0
threshold the method will output model after maximum number of
iterations reached.
4. LMeds – the least median of squared error distances. In the
framework finding median is efficiently implement with $O(n)$
complexity using quick-sort algorithm. Note, LMeds does not have
to work properly when inlier ratio is less than 50%, in other
cases this method is robust and does not require threshold.
3. Error metric which describes error distance of point to
estimated model.
1. Re-projection distance – used for affine, homography and
projection matrices. For homography also symmetric re-projection
distance can be used.
2. Sampson distance – used for Fundamental matrix.
3. Symmetric Geometric distance – used for Essential matrix.
4. Degeneracy:
1. DEGENSAC – method \[7\] which for Fundamental matrix estimation
efficiently verifies and recovers model which has at least 5
points in minimal sample lying on the dominant plane.
2. Collinearity test – for affine and homography matrix estimation
checks if no 3 points lying on the line. For homography matrix
since points are planar is applied test which checks if points
in minimal sample lie on the same side w.r.t. to any line
crossing any two points in sample (does not assume reflection).
3. Oriented epipolar constraint – method \[6\] for epipolar
geometry which verifies model (fundamental and essential matrix)
to have points visible in the front of the camera.
5. SPRT verification – method \[9\] which verifies model by its
evaluation on randomly shuffled points using statistical properties
given by probability of inlier, relative time for estimation,
average number of output models etc. Significantly speeding up
framework, because bad model can be rejected very quickly without
explicitly computing error for every point.
6. Local Optimization:
1. Locally Optimized RANSAC – method \[5\] that iteratively
improves so-far-the-best model by non-minimal estimation. *The
default option in framework. This procedure is the fastest and
not worse than others local optimization methods.*
2. Graph-Cut RANSAC – method \[1\] that refine so-far-the-best
model, however, it exploits spatial coherence of the
data points. *This procedure is quite precise however
computationally slower.*
3. Sigma Consensus – method \[3\] which improves model by applying
non-minimal weighted estimation, where weights are computed with
the same logic as in MAGSAC score. This method is better to use
together with MAGSAC score.
7. Termination:
1. Standard – standard equation for independent and
uniform sampling.
2. PROSAC – termination for PROSAC.
3. SPRT – termination for SPRT.
8. Solver. In the framework there are minimal and non-minimal solvers.
In minimal solver standard methods for estimation is applied. In
non-minimal solver usually the covariance matrix is built and the
model is found as the eigen vector corresponding to the highest
eigen value.
1. Affine2D matrix
2. Homography matrix – for minimal solver is used RHO
(Gaussian elimination) algorithm from OpenCV.
3. Fundamental matrix – for 7-points algorithm two null vectors are
found using Gaussian elimination (eliminating to upper
triangular matrix and back-substitution) instead of SVD and then
solving 3-degrees polynomial. For 8-points solver Gaussian
elimination is used too.
4. Essential matrix – 4 null vectors are found using
Gaussian elimination. Then the solver based on Gröbner basis
described in \[11\] is used. Essential matrix can be computed
only if <span style="font-variant:small-caps;">LAPACK</span> or
<span style="font-variant:small-caps;">Eigen</span> are
installed as it requires eigen decomposition with complex
eigen values.
5. Perspective-n-Point – the minimal solver is classical 3 points
with up to 4 solutions. For RANSAC the low number of sample size
plays significant role as it requires less iterations,
furthermore in average P3P solver has around 1.39
estimated models. Also, in new version of `solvePnPRansac(...)`
with `UsacParams` there is an options to pass empty intrinsic
matrix `InputOutputArray cameraMatrix`. If matrix is empty than
using Direct Linear Transformation algorithm (PnP with 6 points)
framework outputs not only rotation and translation vector but
also calibration matrix.
Also, the framework can be run in parallel. The parallelization is done
in the way that multiple RANSACs are created and they share two atomic
variables `bool success` and `int num_hypothesis_tested` which
determines when all RANSACs must terminate. If one of RANSAC terminated
successfully then all other RANSAC will terminate as well. In the end
the best model is synchronized from all threads. If PROSAC sampler is
used then threads must share the same sampler since sampling is done
sequentially. However, using default options of framework parallel
RANSAC is not deterministic since it depends on how often each thread is
running. The easiest way to make it deterministic is using PROSAC
sampler without SPRT and Local Optimization and not for Fundamental
matrix, because they internally use random generators.\
\
For NAPSAC, Progressive NAPSAC or Graph-Cut methods is required to build
a neighborhood graph. In framework there are 3 options to do it:
1. `NEIGH_FLANN_KNN` – estimate neighborhood graph using OpenCV FLANN
K nearest-neighbors. The default value for KNN is 7. KNN method may
work good for sampling but not good for GC-RANSAC.
2. `NEIGH_FLANN_RADIUS` – similarly as in previous case finds neighbor
points which distance is less than 20 pixels.
3. `NEIGH_GRID` – for finding points’ neighborhood tiles points in
cells using hash-table. The method is described in \[2\]. Less
accurate than `NEIGH_FLANN_RADIUS`, although significantly faster.
Note, `NEIGH_FLANN_RADIUS` and `NEIGH_FLANN_RADIUS` are not able to PnP
solver, since there are 3D object points.\
\
New flags:
1. `USAC_DEFAULT` – has standard LO-RANSAC.
2. `USAC_PARALLEL` – has LO-RANSAC and RANSACs run in parallel.
3. `USAC_ACCURATE` – has GC-RANSAC.
4. `USAC_FAST` – has LO-RANSAC with smaller number iterations in local
optimization step. Uses RANSAC score to maximize number of inliers
and terminate earlier.
5. `USAC_PROSAC` – has PROSAC sampling. Note, points must be sorted.
6. `USAC_FM_8PTS` – has LO-RANSAC. Only valid for Fundamental matrix
with 8-points solver.
7. `USAC_MAGSAC` – has MAGSAC++.
Every flag uses SPRT verification. And in the end the final
so-far-the-best model is polished by non minimal estimation of all found
inliers.\
\
A few other important parameters:
1. `randomGeneratorState` – since every USAC solver is deterministic in
OpenCV (i.e., for the same points and parameters returns the
same result) by providing new state it will output new model.
2. `loIterations` – number of iterations for Local Optimization method.
*The default value is 10*. By increasing `loIterations` the output
model could be more accurate, however, the computationial time may
also increase.
3. `loSampleSize` – maximum sample number for Local Optimization. *The
default value is 14*. Note, that by increasing `loSampleSize` the
accuracy of model can increase as well as the computational time.
However, it is recommended to keep value less than 100, because
estimation on low number of points is faster and more robust.
Samples:
There are three new sample files in opencv/samples directory.
1. `epipolar_lines.cpp` – input arguments of `main` function are two
pathes to images. Then correspondences are found using
SIFT detector. Fundamental matrix is found using RANSAC from
tentaive correspondences and epipolar lines are plot.
2. `essential_mat_reconstr.cpp` – input arguments are path to data file
containing image names and single intrinsic matrix and directory
where these images located. Correspondences are found using SIFT.
The essential matrix is estimated using RANSAC and decomposed to
rotation and translation. Then by building two relative poses with
projection matrices image points are triangulated to object points.
By running RANSAC with 3D plane fitting object points as well as
correspondences are clustered into planes.
3. `essential_mat_reconstr.py` – the same functionality as in .cpp
file, however instead of clustering points to plane the 3D map of
object points is plot.
References:
1\. Daniel Barath and Jiří Matas. 2018. Graph-Cut RANSAC. In *Proceedings
of the iEEE conference on computer vision and pattern recognition*,
6733–6741.
2\. Daniel Barath, Maksym Ivashechkin, and Jiri Matas. 2019. Progressive
NAPSAC: Sampling from gradually growing neighborhoods. *arXiv preprint
arXiv:1906.02295*.
3\. Daniel Barath, Jana Noskova, Maksym Ivashechkin, and Jiri Matas.
2020. MAGSAC++, a fast, reliable and accurate robust estimator. In
*Proceedings of the iEEE/CVF conference on computer vision and pattern
recognition (cVPR)*.
4\. O. Chum and J. Matas. 2005. Matching with PROSAC-progressive sample
consensus. In *Computer vision and pattern recognition*.
5\. O. Chum, J. Matas, and J. Kittler. 2003. Locally optimized RANSAC. In
*Joint pattern recognition symposium*.
6\. O. Chum, T. Werner, and J. Matas. 2004. Epipolar geometry estimation
via RANSAC benefits from the oriented epipolar constraint. In
*International conference on pattern recognition*.
7\. Ondrej Chum, Tomas Werner, and Jiri Matas. 2005. Two-view geometry
estimation unaffected by a dominant plane. In *2005 iEEE computer
society conference on computer vision and pattern recognition
(cVPR’05)*, 772–779.
8\. M. A. Fischler and R. C. Bolles. 1981. Random sample consensus: A
paradigm for model fitting with applications to image analysis and
automated cartography. *Communications of the ACM*.
9\. Jiri Matas and Ondrej Chum. 2005. Randomized RANSAC with sequential
probability ratio test. In *Tenth iEEE international conference on
computer vision (iCCV’05) volume 1*, 1727–1732.
10\. D. R. Myatt, P. H. S. Torr, S. J. Nasuto, J. M. Bishop, and R.
Craddock. 2002. NAPSAC: High noise, high dimensional robust estimation.
In *In bMVC02*, 458–467.
11\. Henrik Stewénius, Christopher Engels, and David Nistér. 2006. Recent
developments on direct relative orientation.

1
modules/calib3d/CMakeLists.txt
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@ -9,3 +9,4 @@ endif()
ocv_define_module(calib3d opencv_imgproc opencv_features2d opencv_flann ${debug_modules}
WRAP java objc python js
)
ocv_target_link_libraries(${the_module} ${LAPACK_LIBRARIES})

62
modules/calib3d/include/opencv2/calib3d.hpp
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@ -441,9 +441,16 @@ namespace cv
//! @{
//! type of the robust estimation algorithm
enum { LMEDS = 4, //!< least-median of squares algorithm
RANSAC = 8, //!< RANSAC algorithm
RHO = 16 //!< RHO algorithm
enum { LMEDS = 4, //!< least-median of squares algorithm
RANSAC = 8, //!< RANSAC algorithm
RHO = 16, //!< RHO algorithm
USAC_DEFAULT = 32, //!< USAC algorithm, default settings
USAC_PARALLEL = 33, //!< USAC, parallel version
USAC_FM_8PTS = 34, //!< USAC, fundamental matrix 8 points
USAC_FAST = 35, //!< USAC, fast settings
USAC_ACCURATE = 36, //!< USAC, accurate settings
USAC_PROSAC = 37, //!< USAC, sorted points, runs PROSAC
USAC_MAGSAC = 38 //!< USAC, sorted points, runs PROSAC
};
enum SolvePnPMethod {
@ -526,6 +533,27 @@ enum HandEyeCalibrationMethod
CALIB_HAND_EYE_DANIILIDIS = 4 //!< Hand-Eye Calibration Using Dual Quaternions @cite Daniilidis98
};
enum SamplingMethod { SAMPLING_UNIFORM, SAMPLING_PROGRESSIVE_NAPSAC, SAMPLING_NAPSAC,
SAMPLING_PROSAC };
enum LocalOptimMethod {LOCAL_OPTIM_NULL, LOCAL_OPTIM_INNER_LO, LOCAL_OPTIM_INNER_AND_ITER_LO,
LOCAL_OPTIM_GC, LOCAL_OPTIM_SIGMA};
enum ScoreMethod {SCORE_METHOD_RANSAC, SCORE_METHOD_MSAC, SCORE_METHOD_MAGSAC, SCORE_METHOD_LMEDS};
enum NeighborSearchMethod { NEIGH_FLANN_KNN, NEIGH_GRID, NEIGH_FLANN_RADIUS };
struct CV_EXPORTS_W_SIMPLE UsacParams
{ // in alphabetical order
double confidence = 0.99;
bool isParallel = false;
int loIterations = 5;
LocalOptimMethod loMethod = LocalOptimMethod::LOCAL_OPTIM_INNER_LO;
int loSampleSize = 14;
int maxIterations = 5000;
NeighborSearchMethod neighborsSearch = NeighborSearchMethod::NEIGH_GRID;
int randomGeneratorState = 0;
SamplingMethod sampler = SamplingMethod::SAMPLING_UNIFORM;
ScoreMethod score = ScoreMethod::SCORE_METHOD_MSAC;
double threshold = 1.5;
};
/** @brief Converts a rotation matrix to a rotation vector or vice versa.
@ -696,6 +724,10 @@ CV_EXPORTS_W Mat findHomography( InputArray srcPoints, InputArray dstPoints,
CV_EXPORTS Mat findHomography( InputArray srcPoints, InputArray dstPoints,
OutputArray mask, int method = 0, double ransacReprojThreshold = 3 );
CV_EXPORTS_W Mat findHomography(InputArray srcPoints, InputArray dstPoints, OutputArray mask,
const UsacParams &params);
/** @brief Computes an RQ decomposition of 3x3 matrices.
@param src 3x3 input matrix.
@ -1083,6 +1115,16 @@ CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoint
float reprojectionError = 8.0, double confidence = 0.99,
OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE );
/*
Finds rotation and translation vector.
If cameraMatrix is given then run P3P. Otherwise run linear P6P and output cameraMatrix too.
*/
CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
InputOutputArray cameraMatrix, InputArray distCoeffs,
OutputArray rvec, OutputArray tvec, OutputArray inliers,
const UsacParams &params=UsacParams());
/** @brief Finds an object pose from 3 3D-2D point correspondences.
@param objectPoints Array of object points in the object coordinate space, 3x3 1-channel or
@ -2451,6 +2493,10 @@ CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
OutputArray mask, int method = FM_RANSAC,
double ransacReprojThreshold = 3., double confidence = 0.99 );
CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
OutputArray mask, const UsacParams &params);
/** @brief Calculates an essential matrix from the corresponding points in two images.
@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
@ -2573,6 +2619,12 @@ CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
double prob = 0.999, double threshold = 1.0,
OutputArray mask = noArray() );
CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
InputArray cameraMatrix1, InputArray cameraMatrix2,
InputArray dist_coeff1, InputArray dist_coeff2, OutputArray mask,
const UsacParams &params);
/** @brief Decompose an essential matrix to possible rotations and translation.
@param E The input essential matrix.
@ -3037,6 +3089,10 @@ CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray from, InputArray to, OutputArra
size_t maxIters = 2000, double confidence = 0.99,
size_t refineIters = 10);
CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray pts1, InputArray pts2, OutputArray inliers,
const UsacParams &params);
/** @brief Computes an optimal limited affine transformation with 4 degrees of freedom between
two 2D point sets.

20
modules/calib3d/src/five-point.cpp
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@ -31,6 +31,8 @@
#include "precomp.hpp"
#include "usac.hpp"
namespace cv
{
@ -407,6 +409,10 @@ cv::Mat cv::findEssentialMat( InputArray _points1, InputArray _points2, InputArr
{
CV_INSTRUMENT_REGION();
if (method >= 32 && method <= 38)
return usac::findEssentialMat(_points1, _points2, _cameraMatrix,
method, prob, threshold, _mask);
Mat points1, points2, cameraMatrix;
_points1.getMat().convertTo(points1, CV_64F);
_points2.getMat().convertTo(points2, CV_64F);
@ -487,6 +493,20 @@ cv::Mat cv::findEssentialMat( InputArray _points1, InputArray _points2,
return findEssentialMat(_pointsUntistorted1, _pointsUntistorted2, cm0, method, prob, threshold, _mask);
}
cv::Mat cv::findEssentialMat( InputArray points1, InputArray points2,
InputArray cameraMatrix1, InputArray cameraMatrix2,
InputArray dist_coeff1, InputArray dist_coeff2, OutputArray mask, const UsacParams &params) {
Ptr<usac::Model> model;
usac::setParameters(model, usac::EstimationMethod::Essential, params, mask.needed());
Ptr<usac::RansacOutput> ransac_output;
if (usac::run(model, points1, points2, model->getRandomGeneratorState(),
ransac_output, cameraMatrix1, cameraMatrix2, dist_coeff1, dist_coeff2)) {
usac::saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel();
} else return Mat();
}
int cv::recoverPose( InputArray E, InputArray _points1, InputArray _points2,
InputArray _cameraMatrix, OutputArray _R, OutputArray _t, double distanceThresh,
InputOutputArray _mask, OutputArray triangulatedPoints)

36
modules/calib3d/src/fundam.cpp
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@ -44,6 +44,8 @@
#include "rho.h"
#include <iostream>
#include "usac.hpp"
namespace cv
{
@ -353,6 +355,10 @@ cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
{
CV_INSTRUMENT_REGION();
if (method >= 32 && method <= 38)
return usac::findHomography(_points1, _points2, method, ransacReprojThreshold,
_mask, maxIters, confidence);
const double defaultRANSACReprojThreshold = 3;
bool result = false;
@ -439,6 +445,18 @@ cv::Mat cv::findHomography( InputArray _points1, InputArray _points2,
}
cv::Mat cv::findHomography(InputArray srcPoints, InputArray dstPoints, OutputArray mask,
const UsacParams &params) {
Ptr<usac::Model> model;
usac::setParameters(model, usac::EstimationMethod::Homography, params, mask.needed());
Ptr<usac::RansacOutput> ransac_output;
if (usac::run(model, srcPoints, dstPoints, model->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
usac::saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel() / ransac_output->getModel().at<double>(2,2);
} else return Mat();
}
/* Estimation of Fundamental Matrix from point correspondences.
The original code has been written by Valery Mosyagin */
@ -813,6 +831,10 @@ cv::Mat cv::findFundamentalMat( InputArray _points1, InputArray _points2,
{
CV_INSTRUMENT_REGION();
if (method >= 32 && method <= 38)
return usac::findFundamentalMat(_points1, _points2, method,
ransacReprojThreshold, confidence, maxIters, _mask);
Mat points1 = _points1.getMat(), points2 = _points2.getMat();
Mat m1, m2, F;
int npoints = -1;
@ -885,6 +907,20 @@ cv::Mat cv::findFundamentalMat( cv::InputArray points1, cv::InputArray points2,
return cv::findFundamentalMat(points1, points2, method, ransacReprojThreshold, confidence, 1000, mask);
}
cv::Mat cv::findFundamentalMat( InputArray points1, InputArray points2,
OutputArray mask, const UsacParams &params) {
Ptr<usac::Model> model;
setParameters(model, usac::EstimationMethod::Fundamental, params, mask.needed());
Ptr<usac::RansacOutput> ransac_output;
if (usac::run(model, points1, points2, model->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
usac::saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel();
} else return Mat();
}
void cv::computeCorrespondEpilines( InputArray _points, int whichImage,
InputArray _Fmat, OutputArray _lines )

19
modules/calib3d/src/ptsetreg.cpp
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@ -47,6 +47,8 @@
#include <iterator>
#include <limits>
#include "usac.hpp"
namespace cv
{
@ -927,6 +929,11 @@ Mat estimateAffine2D(InputArray _from, InputArray _to, OutputArray _inliers,
const size_t maxIters, const double confidence,
const size_t refineIters)
{
if (method >= 32 && method <= 38)
return cv::usac::estimateAffine2D(_from, _to, _inliers, method,
ransacReprojThreshold, (int)maxIters, confidence, (int)refineIters);
Mat from = _from.getMat(), to = _to.getMat();
int count = from.checkVector(2);
bool result = false;
@ -996,6 +1003,18 @@ Mat estimateAffine2D(InputArray _from, InputArray _to, OutputArray _inliers,
return H;
}
Mat estimateAffine2D(InputArray _from, InputArray _to, OutputArray inliers,
const UsacParams &params) {
Ptr<usac::Model> model;
usac::setParameters(model, usac::EstimationMethod::Affine, params, inliers.needed());
Ptr<usac::RansacOutput> ransac_output;
if (usac::run(model, _from, _to, model->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
usac::saveMask(inliers, ransac_output->getInliersMask());
return ransac_output->getModel().rowRange(0,2);
} else return Mat();
}
Mat estimateAffinePartial2D(InputArray _from, InputArray _to, OutputArray _inliers,
const int method, const double ransacReprojThreshold,
const size_t maxIters, const double confidence,

29
modules/calib3d/src/solvepnp.cpp
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@ -49,6 +49,8 @@
#include "ippe.hpp"
#include "calib3d_c_api.h"
#include "usac.hpp"
namespace cv
{
#if defined _DEBUG || defined CV_STATIC_ANALYSIS
@ -201,6 +203,11 @@ bool solvePnPRansac(InputArray _opoints, InputArray _ipoints,
{
CV_INSTRUMENT_REGION();
if (flags >= 32 && flags <= 38)
return usac::solvePnPRansac(_opoints, _ipoints, _cameraMatrix, _distCoeffs,
_rvec, _tvec, useExtrinsicGuess, iterationsCount, reprojectionError,
confidence, _inliers, flags);
Mat opoints0 = _opoints.getMat(), ipoints0 = _ipoints.getMat();
Mat opoints, ipoints;
if( opoints0.depth() == CV_64F || !opoints0.isContinuous() )
@ -342,6 +349,28 @@ bool solvePnPRansac(InputArray _opoints, InputArray _ipoints,
return true;
}
bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
InputOutputArray cameraMatrix, InputArray distCoeffs,
OutputArray rvec, OutputArray tvec, OutputArray inliers,
const UsacParams &params) {
Ptr<usac::Model> model_params;
usac::setParameters(model_params, cameraMatrix.empty() ? usac::EstimationMethod::P6P :
usac::EstimationMethod::P3P, params, inliers.needed());
Ptr<usac::RansacOutput> ransac_output;
if (usac::run(model_params, imagePoints, objectPoints, model_params->getRandomGeneratorState(),
ransac_output, cameraMatrix, noArray(), distCoeffs, noArray())) {
usac::saveMask(inliers, ransac_output->getInliersMask());
const Mat &model = ransac_output->getModel();
model.col(0).copyTo(rvec);
model.col(1).copyTo(tvec);
if (cameraMatrix.empty())
model.colRange(2, 5).copyTo(cameraMatrix);
return true;
} else return false;
}
int solveP3P( InputArray _opoints, InputArray _ipoints,
InputArray _cameraMatrix, InputArray _distCoeffs,
OutputArrayOfArrays _rvecs, OutputArrayOfArrays _tvecs, int flags) {

800
modules/calib3d/src/usac.hpp
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@ -0,0 +1,800 @@
// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#ifndef OPENCV_USAC_USAC_HPP
#define OPENCV_USAC_USAC_HPP
namespace cv { namespace usac {
enum EstimationMethod { Homography, Fundamental, Fundamental8, Essential, Affine, P3P, P6P};
enum VerificationMethod { NullVerifier, SprtVerifier };
enum PolishingMethod { NonePolisher, LSQPolisher };
enum ErrorMetric {DIST_TO_LINE, SAMPSON_ERR, SGD_ERR, SYMM_REPR_ERR, FORW_REPR_ERR, RERPOJ};
// Abstract Error class
class Error : public Algorithm {
public:
// set model to use getError() function
virtual void setModelParameters (const Mat &model) = 0;
// returns error of point wih @point_idx w.r.t. model
virtual float getError (int point_idx) const = 0;
virtual const std::vector<float> &getErrors (const Mat &model) = 0;
virtual Ptr<Error> clone () const = 0;
};
// Symmetric Reprojection Error for Homography
class ReprojectionErrorSymmetric : public Error {
public:
static Ptr<ReprojectionErrorSymmetric> create(const Mat &points);
};
// Forward Reprojection Error for Homography
class ReprojectionErrorForward : public Error {
public:
static Ptr<ReprojectionErrorForward> create(const Mat &points);
};
// Sampson Error for Fundamental matrix
class SampsonError : public Error {
public:
static Ptr<SampsonError> create(const Mat &points);
};
// Symmetric Geometric Distance (to epipolar lines) for Fundamental and Essential matrix
class SymmetricGeometricDistance : public Error {
public:
static Ptr<SymmetricGeometricDistance> create(const Mat &points);
};
// Reprojection Error for Projection matrix
class ReprojectionErrorPmatrix : public Error {
public:
static Ptr<ReprojectionErrorPmatrix> create(const Mat &points);
};
// Reprojection Error for Affine matrix
class ReprojectionErrorAffine : public Error {
public:
static Ptr<ReprojectionErrorAffine> create(const Mat &points);
};
// Normalizing transformation of data points
class NormTransform : public Algorithm {
public:
/*
* @norm_points is output matrix of size pts_size x 4
* @sample constains indices of points
* @sample_number is number of used points in sample <0; sample_number)
* @T1, T2 are output transformation matrices
*/
virtual void getNormTransformation (Mat &norm_points, const std::vector<int> &sample,
int sample_number, Matx33d &T1, Matx33d &T2) const = 0;
static Ptr<NormTransform> create (const Mat &points);
};
/////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// SOLVER ///////////////////////////////////////////
class MinimalSolver : public Algorithm {
public:
// Estimate models from minimal sample. models.size() == number of found solutions
virtual int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const = 0;
// return minimal sample size required for estimation.
virtual int getSampleSize() const = 0;
// return maximum number of possible solutions.
virtual int getMaxNumberOfSolutions () const = 0;
virtual Ptr<MinimalSolver> clone () const = 0;
};
//-------------------------- HOMOGRAPHY MATRIX -----------------------
class HomographyMinimalSolver4ptsGEM : public MinimalSolver {
public:
static Ptr<HomographyMinimalSolver4ptsGEM> create(const Mat &points_);
};
//-------------------------- FUNDAMENTAL MATRIX -----------------------
class FundamentalMinimalSolver7pts : public MinimalSolver {
public:
static Ptr<FundamentalMinimalSolver7pts> create(const Mat &points_);
};
class FundamentalMinimalSolver8pts : public MinimalSolver {
public:
static Ptr<FundamentalMinimalSolver8pts> create(const Mat &points_);
};
//-------------------------- ESSENTIAL MATRIX -----------------------
class EssentialMinimalSolverStewenius5pts : public MinimalSolver {
public:
static Ptr<EssentialMinimalSolverStewenius5pts> create(const Mat &points_);
};
//-------------------------- PNP -----------------------
class PnPMinimalSolver6Pts : public MinimalSolver {
public:
static Ptr<PnPMinimalSolver6Pts> create(const Mat &points_);
};
class P3PSolver : public MinimalSolver {
public:
static Ptr<P3PSolver> create(const Mat &points_, const Mat &calib_norm_pts, const Mat &K);
};
//-------------------------- AFFINE -----------------------
class AffineMinimalSolver : public MinimalSolver {
public:
static Ptr<AffineMinimalSolver> create(const Mat &points_);
};
//////////////////////////////////////// NON MINIMAL SOLVER ///////////////////////////////////////
class NonMinimalSolver : public Algorithm {
public:
// Estimate models from non minimal sample. models.size() == number of found solutions
virtual int estimate (const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const = 0;
// return minimal sample size required for non-minimal estimation.
virtual int getMinimumRequiredSampleSize() const = 0;
// return maximum number of possible solutions.
virtual int getMaxNumberOfSolutions () const = 0;
virtual Ptr<NonMinimalSolver> clone () const = 0;
};
//-------------------------- HOMOGRAPHY MATRIX -----------------------
class HomographyNonMinimalSolver : public NonMinimalSolver {
public:
static Ptr<HomographyNonMinimalSolver> create(const Mat &points_);
};
//-------------------------- FUNDAMENTAL MATRIX -----------------------
class FundamentalNonMinimalSolver : public NonMinimalSolver {
public:
static Ptr<FundamentalNonMinimalSolver> create(const Mat &points_);
};
//-------------------------- ESSENTIAL MATRIX -----------------------
class EssentialNonMinimalSolver : public NonMinimalSolver {
public:
static Ptr<EssentialNonMinimalSolver> create(const Mat &points_);
};
//-------------------------- PNP -----------------------
class PnPNonMinimalSolver : public NonMinimalSolver {
public:
static Ptr<PnPNonMinimalSolver> create(const Mat &points);
};
class DLSPnP : public NonMinimalSolver {
public:
static Ptr<DLSPnP> create(const Mat &points_, const Mat &calib_norm_pts, const Mat &K);
};
//-------------------------- AFFINE -----------------------
class AffineNonMinimalSolver : public NonMinimalSolver {
public:
static Ptr<AffineNonMinimalSolver> create(const Mat &points_);
};
//////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// SCORE ///////////////////////////////////////////
class Score {
public:
int inlier_number;
double score;
Score () { // set worst case
inlier_number = 0;
score = std::numeric_limits<double>::max();
}
Score (int inlier_number_, double score_) { // copy constructor
inlier_number = inlier_number_;
score = score_;
}
// Compare two scores. Objective is minimization of score. Lower score is better.
inline bool isBetter (const Score &score2) const {
return score < score2.score;
}
};
////////////////////////////////////////// QUALITY ///////////////////////////////////////////
class Quality : public Algorithm {
public:
virtual ~Quality() override = default;
/*
* Calculates number of inliers and score of the @model.
* return Score with calculated inlier_number and score.
* @model: Mat current model, e.g., H matrix.
*/
virtual Score getScore (const Mat &model) const = 0;
virtual Score getScore (const std::vector<float> &/*errors*/) const {
CV_Error(cv::Error::StsNotImplemented, "getScore(errors)");
}
// get @inliers of the @model. Assume threshold is given
// @inliers must be preallocated to maximum points size.
virtual int getInliers (const Mat &model, std::vector<int> &inliers) const = 0;
// get @inliers of the @model for given threshold
virtual int getInliers (const Mat &model, std::vector<int> &inliers, double thr) const = 0;
// Set the best score, so evaluation of the model can terminate earlier
virtual void setBestScore (double best_score_) = 0;
// set @inliers_mask: true if point i is inlier, false - otherwise.
virtual int getInliers (const Mat &model, std::vector<bool> &inliers_mask) const = 0;
virtual int getPointsSize() const = 0;
virtual Ptr<Quality> clone () const = 0;
static int getInliers (const Ptr<Error> &error, const Mat &model,
std::vector<bool> &inliers_mask, double threshold);
static int getInliers (const Ptr<Error> &error, const Mat &model,
std::vector<int> &inliers, double threshold);
};
// RANSAC (binary) quality
class RansacQuality : public Quality {
public:
static Ptr<RansacQuality> create(int points_size_, double threshold_,const Ptr<Error> &error_);
};
// M-estimator quality - truncated Squared error
class MsacQuality : public Quality {
public:
static Ptr<MsacQuality> create(int points_size_, double threshold_, const Ptr<Error> &error_);
};
// Marginlizing Sample Consensus quality, D. Barath et al.
class MagsacQuality : public Quality {
public:
static Ptr<MagsacQuality> create(double maximum_thr, int points_size_,const Ptr<Error> &error_,
double tentative_inlier_threshold_, int DoF, double sigma_quantile,
double upper_incomplete_of_sigma_quantile,
double lower_incomplete_of_sigma_quantile, double C_);
};
// Least Median of Squares Quality
class LMedsQuality : public Quality {
public:
static Ptr<LMedsQuality> create(int points_size_, double threshold_, const Ptr<Error> &error_);
};
//////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////// DEGENERACY //////////////////////////////////
class Degeneracy : public Algorithm {
public:
virtual ~Degeneracy() override = default;
/*
* Check if sample causes degenerate configurations.
* For example, test if points are collinear.
*/
virtual bool isSampleGood (const std::vector<int> &/*sample*/) const {
return true;
}
/*
* Check if model satisfies constraints.
* For example, test if epipolar geometry satisfies oriented constraint.
*/
virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/) const {
return true;
}
virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/,
int /*sample_size*/) const {
return true;
}
/*
* Fix degenerate model.
* Return true if model is degenerate, false - otherwise
*/
virtual bool recoverIfDegenerate (const std::vector<int> &/*sample*/,const Mat &/*best_model*/,
Mat &/*non_degenerate_model*/, Score &/*non_degenerate_model_score*/) {
return false;
}
virtual Ptr<Degeneracy> clone(int /*state*/) const { return makePtr<Degeneracy>(); }
};
class EpipolarGeometryDegeneracy : public Degeneracy {
public:
static void recoverRank (Mat &model);
static Ptr<EpipolarGeometryDegeneracy> create (const Mat &points_, int sample_size_);
};
class EssentialDegeneracy : public EpipolarGeometryDegeneracy {
public:
static Ptr<EssentialDegeneracy>create (const Mat &points, int sample_size);
};
class HomographyDegeneracy : public Degeneracy {
public:
static Ptr<HomographyDegeneracy> create(const Mat &points_);
};
class FundamentalDegeneracy : public EpipolarGeometryDegeneracy {
public:
// threshold for homography is squared so is around 2.236 pixels
static Ptr<FundamentalDegeneracy> create (int state, const Ptr<Quality> &quality_,
const Mat &points_, int sample_size_, double homography_threshold);
};
/////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////// ESTIMATOR //////////////////////////////////
class Estimator : public Algorithm{
public:
/*
* Estimate models with minimal solver.
* Return number of valid solutions after estimation.
* Return models accordingly to number of solutions.
* Note, vector of models must allocated before.
* Note, not all degenerate tests are included in estimation.
*/
virtual int
estimateModels (const std::vector<int> &sample, std::vector<Mat> &models) const = 0;
/*
* Estimate model with non-minimal solver.
* Return number of valid solutions after estimation.
* Note, not all degenerate tests are included in estimation.
*/
virtual int
estimateModelNonMinimalSample (const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const = 0;
// return minimal sample size required for minimal estimation.
virtual int getMinimalSampleSize () const = 0;
// return minimal sample size required for non-minimal estimation.
virtual int getNonMinimalSampleSize () const = 0;
// return maximum number of possible solutions of minimal estimation.
virtual int getMaxNumSolutions () const = 0;
// return maximum number of possible solutions of non-minimal estimation.
virtual int getMaxNumSolutionsNonMinimal () const = 0;
virtual Ptr<Estimator> clone() const = 0;
};
class HomographyEstimator : public Estimator {
public:
static Ptr<HomographyEstimator> create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_);
};
class FundamentalEstimator : public Estimator {
public:
static Ptr<FundamentalEstimator> create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_);
};
class EssentialEstimator : public Estimator {
public:
static Ptr<EssentialEstimator> create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_);
};
class AffineEstimator : public Estimator {
public:
static Ptr<AffineEstimator> create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_);
};
class PnPEstimator : public Estimator {
public:
static Ptr<PnPEstimator> create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_);
};
//////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// MODEL VERIFIER ////////////////////////////////////
class ModelVerifier : public Algorithm {
public:
virtual ~ModelVerifier() override = default;
// Return true if model is good, false - otherwise.
virtual bool isModelGood(const Mat &model) = 0;
// Return true if score was computed during evaluation.
virtual bool getScore(Score &score) const = 0;
// update verifier by given inlier number
virtual void update (int highest_inlier_number) = 0;
virtual const std::vector<float> &getErrors() const = 0;
virtual bool hasErrors () const = 0;
virtual Ptr<ModelVerifier> clone (int state) const = 0;
static Ptr<ModelVerifier> create();
};
struct SPRT_history {
/*
* delta:
* The probability of a data point being consistent
* with a ‘bad’ model is modeled as a probability of
* a random event with Bernoulli distribution with parameter
* δ : p(1|Hb) = δ.
* epsilon:
* The probability p(1|Hg) = ε
* that any randomly chosen data point is consistent with a ‘good’ model
* is approximated by the fraction of inliers ε among the data
* points
* A is the decision threshold, the only parameter of the Adapted SPRT
*/
double epsilon, delta, A;
// number of samples processed by test
int tested_samples; // k
SPRT_history () {
tested_samples = 0;
}
};
///////////////////////////////// SPRT VERIFIER /////////////////////////////////////////
/*
* Matas, Jiri, and Ondrej Chum. "Randomized RANSAC with sequential probability ratio test."
* Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1. Vol. 2. IEEE, 2005.
*/
class SPRT : public ModelVerifier {
public:
// return constant reference of vector of SPRT histories for SPRT termination.
virtual const std::vector<SPRT_history> &getSPRTvector () const = 0;
static Ptr<SPRT> create (int state, const Ptr<Error> &err_, int points_size_,
double inlier_threshold_, double prob_pt_of_good_model,
double prob_pt_of_bad_model, double time_sample, double avg_num_models,
ScoreMethod score_type_);
};
//////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////// SAMPLER ///////////////////////////////////////
class Sampler : public Algorithm {
public:
virtual ~Sampler() override = default;
// set new points size
virtual void setNewPointsSize (int points_size) = 0;
// generate sample. Fill @sample with indices of points.
virtual void generateSample (std::vector<int> &sample) = 0;
virtual Ptr<Sampler> clone (int state) const = 0;
};
////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////// NEIGHBORHOOD GRAPH /////////////////////////////////////////
class NeighborhoodGraph : public Algorithm {
public:
virtual ~NeighborhoodGraph() override = default;
// Return neighbors of the point with index @point_idx_ in the graph.
virtual const std::vector<int> &getNeighbors(int point_idx_) const = 0;
};
class RadiusSearchNeighborhoodGraph : public NeighborhoodGraph {
public:
static Ptr<RadiusSearchNeighborhoodGraph> create (const Mat &points, int points_size,
double radius_, int flann_search_params, int num_kd_trees);
};
class FlannNeighborhoodGraph : public NeighborhoodGraph {
public:
static Ptr<FlannNeighborhoodGraph> create(const Mat &points, int points_size,
int k_nearest_neighbors_, bool get_distances, int flann_search_params, int num_kd_trees);
virtual const std::vector<double> &getNeighborsDistances (int idx) const = 0;
};
class GridNeighborhoodGraph : public NeighborhoodGraph {
public:
static Ptr<GridNeighborhoodGraph> create(const Mat &points, int points_size,
int cell_size_x_img1_, int cell_size_y_img1_,
int cell_size_x_img2_, int cell_size_y_img2_);
};
////////////////////////////////////// UNIFORM SAMPLER ////////////////////////////////////////////
class UniformSampler : public Sampler {
public:
static Ptr<UniformSampler> create(int state, int sample_size_, int points_size_);
};
/////////////////////////////////// PROSAC (SIMPLE) SAMPLER ///////////////////////////////////////
class ProsacSimpleSampler : public Sampler {
public:
static Ptr<ProsacSimpleSampler> create(int state, int points_size_, int sample_size_,
int max_prosac_samples_count);
};
////////////////////////////////////// PROSAC SAMPLER ////////////////////////////////////////////
class ProsacSampler : public Sampler {
public:
static Ptr<ProsacSampler> create(int state, int points_size_, int sample_size_,
int growth_max_samples);
// return number of samples generated (for prosac termination).
virtual int getKthSample () const = 0;
// return constant reference of growth function of prosac sampler (for prosac termination)
virtual const std::vector<int> &getGrowthFunction () const = 0;
virtual void setTerminationLength (int termination_length) = 0;
};
////////////////////////// NAPSAC (N adjacent points sample consensus) SAMPLER ////////////////////
class NapsacSampler : public Sampler {
public:
static Ptr<NapsacSampler> create(int state, int points_size_, int sample_size_,
const Ptr<NeighborhoodGraph> &neighborhood_graph_);
};
////////////////////////////////////// P-NAPSAC SAMPLER /////////////////////////////////////////
class ProgressiveNapsac : public Sampler {
public:
static Ptr<ProgressiveNapsac> create(int state, int points_size_, int sample_size_,
const std::vector<Ptr<NeighborhoodGraph>> &layers, int sampler_length);
};
/////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////// TERMINATION ///////////////////////////////////////////
class TerminationCriteria : public Algorithm {
public:
// update termination object by given @model and @inlier number.
// and return maximum number of predicted iteration
virtual int update(const Mat &model, int inlier_number) = 0;
// clone termination
virtual Ptr<TerminationCriteria> clone () const = 0;
};
//////////////////////////////// STANDARD TERMINATION ///////////////////////////////////////////
class StandardTerminationCriteria : public TerminationCriteria {
public:
static Ptr<StandardTerminationCriteria> create(double confidence, int points_size_,
int sample_size_, int max_iterations_);
};
///////////////////////////////////// SPRT TERMINATION //////////////////////////////////////////
class SPRTTermination : public TerminationCriteria {
public:
static Ptr<SPRTTermination> create(const std::vector<SPRT_history> &sprt_histories_,
double confidence, int points_size_, int sample_size_, int max_iterations_);
};
///////////////////////////// PROGRESSIVE-NAPSAC-SPRT TERMINATION /////////////////////////////////
class SPRTPNapsacTermination : public TerminationCriteria {
public:
static Ptr<SPRTPNapsacTermination> create(const std::vector<SPRT_history>&
sprt_histories_, double confidence, int points_size_, int sample_size_,
int max_iterations_, double relax_coef_);
};
////////////////////////////////////// PROSAC TERMINATION /////////////////////////////////////////
class ProsacTerminationCriteria : public TerminationCriteria {
public:
static Ptr<ProsacTerminationCriteria> create(const Ptr<ProsacSampler> &sampler_,
const Ptr<Error> &error_, int points_size_, int sample_size, double confidence,
int max_iters, int min_termination_length, double beta, double non_randomness_phi,
double inlier_thresh);
};
//////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////// UTILS ////////////////////////////////////////////////
namespace Utils {
/*
* calibrate points: [x'; 1] = K^-1 [x; 1]
* @points is matrix N x 4.
* @norm_points is output matrix N x 4 with calibrated points.
*/
void calibratePoints (const Mat &K1, const Mat &K2, const Mat &points, Mat &norm_points);
void calibrateAndNormalizePointsPnP (const Mat &K, const Mat &pts, Mat &calib_norm_pts);
void normalizeAndDecalibPointsPnP (const Mat &K, Mat &pts, Mat &calib_norm_pts);
void decomposeProjection (const Mat &P, Mat &K_, Mat &R, Mat &t, bool same_focal=false);
double getCalibratedThreshold (double threshold, const Mat &K1, const Mat &K2);
float findMedian (std::vector<float> &array);
}
namespace Math {
// return skew symmetric matrix
Matx33d getSkewSymmetric(const Vec3d &v_);
// eliminate matrix with m rows and n columns to be upper triangular.
void eliminateUpperTriangular (std::vector<double> &a, int m, int n);
Matx33d rotVec2RotMat (const Vec3d &v);
Vec3d rotMat2RotVec (const Matx33d &R);
}
///////////////////////////////////////// RANDOM GENERATOR /////////////////////////////////////
class RandomGenerator : public Algorithm {
public:
virtual ~RandomGenerator() override = default;
// interval is <0, max_range);
virtual void resetGenerator (int max_range) = 0;
// return sample filled with random numbers
virtual void generateUniqueRandomSet (std::vector<int> &sample) = 0;
// fill @sample of size @subset_size with random numbers in range <0, @max_range)
virtual void generateUniqueRandomSet (std::vector<int> &sample, int subset_size,
int max_range) = 0;
// fill @sample of size @sample.size() with random numbers in range <0, @max_range)
virtual void generateUniqueRandomSet (std::vector<int> &sample, int max_range) = 0;
// return subset=sample size
virtual void setSubsetSize (int subset_sz) = 0;
virtual int getSubsetSize () const = 0;
// return random number from <0, max_range), where max_range is from constructor
virtual int getRandomNumber () = 0;
// return random number from <0, max_rng)
virtual int getRandomNumber (int max_rng) = 0;
virtual const std::vector<int> &generateUniqueRandomSubset (std::vector<int> &array1,
int size1) = 0;
virtual Ptr<RandomGenerator> clone (int state) const = 0;
};
class UniformRandomGenerator : public RandomGenerator {
public:
static Ptr<UniformRandomGenerator> create (int state);
static Ptr<UniformRandomGenerator> create (int state, int max_range, int subset_size_);
};
///////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////// LOCAL OPTIMIZATION /////////////////////////////////////////
class LocalOptimization : public Algorithm {
public:
virtual ~LocalOptimization() override = default;
/*
* Refine so-far-the-best RANSAC model in local optimization step.
* @best_model: so-far-the-best model
* @new_model: output refined new model.
* @new_model_score: score of @new_model.
* Returns bool if model was refined successfully, false - otherwise
*/
virtual bool refineModel (const Mat &best_model, const Score &best_model_score,
Mat &new_model, Score &new_model_score) = 0;
virtual Ptr<LocalOptimization> clone(int state) const = 0;
};
//////////////////////////////////// GRAPH CUT LO ////////////////////////////////////////
class GraphCut : public LocalOptimization {
public:
static Ptr<GraphCut>
create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
const Ptr<Quality> &quality_, const Ptr<NeighborhoodGraph> &neighborhood_graph_,
const Ptr<RandomGenerator> &lo_sampler_, double threshold_,
double spatial_coherence_term, int gc_iters);
};
//////////////////////////////////// INNER + ITERATIVE LO ///////////////////////////////////////
class InnerIterativeLocalOptimization : public LocalOptimization {
public:
static Ptr<InnerIterativeLocalOptimization>
create(const Ptr<Estimator> &estimator_, const Ptr<Quality> &quality_,
const Ptr<RandomGenerator> &lo_sampler_, int pts_size, double threshold_,
bool is_iterative_, int lo_iter_sample_size_, int lo_inner_iterations,
int lo_iter_max_iterations, double threshold_multiplier);
};
class SigmaConsensus : public LocalOptimization {
public:
static Ptr<SigmaConsensus>
create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
const Ptr<Quality> &quality, const Ptr<ModelVerifier> &verifier_,
int max_lo_sample_size, int number_of_irwls_iters_,
int DoF, double sigma_quantile, double upper_incomplete_of_sigma_quantile,
double C_, double maximum_thr);
};
///////////////////////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////// FINAL MODEL POLISHER //////////////////////////////////////
class FinalModelPolisher : public Algorithm {
public:
virtual ~FinalModelPolisher() override = default;
/*
* Polish so-far-the-best RANSAC model in the end of RANSAC.
* @model: input final RANSAC model.
* @new_model: output polished model.
* @new_score: score of output model.
* Return true if polishing was successful, false - otherwise.
*/
virtual bool polishSoFarTheBestModel (const Mat &model, const Score &best_model_score,
Mat &new_model, Score &new_model_score) = 0;
};
///////////////////////////////////// LEAST SQUARES POLISHER //////////////////////////////////////
class LeastSquaresPolishing : public FinalModelPolisher {
public:
static Ptr<LeastSquaresPolishing> create (const Ptr<Estimator> &estimator_,
const Ptr<Quality> &quality_, int lsq_iterations);
};
/////////////////////////////////// RANSAC OUTPUT ///////////////////////////////////
class RansacOutput : public Algorithm {
public:
virtual ~RansacOutput() override = default;
static Ptr<RansacOutput> create(const Mat &model_,
const std::vector<bool> &inliers_mask_,
int time_mcs_, double score_, int number_inliers_, int number_iterations_,
int number_estimated_models_, int number_good_models_);
// Return inliers' indices. size of vector = number of inliers
virtual const std::vector<int > &getInliers() = 0;
// Return inliers mask. Vector of points size. 1-inlier, 0-outlier.
virtual const std::vector<bool> &getInliersMask() const = 0;
virtual int getTimeMicroSeconds() const = 0;
virtual int getTimeMicroSeconds1() const = 0;
virtual int getTimeMilliSeconds2() const = 0;
virtual int getTimeSeconds3() const = 0;
virtual int getNumberOfInliers() const = 0;
virtual int getNumberOfMainIterations() const = 0;
virtual int getNumberOfGoodModels () const = 0;
virtual int getNumberOfEstimatedModels () const = 0;
virtual const Mat &getModel() const = 0;
};
////////////////////////////////////////////// MODEL /////////////////////////////////////////////
class Model : public Algorithm {
public:
virtual bool isFundamental () const = 0;
virtual bool isHomography () const = 0;
virtual bool isEssential () const = 0;
virtual bool isPnP () const = 0;
// getters
virtual int getSampleSize () const = 0;
virtual bool isParallel() const = 0;
virtual int getMaxNumHypothesisToTestBeforeRejection() const = 0;
virtual PolishingMethod getFinalPolisher () const = 0;
virtual LocalOptimMethod getLO () const = 0;
virtual ErrorMetric getError () const = 0;
virtual EstimationMethod getEstimator () const = 0;
virtual ScoreMethod getScore () const = 0;
virtual int getMaxIters () const = 0;
virtual double getConfidence () const = 0;
virtual double getThreshold () const = 0;
virtual VerificationMethod getVerifier () const = 0;
virtual SamplingMethod getSampler () const = 0;
virtual double getTimeForModelEstimation () const = 0;
virtual double getSPRTdelta () const = 0;
virtual double getSPRTepsilon () const = 0;
virtual double getSPRTavgNumModels () const = 0;
virtual NeighborSearchMethod getNeighborsSearch () const = 0;
virtual int getKNN () const = 0;
virtual int getCellSize () const = 0;
virtual int getGraphRadius() const = 0;
virtual double getRelaxCoef () const = 0;
virtual int getFinalLSQIterations () const = 0;
virtual int getDegreesOfFreedom () const = 0;
virtual double getSigmaQuantile () const = 0;
virtual double getUpperIncompleteOfSigmaQuantile () const = 0;
virtual double getLowerIncompleteOfSigmaQuantile () const = 0;
virtual double getC () const = 0;
virtual double getMaximumThreshold () const = 0;
virtual double getGraphCutSpatialCoherenceTerm () const = 0;
virtual int getLOSampleSize () const = 0;
virtual int getLOThresholdMultiplier() const = 0;
virtual int getLOIterativeSampleSize() const = 0;
virtual int getLOIterativeMaxIters() const = 0;
virtual int getLOInnerMaxIters() const = 0;
virtual const std::vector<int> &getGridCellNumber () const = 0;
virtual int getRandomGeneratorState () const = 0;
// setters
virtual void setLocalOptimization (LocalOptimMethod lo_) = 0;
virtual void setKNearestNeighhbors (int knn_) = 0;
virtual void setNeighborsType (NeighborSearchMethod neighbors) = 0;
virtual void setCellSize (int cell_size_) = 0;
virtual void setParallel (bool is_parallel) = 0;
virtual void setVerifier (VerificationMethod verifier_) = 0;
virtual void setPolisher (PolishingMethod polisher_) = 0;
virtual void setError (ErrorMetric error_) = 0;
virtual void setLOIterations (int iters) = 0;
virtual void setLOIterativeIters (int iters) = 0;
virtual void setLOSampleSize (int lo_sample_size) = 0;
virtual void setRandomGeneratorState (int state) = 0;
virtual void maskRequired (bool required) = 0;
virtual bool isMaskRequired () const = 0;
static Ptr<Model> create(double threshold_, EstimationMethod estimator_, SamplingMethod sampler_,
double confidence_=0.95, int max_iterations_=5000, ScoreMethod score_ =ScoreMethod::SCORE_METHOD_MSAC);
};
Mat findHomography(InputArray srcPoints, InputArray dstPoints, int method,
double ransacReprojThreshold, OutputArray mask,
const int maxIters, const double confidence);
Mat findFundamentalMat( InputArray points1, InputArray points2,
int method, double ransacReprojThreshold, double confidence,
int maxIters, OutputArray mask=noArray());
bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
InputArray cameraMatrix, InputArray distCoeffs,
OutputArray rvec, OutputArray tvec,
bool useExtrinsicGuess, int iterationsCount,
float reprojectionError, double confidence,
OutputArray inliers, int flags);
Mat findEssentialMat( InputArray points1, InputArray points2,
InputArray cameraMatrix1,
int method, double prob,
double threshold, OutputArray mask);
Mat estimateAffine2D(InputArray from, InputArray to, OutputArray inliers,
int method, double ransacReprojThreshold, int maxIters,
double confidence, int refineIters);
void saveMask (OutputArray mask, const std::vector<bool> &inliers_mask);
void setParameters (Ptr<Model> &params, EstimationMethod estimator, const UsacParams &usac_params,
bool mask_need);
bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2, int state,
Ptr<RansacOutput> &ransac_output, InputArray K1_, InputArray K2_,
InputArray dist_coeff1, InputArray dist_coeff2);
}}
#endif //OPENCV_USAC_USAC_HPP

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
namespace cv { namespace usac {
class EpipolarGeometryDegeneracyImpl : public EpipolarGeometryDegeneracy {
private:
const Mat * points_mat;
const float * const points; // i-th row xi1 yi1 xi2 yi2
const int min_sample_size;
public:
explicit EpipolarGeometryDegeneracyImpl (const Mat &points_, int sample_size_) :
points_mat(&points_), points ((float*) points_.data), min_sample_size (sample_size_) {}
/*
* Do oriented constraint to verify if epipolar geometry is in front or behind the camera.
* Return: true if all points are in front of the camers w.r.t. tested epipolar geometry - satisfies constraint.
* false - otherwise.
*/
inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
return isModelValid(F, sample, min_sample_size);
}
/* Oriented constraint:
* x'^T F x = 0
* e' × x' ~+ Fx <=> λe' × x' = Fx, λ > 0
* e × x ~+ x'^T F
*/
inline bool isModelValid(const Mat &F_, const std::vector<int> &sample, int sample_size_) const override {
// F is of rank 2, taking cross product of two rows we obtain null vector of F
Vec3d ec_mat = F_.row(0).cross(F_.row(2));
auto * ec = ec_mat.val; // of size 3x1
// e is zero vector, recompute e
if (ec[0] <= 1.9984e-15 && ec[0] >= -1.9984e-15 &&
ec[1] <= 1.9984e-15 && ec[1] >= -1.9984e-15 &&
ec[2] <= 1.9984e-15 && ec[2] >= -1.9984e-15) {
ec_mat = F_.row(1).cross(F_.row(2));
ec = ec_mat.val;
}
// F is 9x1 row-major ordered F matrix. ec is 3x1
const auto * const F = (double *) F_.data;
// without loss of generality, let the first point in sample be in front of the camera.
int pt = 4*sample[0];
// s1 = F11 * x2 + F21 * y2 + F31 * 1
// s2 = e'_2 * 1 - e'_3 * y1
// sign1 = s1 * s2
const double sign1 = (F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1]);
int num_pts_behind = 0;
for (int i = 1; i < sample_size_; i++) {
pt = 4 * sample[i];
// if signum of the first point and tested point differs
// then two points are on different sides of the camera.
if (sign1*(F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1])<0)
// if 3 points are behind the camera for non-minimal sample then model is
// not valid. Testing by one point as in case for minimal sample is not very
// precise. The number 3 was chosen experimentally.
if (min_sample_size == sample_size_ || ++num_pts_behind >= 3)
return false;
}
return true;
}
Ptr<Degeneracy> clone(int /*state*/) const override {
return makePtr<EpipolarGeometryDegeneracyImpl>(*points_mat, min_sample_size);
}
};
void EpipolarGeometryDegeneracy::recoverRank (Mat &model) {
/*
* Do singular value decomposition.
* Make last eigen value zero of diagonal matrix of singular values.
*/
Matx33d U, Vt;
Vec3d w;
SVD::compute(model, w, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
model = Mat(U * Matx33d(w(0), 0, 0, 0, w(1), 0, 0, 0, 0) * Vt);
}
Ptr<EpipolarGeometryDegeneracy> EpipolarGeometryDegeneracy::create (const Mat &points_,
int sample_size_) {
return makePtr<EpipolarGeometryDegeneracyImpl>(points_, sample_size_);
}
class HomographyDegeneracyImpl : public HomographyDegeneracy {
private:
const Mat * points_mat;
const float * const points;
public:
explicit HomographyDegeneracyImpl (const Mat &points_) :
points_mat(&points_), points ((float *)points_.data) {}
inline bool isSampleGood (const std::vector<int> &sample) const override {
const int smpl1 = 4*sample[0], smpl2 = 4*sample[1], smpl3 = 4*sample[2], smpl4 = 4*sample[3];
// planar correspondences must lie on the same side of any line from two points in sample
const float x1 = points[smpl1], y1 = points[smpl1+1], X1 = points[smpl1+2], Y1 = points[smpl1+3];
const float x2 = points[smpl2], y2 = points[smpl2+1], X2 = points[smpl2+2], Y2 = points[smpl2+3];
const float x3 = points[smpl3], y3 = points[smpl3+1], X3 = points[smpl3+2], Y3 = points[smpl3+3];
const float x4 = points[smpl4], y4 = points[smpl4+1], X4 = points[smpl4+2], Y4 = points[smpl4+3];
// line from points 1 and 2
const float ab_cross_x = y1 - y2, ab_cross_y = x2 - x1, ab_cross_z = x1 * y2 - y1 * x2;
const float AB_cross_x = Y1 - Y2, AB_cross_y = X2 - X1, AB_cross_z = X1 * Y2 - Y1 * X2;
// check if points 3 and 4 are on the same side of line ab on both images
if ((ab_cross_x * x3 + ab_cross_y * y3 + ab_cross_z) *
(AB_cross_x * X3 + AB_cross_y * Y3 + AB_cross_z) < 0)
return false;
if ((ab_cross_x * x4 + ab_cross_y * y4 + ab_cross_z) *
(AB_cross_x * X4 + AB_cross_y * Y4 + AB_cross_z) < 0)
return false;
// line from points 3 and 4
const float cd_cross_x = y3 - y4, cd_cross_y = x4 - x3, cd_cross_z = x3 * y4 - y3 * x4;
const float CD_cross_x = Y3 - Y4, CD_cross_y = X4 - X3, CD_cross_z = X3 * Y4 - Y3 * X4;
// check if points 1 and 2 are on the same side of line cd on both images
if ((cd_cross_x * x1 + cd_cross_y * y1 + cd_cross_z) *
(CD_cross_x * X1 + CD_cross_y * Y1 + CD_cross_z) < 0)
return false;
if ((cd_cross_x * x2 + cd_cross_y * y2 + cd_cross_z) *
(CD_cross_x * X2 + CD_cross_y * Y2 + CD_cross_z) < 0)
return false;
// Checks if points are not collinear
// If area of triangle constructed with 3 points is less then threshold then points are collinear:
// |x1 y1 1| |x1 y1 1|
// (1/2) det |x2 y2 1| = (1/2) det |x2-x1 y2-y1 0| = (1/2) det |x2-x1 y2-y1| < threshold
// |x3 y3 1| |x3-x1 y3-y1 0| |x3-x1 y3-y1|
// for points on the first image
if (fabsf((x2-x1) * (y3-y1) - (y2-y1) * (x3-x1)) * 0.5 < FLT_EPSILON) return false; //1,2,3
if (fabsf((x2-x1) * (y4-y1) - (y2-y1) * (x4-x1)) * 0.5 < FLT_EPSILON) return false; //1,2,4
if (fabsf((x3-x1) * (y4-y1) - (y3-y1) * (x4-x1)) * 0.5 < FLT_EPSILON) return false; //1,3,4
if (fabsf((x3-x2) * (y4-y2) - (y3-y2) * (x4-x2)) * 0.5 < FLT_EPSILON) return false; //2,3,4
// for points on the second image
if (fabsf((X2-X1) * (Y3-Y1) - (Y2-Y1) * (X3-X1)) * 0.5 < FLT_EPSILON) return false; //1,2,3
if (fabsf((X2-X1) * (Y4-Y1) - (Y2-Y1) * (X4-X1)) * 0.5 < FLT_EPSILON) return false; //1,2,4
if (fabsf((X3-X1) * (Y4-Y1) - (Y3-Y1) * (X4-X1)) * 0.5 < FLT_EPSILON) return false; //1,3,4
if (fabsf((X3-X2) * (Y4-Y2) - (Y3-Y2) * (X4-X2)) * 0.5 < FLT_EPSILON) return false; //2,3,4
return true;
}
Ptr<Degeneracy> clone(int /*state*/) const override {
return makePtr<HomographyDegeneracyImpl>(*points_mat);
}
};
Ptr<HomographyDegeneracy> HomographyDegeneracy::create (const Mat &points_) {
return makePtr<HomographyDegeneracyImpl>(points_);
}
///////////////////////////////// Fundamental Matrix Degeneracy ///////////////////////////////////
class FundamentalDegeneracyImpl : public FundamentalDegeneracy {
private:
RNG rng;
const Ptr<Quality> quality;
const float * const points;
const Mat * points_mat;
const Ptr<ReprojectionErrorForward> h_reproj_error;
const EpipolarGeometryDegeneracyImpl ep_deg;
// threshold to find inliers for homography model
const double homography_threshold, log_conf = log(0.05);
// points (1-7) to verify in sample
std::vector<std::vector<int>> h_sample {{0,1,2},{3,4,5},{0,1,6},{3,4,6},{2,5,6}};
const int points_size, sample_size;
public:
FundamentalDegeneracyImpl (int state, const Ptr<Quality> &quality_, const Mat &points_,
int sample_size_, double homography_threshold_) :
rng (state), quality(quality_), points((float *) points_.data), points_mat(&points_),
h_reproj_error(ReprojectionErrorForward::create(points_)),
ep_deg (points_, sample_size_), homography_threshold (homography_threshold_),
points_size (quality_->getPointsSize()), sample_size (sample_size_) {
if (sample_size_ == 8) {
// add more homography samples to test for 8-points F
h_sample.emplace_back(std::vector<int>{0, 1, 7});
h_sample.emplace_back(std::vector<int>{0, 2, 7});
h_sample.emplace_back(std::vector<int>{3, 5, 7});
h_sample.emplace_back(std::vector<int>{3, 6, 7});
h_sample.emplace_back(std::vector<int>{2, 4, 7});
}
}
inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
return ep_deg.isModelValid(F, sample);
}
inline bool isModelValid(const Mat &F, const std::vector<int> &sample, int sample_size_) const override {
return ep_deg.isModelValid(F, sample, sample_size_);
}
bool recoverIfDegenerate (const std::vector<int> &sample, const Mat &F_best,
Mat &non_degenerate_model, Score &non_degenerate_model_score) override {
non_degenerate_model_score = Score(); // set worst case
// According to Two-view Geometry Estimation Unaffected by a Dominant Plane
// (http://cmp.felk.cvut.cz/~matas/papers/chum-degen-cvpr05.pdf)
// only 5 homographies enough to test
// triplets {1,2,3}, {4,5,6}, {1,2,7}, {4,5,7} and {3,6,7}
// H = A - e' (M^-1 b)^T
// A = [e']_x F
// b_i = (x′i × (A xi))^T (x′i × e′)‖x′i×e′‖^−2,
// M is a 3×3 matrix with rows x^T_i
// epipole e' is left nullspace of F s.t. e′^T F=0,
// find e', null space of F^T
Vec3d e_prime = F_best.col(0).cross(F_best.col(2));
if (fabs(e_prime(0)) < 1e-10 && fabs(e_prime(1)) < 1e-10 &&
fabs(e_prime(2)) < 1e-10) // if e' is zero
e_prime = F_best.col(1).cross(F_best.col(2));
const Matx33d A = Math::getSkewSymmetric(e_prime) * Matx33d(F_best);
Vec3d xi_prime(0,0,1), xi(0,0,1), b;
Matx33d M(0,0,1,0,0,1,0,0,1); // last column of M is 1
bool is_model_degenerate = false;
for (const auto &h_i : h_sample) { // only 5 samples
for (int pt_i = 0; pt_i < 3; pt_i++) {
// find b and M
const int smpl = 4*sample[h_i[pt_i]];
xi[0] = points[smpl];
xi[1] = points[smpl+1];
xi_prime[0] = points[smpl+2];
xi_prime[1] = points[smpl+3];
// (x′i × e')
const Vec3d xprime_X_eprime = xi_prime.cross(e_prime);
// (x′i × (A xi))
const Vec3d xprime_X_Ax = xi_prime.cross(A * xi);
// x′i × (A xi))^T (x′i × e′) / ‖x′i×e′‖^2,
b[pt_i] = xprime_X_Ax.dot(xprime_X_eprime) /
std::pow(norm(xprime_X_eprime), 2);
// M from x^T
M(pt_i, 0) = xi[0];
M(pt_i, 1) = xi[1];
}
// compute H
const Matx33d H = A - e_prime * (M.inv() * b).t();
int inliers_on_plane = 0;
h_reproj_error->setModelParameters(Mat(H));
// find inliers from sample, points related to H, x' ~ Hx
for (int s = 0; s < sample_size; s++)
if (h_reproj_error->getError(sample[s]) < homography_threshold)
inliers_on_plane++;
// if there are at least 5 points lying on plane then F is degenerate
if (inliers_on_plane >= 5) {
is_model_degenerate = true;
Mat newF;
const Score newF_score = planeAndParallaxRANSAC(H, newF);
if (newF_score.isBetter(non_degenerate_model_score)) {
// store non degenerate model
non_degenerate_model_score = newF_score;
newF.copyTo(non_degenerate_model);
}
}
}
return is_model_degenerate;
}
Ptr<Degeneracy> clone(int state) const override {
return makePtr<FundamentalDegeneracyImpl>(state, quality->clone(), *points_mat,
sample_size, homography_threshold);
}
private:
// RANSAC with plane-and-parallax to find new Fundamental matrix
Score planeAndParallaxRANSAC (const Matx33d &H, Mat &best_F) {
int max_iters = 100; // with 95% confidence assume at least 17% of inliers
Score best_score;
for (int iters = 0; iters < max_iters; iters++) {
// draw two random points
int h_outlier1 = rng.uniform(0, points_size);
int h_outlier2 = rng.uniform(0, points_size);
while (h_outlier1 == h_outlier2)
h_outlier2 = rng.uniform(0, points_size);
// find outliers of homography H
if (h_reproj_error->getError(h_outlier1) > homography_threshold &&
h_reproj_error->getError(h_outlier2) > homography_threshold) {
// do plane and parallax with outliers of H
const Vec3d pt1 (points[4*h_outlier1], points[4*h_outlier1+1], 1);
const Vec3d pt2 (points[4*h_outlier2], points[4*h_outlier2+1], 1);
const Vec3d pt1_prime (points[4*h_outlier1+2],points[4*h_outlier1+3],1);
const Vec3d pt2_prime (points[4*h_outlier2+2],points[4*h_outlier2+3],1);
// F = [(p1' x Hp1) x (p2' x Hp2)]_x H
const Matx33d F = Math::getSkewSymmetric((pt1_prime.cross(H * pt1)).cross
(pt2_prime.cross(H * pt2))) * H;
const Score score = quality->getScore(Mat(F));
if (score.isBetter(best_score)) {
best_score = score;
best_F = Mat(F);
const double predicted_iters = log_conf / log(1 - std::pow
(static_cast<double>(score.inlier_number) / points_size, 2));
if (! std::isinf(predicted_iters) && predicted_iters < max_iters)
max_iters = static_cast<int>(predicted_iters);
}
}
}
return best_score;
}
};
Ptr<FundamentalDegeneracy> FundamentalDegeneracy::create (int state, const Ptr<Quality> &quality_,
const Mat &points_, int sample_size_, double homography_threshold_) {
return makePtr<FundamentalDegeneracyImpl>(state, quality_, points_, sample_size_,
homography_threshold_);
}
class EssentialDegeneracyImpl : public EssentialDegeneracy {
private:
const Mat * points_mat;
const int sample_size;
const EpipolarGeometryDegeneracyImpl ep_deg;
public:
explicit EssentialDegeneracyImpl (const Mat &points, int sample_size_) :
points_mat(&points), sample_size(sample_size_), ep_deg (points, sample_size_) {}
inline bool isModelValid(const Mat &E, const std::vector<int> &sample) const override {
return ep_deg.isModelValid(E, sample);
}
Ptr<Degeneracy> clone(int /*state*/) const override {
return makePtr<EssentialDegeneracyImpl>(*points_mat, sample_size);
}
};
Ptr<EssentialDegeneracy> EssentialDegeneracy::create (const Mat &points_, int sample_size_) {
return makePtr<EssentialDegeneracyImpl>(points_, sample_size_);
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
// Copyright (C) 2019 Czech Technical University.
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following
// disclaimer in the documentation and/or other materials provided
// with the distribution.
//
// * Neither the name of Czech Technical University nor the
// names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Please contact the author of this library if you have any questions.
// Author: Daniel Barath (barath.daniel@sztaki.mta.hu)
// Modification: Maksym Ivashechkin (ivashmak@cmp.felk.cvut.cz)
#include "../precomp.hpp"
#include "../usac.hpp"
#if defined(HAVE_EIGEN)
#include <Eigen/Eigen>
#elif defined(HAVE_LAPACK)
#include "opencv_lapack.h"
#endif
namespace cv { namespace usac {
// This is the estimator class for estimating a homography matrix between two images. A model estimation method and error calculation method are implemented
class DLSPnPImpl : public DLSPnP {
private:
const Mat * points_mat, * calib_norm_points_mat, * K_mat;
#if defined(HAVE_LAPACK) || defined(HAVE_EIGEN)
const Mat &K;
const float * const calib_norm_points, * const points;
#endif
public:
explicit DLSPnPImpl (const Mat &points_, const Mat &calib_norm_points_, const Mat &K_) :
points_mat(&points_), calib_norm_points_mat(&calib_norm_points_), K_mat (&K_)
#if defined(HAVE_LAPACK) || defined(HAVE_EIGEN)
, K(K_), calib_norm_points((float*)calib_norm_points_.data), points((float*)points_.data)
#endif
{}
// return minimal sample size required for non-minimal estimation.
int getMinimumRequiredSampleSize() const override { return 3; }
// return maximum number of possible solutions.
int getMaxNumberOfSolutions () const override { return 27; }
Ptr<NonMinimalSolver> clone () const override {
return makePtr<DLSPnPImpl>(*points_mat, *calib_norm_points_mat, *K_mat);
}
#if defined(HAVE_LAPACK) || defined(HAVE_EIGEN)
int estimate(const std::vector<int> &sample, int sample_number,
std::vector<Mat> &models_, const std::vector<double> &/*weights_*/) const override {
if (sample_number < getMinimumRequiredSampleSize())
return 0;
// Estimate the model parameters from the given point sample
// using weighted fitting if possible.
// Holds the normalized feature positions cross multiplied with itself
// i.e. n * n^t. This value is used multiple times so it is efficient to
// pre-compute it.
std::vector<Matx33d> normalized_feature_cross(sample_number);
std::vector<Vec3d> world_points(sample_number);
const Matx33d eye = Matx33d::eye();
// The bottom-right symmetric block matrix of inverse(A^T * A). Matrix H from
// Eq. 25 in the Appendix of the DLS paper.
Matx33d h_inverse = sample_number * eye;
// Compute V*W*b with the rotation parameters factored out. This is the
// translation parameterized by the 9 entries of the rotation matrix.
Matx<double, 3, 9> translation_factor = Matx<double, 3, 9>::zeros();
for (int i = 0; i < sample_number; i++) {
const int idx_world = 5 * sample[i], idx_calib = 3 * sample[i];
Vec3d normalized_feature_pos(calib_norm_points[idx_calib],
calib_norm_points[idx_calib+1],
calib_norm_points[idx_calib+2]);
normalized_feature_cross[i] = normalized_feature_pos * normalized_feature_pos.t();
world_points[i] = Vec3d(points[idx_world + 2], points[idx_world + 3], points[idx_world + 4]);
h_inverse -= normalized_feature_cross[i];
translation_factor += (normalized_feature_cross[i] - eye) * leftMultiplyMatrix(world_points[i]);
}
const Matx33d h_matrix = h_inverse.inv();
translation_factor = h_matrix * translation_factor;
// Compute the cost function J' of Eq. 17 in DLS paper. This is a factorized
// version where the rotation matrix parameters have been pulled out. The
// entries to this equation are the coefficients to the cost function which is
// a quartic in the rotation parameters.
Matx<double, 9, 9> ls_cost_coefficients = Matx<double, 9, 9>::zeros();
for (int i = 0; i < sample_number; i++)
ls_cost_coefficients +=
(leftMultiplyMatrix(world_points[i]) + translation_factor).t() *
(eye - normalized_feature_cross[i]) *
(leftMultiplyMatrix(world_points[i]) + translation_factor);
// Extract the coefficients of the jacobian (Eq. 18) from the
// ls_cost_coefficients matrix. The jacobian represent 3 monomials in the
// rotation parameters. Each entry of the jacobian will be 0 at the roots of
// the polynomial, so we can arrange a system of polynomials from these
// equations.
double f1_coeff[20], f2_coeff[20], f3_coeff[20];
extractJacobianCoefficients(ls_cost_coefficients.val, f1_coeff, f2_coeff, f3_coeff);
// We create one equation with random terms that is generally non-zero at the
// roots of our system.
RNG rng;
const double macaulay_term[4] = { 100 * rng.uniform(-1.,1.), 100 * rng.uniform(-1.,1.),
100 * rng.uniform(-1.,1.), 100 * rng.uniform(-1.,1.) };
// Create Macaulay matrix that will be used to solve our polynonomial system.
Mat macaulay_matrix = Mat_<double>::zeros(120, 120);
createMacaulayMatrix(f1_coeff, f2_coeff, f3_coeff, macaulay_term, (double*)macaulay_matrix.data);
// Via the Schur complement trick, the top-left of the Macaulay matrix
// contains a multiplication matrix whose eigenvectors correspond to solutions
// to our system of equations.
Mat sol;
if (!solve(macaulay_matrix.colRange(27, 120).rowRange(27, 120),
macaulay_matrix.colRange(0 , 27).rowRange(27, 120), sol, DECOMP_LU))
return 0;
const Mat solution_polynomial = macaulay_matrix.colRange(0,27).rowRange(0,27) -
(macaulay_matrix.colRange(27,120).rowRange(0,27) * sol);
// Extract eigenvectors of the solution polynomial to obtain the roots which
// are contained in the entries of the eigenvectors.
#ifdef HAVE_EIGEN
Eigen::Map<Eigen::Matrix<double, 27, 27>> sol_poly((double*)solution_polynomial.data);
const Eigen::EigenSolver<Eigen::MatrixXd> eigen_solver(sol_poly);
const auto &eigen_vectors = eigen_solver.eigenvectors();
const auto &eigen_values = eigen_solver.eigenvalues();
#else
int mat_order = 27, info, lda = 27, ldvl = 1, ldvr = 27, lwork = 500;
double wr[27], wi[27] = {0}; // 27 = mat_order
std::vector<double> work(lwork), eig_vecs(729);
char jobvl = 'N', jobvr = 'V'; // only left eigen vectors are computed
dgeev_(&jobvl, &jobvr, &mat_order, (double*)solution_polynomial.data, &lda, wr, wi, nullptr, &ldvl,
&eig_vecs[0], &ldvr, &work[0], &lwork, &info);
if (info != 0) return 0;
#endif
models_ = std::vector<Mat>(); models_.reserve(3);
const int max_pts_to_eval = std::min(sample_number, 100);
std::vector<int> pts_random_shuffle(sample_number);
for (int i = 0; i < sample_number; i++)
pts_random_shuffle[i] = i;
randShuffle(pts_random_shuffle);
for (int i = 0; i < 27; i++) {
// If the rotation solutions are real, treat this as a valid candidate
// rotation.
// The first entry of the eigenvector should equal 1 according to our
// polynomial, so we must divide each solution by the first entry.
#ifdef HAVE_EIGEN
if (eigen_values(i).imag() != 0)
continue;
const double eigen_vec_1i = 1 / eigen_vectors(0, i).real();
const double s1 = eigen_vectors(9, i).real() * eigen_vec_1i,
s2 = eigen_vectors(3, i).real() * eigen_vec_1i,
s3 = eigen_vectors(1, i).real() * eigen_vec_1i;
#else
if (wi[i] != 0)
continue;
const double eigen_vec_1i = 1 / eig_vecs[mat_order*i];
const double s1 = eig_vecs[mat_order*i+9] * eigen_vec_1i,
s2 = eig_vecs[mat_order*i+3] * eigen_vec_1i,
s3 = eig_vecs[mat_order*i+1] * eigen_vec_1i;
#endif
// Compute the rotation (which is the transpose rotation of our solution)
// and translation.
const double qi = s1, qi2 = qi*qi, qj = s2, qj2 = qj*qj, qk = s3, qk2 = qk*qk;
const double s = 1 / (1 + qi2 + qj2 + qk2);
const Matx33d rot_mat (1-2*s*(qj2+qk2), 2*s*(qi*qj+qk), 2*s*(qi*qk-qj),
2*s*(qi*qj-qk), 1-2*s*(qi2+qk2), 2*s*(qj*qk+qi),
2*s*(qi*qk+qj), 2*s*(qj*qk-qi), 1-2*s*(qi2+qj2));
const Matx31d soln_translation = translation_factor * rot_mat.reshape<9,1>();
// Check that all points are in front of the camera. Discard the solution
// if this is not the case.
bool all_points_in_front_of_camera = true;
const Vec3d r3 (rot_mat(2,0),rot_mat(2,1),rot_mat(2,2));
const double z = soln_translation(2);
for (int pt = 0; pt < max_pts_to_eval; pt++) {
if (r3.dot(world_points[pts_random_shuffle[pt]]) + z < 0) {
all_points_in_front_of_camera = false;
break;
}
}
if (all_points_in_front_of_camera) {
Mat model;
// hconcat(rot_mat, soln_translation, model);
hconcat(Math::rotVec2RotMat(Math::rotMat2RotVec(rot_mat)), soln_translation, model);
models_.emplace_back(K * model);
}
}
return static_cast<int>(models_.size());
#else
int estimate(const std::vector<int> &/*sample*/, int /*sample_number*/,
std::vector<Mat> &/*models_*/, const std::vector<double> &/*weights_*/) const override {
return 0;
#endif
}
protected:
#if defined(HAVE_LAPACK) || defined(HAVE_EIGEN)
const int indices[1968] = {
0, 35, 83, 118, 120, 121, 154, 155, 174, 203, 219, 238, 241, 242, 274, 275,
291, 294, 305, 323, 329, 339, 358, 360, 363, 395, 409, 436, 443, 478, 479,
481, 483, 484, 514, 515, 523, 529, 534, 551, 556, 563, 579, 580, 598, 599,
602, 604, 605, 634, 635, 641, 643, 649, 651, 654, 662, 665, 671, 676, 683,
689, 699, 700, 711, 718, 719, 723, 726, 750, 755, 769, 795, 796, 803, 827,
838, 839, 844, 846, 847, 870, 874, 875, 883, 885, 889, 894, 903, 911, 915,
916, 923, 939, 940, 947, 952, 958, 959, 965, 967, 968, 990, 994, 1001, 1003,
1005, 1006, 1009, 1011, 1014, 1022, 1023, 1025, 1026, 1031, 1035, 1036,
1049, 1059, 1060, 1062, 1067, 1071, 1072, 1079, 1080, 1089, 1115, 1116,
1163, 1164, 1168, 1198, 1201, 1209, 1210, 1233, 1234, 1235, 1236, 1254,
1259, 1283, 1284, 1288, 1299, 1317, 1318, 1322, 1330, 1331, 1348, 1353,
1354, 1355, 1356, 1371, 1374, 1377, 1379, 1385, 1403, 1404, 1408, 1409,
1419, 1434, 1437, 1438, 1443, 1449, 1452, 1475, 1476, 1479, 1489, 1516,
1519, 1523, 1524, 1528, 1536, 1558, 1559, 1564, 1570, 1572, 1573, 1593,
1594, 1595, 1596, 1599, 1603, 1607, 1609, 1614, 1619, 1620, 1631, 1636,
1639, 1643, 1644, 1648, 1650, 1656, 1659, 1660, 1677, 1678, 1679, 1685,
1691, 1693, 1694, 1708, 1713, 1714, 1716, 1719, 1721, 1722, 1723, 1727,
1729, 1731, 1734, 1736, 1737, 1739, 1740, 1742, 1745, 1751, 1756, 1759,
1764, 1768, 1769, 1770, 1776, 1779, 1780, 1786, 1791, 1794, 1797, 1799,
1806, 1812, 1815, 1829, 1830, 1835, 1836, 1839, 1849, 1874, 1875, 1876,
1879, 1883, 1884, 1888, 1894, 1896, 1907, 1918, 1919, 1927, 1933, 1935,
1936, 1949, 1950, 1953, 1954, 1956, 1959, 1963, 1964, 1965, 1967, 1969,
1974, 1979, 1980, 1983, 1988, 1991, 1994, 1995, 1996, 1999, 2004, 2008,
2010, 2014, 2016, 2017, 2019, 2020, 2027, 2032, 2037, 2039, 2048, 2054,
2056, 2057, 2068, 2069, 2070, 2073, 2079, 2081, 2082, 2083, 2084, 2085,
2086, 2087, 2091, 2096, 2097, 2099, 2100, 2102, 2103, 2105, 2106, 2108,
2111, 2114, 2115, 2119, 2129, 2130, 2134, 2136, 2137, 2140, 2142, 2146,
2147, 2151, 2152, 2154, 2157, 2169, 2178, 2195, 2196, 2213, 2242, 2243,
2244, 2247, 2248, 2278, 2290, 2298, 2299, 2312, 2313, 2314, 2315, 2316,
2333, 2334, 2339, 2341, 2362, 2363, 2364, 2367, 2368, 2379, 2396, 2397,
2398, 2411, 2419, 2420, 2427, 2428, 2432, 2433, 2434, 2436, 2451, 2453,
2454, 2455, 2457, 2459, 2461, 2465, 2482, 2484, 2487, 2488, 2489, 2499,
2513, 2514, 2516, 2517, 2532, 2538, 2541, 2555, 2556, 2558, 2559, 2569,
2573, 2596, 2598, 2599, 2602, 2603, 2604, 2607, 2608, 2612, 2616, 2638,
2639, 2653, 2659, 2661, 2662, 2672, 2673, 2674, 2676, 2678, 2679, 2680,
2683, 2687, 2689, 2693, 2694, 2699, 2700, 2701, 2711, 2712, 2716, 2718,
2719, 2722, 2724, 2727, 2728, 2730, 2732, 2735, 2736, 2739, 2740, 2756,
2757, 2759, 2774, 2780, 2782, 2783, 2787, 2788, 2792, 2793, 2798, 2799,
2800, 2801, 2802, 2803, 2807, 2811, 2813, 2815, 2816, 2817, 2819, 2820,
2821, 2822, 2825, 2831, 2832, 2838, 2839, 2842, 2847, 2849, 2850, 2852,
2855, 2856, 2860, 2866, 2871, 2873, 2874, 2876, 2877, 2895, 2901, 2904,
2909, 2910, 2916, 2918, 2919, 2929, 2932, 2933, 2953, 2954, 2955, 2956,
2958, 2959, 2962, 2964, 2967, 2968, 2972, 2973, 2974, 2976, 2987, 2999,
3016, 3022, 3024, 3025, 3029, 3030, 3032, 3033, 3038, 3039, 3040, 3043,
3044, 3045, 3047, 3052, 3053, 3059, 3060, 3061, 3063, 3068, 3071, 3072,
3073, 3074, 3075, 3078, 3079, 3082, 3087, 3090, 3092, 3093, 3094, 3095,
3096, 3097, 3100, 3107, 3112, 3116, 3117, 3137, 3143, 3145, 3146, 3147,
3148, 3149, 3152, 3158, 3160, 3161, 3162, 3164, 3165, 3166, 3167, 3172,
3175, 3176, 3177, 3180, 3181, 3182, 3183, 3186, 3188, 3192, 3193, 3194,
3198, 3210, 3212, 3213, 3214, 3215, 3217, 3222, 3226, 3231, 3232, 3233,
3234, 3236, 3255, 3269, 3270, 3276, 3279, 3289, 3309, 3310, 3314, 3315,
3316, 3319, 3324, 3328, 3331, 3334, 3336, 3347, 3350, 3359, 3366, 3390,
3395, 3409, 3429, 3435, 3436, 3443, 3467, 3470, 3478, 3479, 3504, 3509,
3510, 3518, 3519, 3532, 3533, 3549, 3550, 3553, 3554, 3555, 3558, 3559,
3562, 3567, 3571, 3572, 3573, 3574, 3576, 3587, 3590, 3637, 3648, 3652,
3670, 3673, 3677, 3681, 3685, 3691, 3693, 3698, 3749, 3757, 3758, 3770,
3772, 3789, 3790, 3793, 3794, 3797, 3798, 3800, 3806, 3811, 3812, 3813,
3814, 3818, 3830, 3888, 3890, 3893, 3920, 3921, 3922, 3925, 3926, 3927,
3989, 3990, 3999, 4024, 4029, 4030, 4034, 4035, 4039, 4051, 4054, 4056,
4063, 4067, 4070, 4109, 4118, 4132, 4144, 4149, 4150, 4153, 4154, 4158,
4171, 4172, 4173, 4174, 4183, 4190, 4237, 4252, 4264, 4270, 4273, 4277,
4291, 4293, 4298, 4303, 4325, 4354, 4361, 4363, 4369, 4371, 4374, 4382,
4385, 4391, 4396, 4409, 4419, 4420, 4421, 4429, 4431, 4439, 4442, 4474,
4475, 4491, 4494, 4505, 4523, 4529, 4539, 4549, 4558, 4590, 4609, 4624,
4629, 4635, 4636, 4663, 4667, 4670, 4679, 4708, 4713, 4731, 4737, 4739,
4745, 4769, 4785, 4788, 4789, 4794, 4797, 4827, 4828, 4832, 4855, 4857,
4861, 4905, 4908, 4909, 4913, 4914, 4916, 4950, 4984, 4989, 4995, 5023,
5027, 5030, 5067, 5071, 5095, 5098, 5145, 5148, 5153, 5155, 5189, 5224,
5229, 5230, 5234, 5251, 5254, 5263, 5270, 5308, 5337, 5385, 5388, 5389,
5394, 5427, 5455, 5505, 5508, 5513, 5572, 5584, 5590, 5593, 5611, 5613,
5623, 5680, 5684, 5692, 5704, 5707, 5708, 5710, 5712, 5713, 5731, 5733,
5735, 5737, 5743, 5744, 5790, 5803, 5805, 5823, 5824, 5827, 5829, 5831,
5835, 5860, 5863, 5864, 5867, 5870, 5872, 5921, 5925, 5926, 5942, 5943,
5946, 5981, 5982, 5985, 5989, 5991, 5992, 6041, 6062, 6101, 6105, 6109,
6111, 6184, 6190, 6211, 6223, 6281, 6285, 6286, 6302, 6303, 6306, 6307,
6309, 6341, 6342, 6344, 6349, 6350, 6351, 6352, 6424, 6429, 6463, 6470,
6585, 6589, 6644, 6664, 6667, 6668, 6670, 6691, 6697, 6703, 6704, 6825,
6828, 6904, 6907, 6943, 6944, 7006, 7024, 7026, 7027, 7062, 7063, 7064,
7088, 7110, 7121, 7123, 7125, 7126, 7131, 7142, 7143, 7145, 7146, 7151,
7155, 7169, 7180, 7181, 7182, 7187, 7189, 7191, 7192, 7208, 7230, 7241,
7243, 7245, 7246, 7251, 7262, 7263, 7265, 7266, 7267, 7269, 7271, 7275,
7289, 7300, 7302, 7304, 7307, 7310, 7311, 7312, 7362, 7376, 7421, 7425,
7426, 7428, 7504, 7543, 7665, 7726, 7746, 7747, 7781, 7782, 7784, 7785,
7846, 7864, 7866, 7867, 7901, 7902, 7903, 7904, 7966, 7986, 8021, 8022,
8025, 8141, 8145, 8201, 8203, 8211, 8222, 8225, 8231, 8249, 8260, 8261,
8265, 8269, 8271, 8317, 8328, 8332, 8353, 8357, 8361, 8365, 8373, 8378,
8420, 8427, 8428, 8431, 8432, 8433, 8450, 8451, 8453, 8455, 8457, 8458,
8459, 8461, 8465, 8480, 8482, 8486, 8487, 8489, 8513, 8514, 8515, 8516,
8517, 8565, 8583, 8584, 8587, 8589, 8623, 8624, 8630, 8632, 8681, 8685,
8686, 8702, 8703, 8704, 8706, 8707, 8709, 8742, 8743, 8744, 8750, 8751,
8752, 8808, 8810, 8840, 8841, 8845, 8846, 8905, 8909, 8912, 8918, 8920,
8924, 8925, 8927, 8932, 8940, 8941, 8943, 8947, 8948, 8949, 8950, 8952,
8953, 8954, 8958, 8970, 8971, 8972, 8973, 8974, 8975, 8977, 8984, 8990,
8992, 8996, 9021, 9036, 9037, 9038, 9039, 9049, 9050, 9053, 9076, 9077,
9078, 9079, 9080, 9082, 9084, 9086, 9087, 9088, 9092, 9096, 9098, 9119,
9168, 9201, 9205, 9274, 9291, 9294, 9305, 9329, 9339, 9345, 9349, 9387,
9391, 9397, 9400, 9402, 9415, 9416, 9418, 9432, 9437, 9455, 9458, 9461,
9466, 9468, 9473, 9475, 9522, 9524, 9526, 9536, 9546, 9548, 9577, 9581,
9582, 9585, 9586, 9588, 9614, 9628, 9633, 9639, 9641, 9642, 9643, 9647,
9651, 9656, 9657, 9659, 9660, 9662, 9665, 9671, 9679, 9689, 9690, 9696,
9700, 9701, 9706, 9708, 9709, 9711, 9714, 9717, 9751, 9752, 9757, 9758,
9760, 9767, 9768, 9770, 9778, 9780, 9781, 9792, 9797, 9798, 9800, 9801,
9805, 9806, 9810, 9812, 9815, 9818, 9835, 9836, 9869, 9884, 9885, 9887,
9900, 9903, 9904, 9907, 9908, 9909, 9910, 9914, 9930, 9931, 9934, 9937,
9943, 9944, 9950, 9952, 9986, 9987, 9991, 9997, 10000, 10002, 10004, 10006,
10012, 10015, 10016, 10018, 10026, 10028, 10032, 10033, 10037, 10053, 10055,
10057, 10058, 10062, 10066, 10073, 10075, 10096, 10109, 10110, 10113, 10119,
10123, 10124, 10125, 10127, 10139, 10140, 10143, 10147, 10148, 10149, 10150,
10151, 10154, 10155, 10159, 10170, 10171, 10174, 10176, 10177, 10180, 10184,
10187, 10190, 10192, 10197, 10225, 10229, 10231, 10232, 10237, 10238, 10240,
10244, 10245, 10247, 10250, 10252, 10258, 10260, 10261, 10263, 10268, 10272,
10273, 10274, 10277, 10278, 10280, 10286, 10290, 10292, 10293, 10294, 10295,
10297, 10298, 10312, 10315, 10316, 10351, 10357, 10360, 10364, 10368, 10372,
10378, 10388, 10392, 10393, 10397, 10401, 10405, 10413, 10415, 10417, 10418,
10435, 10462, 10471, 10472, 10473, 10477, 10478, 10479, 10480, 10483, 10487,
10490, 10493, 10498, 10499, 10500, 10501, 10511, 10512, 10517, 10518, 10519,
10520, 10522, 10526, 10527, 10530, 10532, 10535, 10536, 10538, 10540, 10555,
10556, 10557, 10587, 10591, 10597, 10600, 10602, 10608, 10615, 10616, 10618,
10632, 10637, 10641, 10645, 10655, 10658, 10666, 10673, 10675, 10711, 10717,
10720, 10724, 10732, 10738, 10747, 10748, 10750, 10752, 10753, 10757, 10771,
10773, 10775, 10777, 10778, 10784, 10795, 10827, 10840, 10842, 10855, 10856,
10872, 10895, 10901, 10905, 10906, 10908, 10913, 10943, 10947, 10948, 10951,
10952, 10957, 10958, 10960, 10961, 10962, 10967, 10970, 10975, 10976, 10977,
10978, 10980, 10981, 10982, 10992, 10997, 10998, 11000, 11006, 11010, 11012,
11015, 11018, 11026, 11031, 11033, 11034, 11035, 11036, 11057, 11068, 11069,
11081, 11082, 11084, 11085, 11086, 11087, 11096, 11097, 11100, 11102, 11103,
11106, 11108, 11114, 11130, 11134, 11137, 11141, 11142, 11146, 11148, 11149,
11151, 11152, 11154, 11177, 11188, 11189, 11201, 11202, 11204, 11205, 11206,
11207, 11216, 11217, 11220, 11222, 11223, 11226, 11227, 11228, 11229, 11230,
11234, 11250, 11251, 11254, 11257, 11262, 11264, 11266, 11270, 11271, 11272,
11274, 11311, 11317, 11320, 11328, 11338, 11352, 11357, 11361, 11365, 11375,
11378, 11395, 11426, 11427, 11440, 11442, 11444, 11446, 11452, 11455, 11456,
11466, 11468, 11472, 11473, 11493, 11495, 11497, 11501, 11502, 11506, 11508,
11513, 11543, 11547, 11548, 11552, 11558, 11560, 11561, 11562, 11567, 11575,
11576, 11577, 11580, 11581, 11582, 11592, 11598, 11610, 11612, 11615, 11621,
11626, 11628, 11629, 11631, 11633, 11634, 11636, 11682, 11684, 11686, 11696,
11706, 11707, 11708, 11710, 11731, 11737, 11741, 11742, 11744, 11746, 11748,
11788, 11801, 11802, 11807, 11816, 11817, 11820, 11822, 11850, 11861, 11865,
11866, 11868, 11869, 11871, 11874, 11922, 11924, 11926, 11936, 11944, 11946,
11947, 11948, 11950, 11971, 11977, 11982, 11983, 11984, 11986, 12051, 12065,
12089, 12105, 12109, 12157, 12158, 12159, 12168, 12170, 12173, 12197, 12198,
12199, 12200, 12201, 12202, 12205, 12206, 12207, 12212, 12216, 12218, 12277,
12278, 12288, 12290, 12317, 12318, 12320, 12321, 12325, 12326, 12332, 12338,
12397, 12408, 12437, 12441, 12445, 12458, 12491, 12508, 12513, 12514, 12516,
12531, 12534, 12537, 12539, 12545, 12564, 12568, 12569, 12579, 12588, 12589,
12594, 12597, 12620, 12627, 12628, 12632, 12633, 12651, 12653, 12655, 12657,
12659, 12661, 12665, 12682, 12687, 12689, 12708, 12709, 12713, 12714, 12716,
12717, 12747, 12748, 12751, 12752, 12770, 12775, 12777, 12778, 12781, 12800,
12806, 12828, 12829, 12833, 12834, 12835, 12836, 12867, 12871, 12888, 12895,
12898, 12921, 12925, 12948, 12953, 12955, 12996, 13008, 13010, 13013, 13040,
13041, 13042, 13044, 13045, 13046, 13047, 13048, 13106, 13107, 13120, 13122,
13124, 13126, 13132, 13135, 13136, 13146, 13147, 13148, 13150, 13152, 13153,
13171, 13173, 13175, 13177, 13182, 13184, 13186, 13193, 13207, 13230, 13234,
13243, 13245, 13249, 13254, 13263, 13267, 13269, 13271, 13275, 13276, 13299,
13300, 13304, 13307, 13310, 13312, 13319, 13338, 13355, 13356, 13370, 13373,
13400, 13402, 13403, 13404, 13406, 13407, 13408, 13438, 13459, 13471, 13472,
13473, 13474, 13476, 13490, 13493, 13494, 13498, 13499, 13501, 13520, 13522,
13524, 13526, 13527, 13528, 13539, 13555, 13556, 13557, 13591, 13592, 13593,
13608, 13610, 13613, 13618, 13619, 13621, 13640, 13641, 13642, 13645, 13646,
13647, 13675, 13676, 13677, 13711, 13712, 13728, 13730, 13738, 13741, 13760,
13761, 13765, 13766, 13795, 13796, 13831, 13848, 13858, 13881, 13885, 13915,
13944, 13949, 13950, 13957, 13958, 13959, 13970, 13972, 13973, 13993, 13994,
13995, 13997, 13998, 13999, 14000, 14002, 14006, 14007, 14012, 14013, 14014,
14016, 14018, 14027, 14069, 14077, 14078, 14088, 14090, 14092, 14113, 14114,
14117, 14118, 14120, 14121, 14125, 14126, 14132, 14133, 14134, 14138, 14187,
14188, 14191, 14192, 14208, 14210, 14215, 14217, 14218, 14221, 14240, 14241,
14245, 14246, 14273, 14274, 14275, 14276, 14307, 14311, 14328, 14335, 14338,
14361, 14365, 14393, 14395
};
void createMacaulayMatrix(const double a[20], const double b[20],
const double c[20], const double u[4], double * macaulay_matrix) const {
// The matrix is very large (14400 elements!) and sparse (1968 non-zero
// elements) so we load it from pre-computed values calculated in matlab.
const double values[1968] = {
u[0], a[0], b[0], c[0], u[3], u[0], a[0], a[9], b[0], b[9], c[0], c[9],
u[3], u[0], a[9], a[13], a[0], b[9], b[0], b[13], c[0], c[9], c[13], u[2],
u[0], a[10], a[0], b[0], b[10], c[10], c[0], u[2], u[3], u[0], a[10], a[4],
a[0], a[9], b[10], b[0], b[9], b[4], c[10], c[0], c[4], c[9], u[2], u[3],
u[0], a[4], a[11], a[0], a[9], a[13], a[10], b[4], b[0], b[10], b[9], b[13],
b[11], c[10], c[4], c[9], c[0], c[11], c[13], u[2], u[0], a[0], a[14],
a[10], b[0], b[10], b[14], c[0], c[14], c[10], u[2], u[3], u[0], a[9],
a[14], a[5], a[10], a[0], a[4], b[14], b[0], b[10], b[9], b[4], b[5], c[14],
c[10], c[9], c[0], c[5], c[4], u[2], u[3], u[0], a[13], a[5], a[10], a[4],
a[9], a[0], a[11], a[14], b[5], b[10], b[9], b[14], b[0], b[4], b[13],
b[11], c[14], c[5], c[4], c[0], c[13], c[10], c[9], c[11], u[1], u[0], a[8],
a[0], b[8], b[0], c[0], c[8], u[1], u[3], u[0], a[0], a[8], a[3], a[9],
b[8], b[0], b[3], b[9], c[9], c[8], c[0], c[3], u[1], u[3], u[0], a[0],
a[9], a[3], a[7], a[13], a[8], b[3], b[0], b[9], b[8], b[7], b[13], c[13],
c[8], c[3], c[0], c[9], c[7], u[1], u[2], u[0], a[2], a[10], a[0], a[8],
b[8], b[0], b[2], b[10], c[10], c[0], c[2], c[8], u[1], u[2], u[3], u[0],
a[10], a[2], a[16], a[4], a[9], a[8], a[0], a[3], b[2], b[10], b[0], b[8],
b[3], b[9], b[16], b[4], c[4], c[0], c[9], c[2], c[8], c[10], c[16], c[3],
u[1], u[2], u[3], u[0], a[10], a[4], a[16], a[11], a[13], a[8], a[0], a[3],
a[9], a[7], a[2], b[16], b[0], b[10], b[4], b[9], b[8], b[2], b[3], b[7],
b[13], b[11], c[11], c[2], c[9], c[13], c[16], c[3], c[0], c[8], c[10],
c[4], c[7], u[1], u[2], u[0], a[0], a[8], a[17], a[14], a[10], a[2], b[0],
b[8], b[2], b[10], b[17], b[14], c[14], c[0], c[10], c[8], c[17], c[2],
u[1], u[2], u[3], u[0], a[9], a[3], a[14], a[17], a[5], a[4], a[2], a[0],
a[8], a[10], a[16], b[17], b[14], b[10], b[8], b[0], b[2], b[9], b[3],
b[16], b[4], b[5], c[5], c[10], c[9], c[4], c[0], c[17], c[2], c[3], c[8],
c[14], c[16], u[1], u[2], u[3], u[0], a[14], a[13], a[7], a[5], a[11], a[2],
a[10], a[16], a[9], a[3], a[8], a[4], a[17], b[10], b[14], b[5], b[4], b[2],
b[3], b[17], b[8], b[9], b[16], b[13], b[7], b[11], c[17], c[4], c[13],
c[11], c[9], c[16], c[8], c[10], c[7], c[2], c[3], c[14], c[5], u[1], u[0],
a[12], a[8], a[0], b[0], b[12], b[8], c[0], c[8], c[12], u[1], u[3], u[0],
a[0], a[8], a[12], a[18], a[3], a[9], b[12], b[8], b[0], b[9], b[18], b[3],
c[9], c[3], c[12], c[0], c[8], c[18], u[1], u[3], u[0], a[0], a[8], a[9],
a[3], a[18], a[7], a[12], a[13], b[18], b[0], b[8], b[3], b[9], b[12],
b[13], b[7], c[13], c[7], c[12], c[18], c[0], c[8], c[9], c[3], u[1], u[2],
u[0], a[1], a[2], a[0], a[8], a[12], a[10], b[12], b[0], b[8], b[10], b[1],
b[2], c[10], c[2], c[0], c[8], c[1], c[12], u[1], u[2], u[3], u[0], a[10],
a[2], a[1], a[16], a[9], a[3], a[0], a[12], a[8], a[18], a[4], b[1], b[2],
b[8], b[10], b[12], b[0], b[18], b[9], b[3], b[4], b[16], c[4], c[16], c[8],
c[9], c[0], c[3], c[1], c[12], c[10], c[2], c[18], u[1], u[2], u[3], u[0],
a[10], a[2], a[4], a[16], a[13], a[7], a[9], a[12], a[8], a[18], a[3], a[1],
a[11], b[10], b[8], b[2], b[16], b[3], b[4], b[12], b[1], b[18], b[9],
b[13], b[7], b[11], c[11], c[1], c[3], c[13], c[9], c[7], c[18], c[8],
c[12], c[10], c[2], c[4], c[16], u[1], u[2], u[0], a[8], a[12], a[17],
a[10], a[2], a[1], a[0], a[14], b[0], b[8], b[12], b[1], b[10], b[2], b[14],
b[17], c[14], c[17], c[10], c[0], c[8], c[2], c[12], c[1], u[1], u[2], u[3],
u[0], a[3], a[18], a[14], a[17], a[4], a[16], a[10], a[1], a[8], a[12],
a[2], a[9], a[5], b[17], b[2], b[14], b[12], b[8], b[1], b[10], b[9], b[3],
b[18], b[4], b[16], b[5], c[5], c[2], c[4], c[9], c[3], c[10], c[16], c[8],
c[1], c[18], c[12], c[14], c[17], u[1], u[2], u[3], u[0], a[14], a[17],
a[7], a[5], a[11], a[4], a[1], a[2], a[3], a[18], a[12], a[16], a[13],
b[14], b[2], b[17], b[16], b[5], b[1], b[18], b[12], b[3], b[4], b[13],
b[7], b[11], c[16], c[11], c[13], c[7], c[4], c[3], c[12], c[2], c[1],
c[18], c[14], c[17], c[5], u[2], a[10], a[2], a[6], a[14], a[17], b[8],
b[0], b[10], b[2], b[17], b[14], b[6], c[6], c[0], c[10], c[14], c[2], c[8],
c[17], u[2], a[10], a[6], a[14], b[0], b[10], b[14], b[6], c[10], c[0],
c[6], c[14], u[2], a[2], a[1], a[14], a[17], a[10], a[6], b[12], b[8],
b[10], b[2], b[1], b[14], b[17], b[6], c[6], c[8], c[14], c[10], c[2],
c[17], c[1], c[12], a[17], a[6], a[1], b[19], b[1], b[17], b[6], c[6],
c[19], c[1], c[17], a[1], a[14], a[17], a[6], a[2], b[19], b[12], b[2],
b[1], b[14], b[17], b[6], c[6], c[12], c[17], c[2], c[1], c[14], c[19],
a[8], a[12], a[19], b[12], b[8], b[19], c[8], c[12], c[19], a[14], a[17],
a[6], b[8], b[2], b[10], b[14], b[17], b[6], c[10], c[14], c[6], c[8],
c[17], c[2], a[17], a[6], a[14], b[12], b[1], b[2], b[14], b[17], b[6],
c[2], c[6], c[14], c[17], c[12], c[1], a[6], a[17], b[19], b[1], b[17],
b[6], c[1], c[17], c[6], c[19], u[3], a[11], a[9], a[13], a[15], a[4],
b[11], b[9], b[4], b[13], b[15], c[4], c[11], c[13], c[0], c[10], c[9],
c[15], u[3], a[13], a[15], a[9], b[13], b[9], b[15], c[9], c[13], c[0],
c[15], a[14], a[6], b[0], b[10], b[14], b[6], c[0], c[14], c[10], c[6],
a[13], a[15], a[7], b[13], b[15], b[7], c[7], c[8], c[9], c[3], c[13],
c[15], a[13], a[7], a[15], b[13], b[7], b[15], c[12], c[3], c[18], c[13],
c[7], c[15], a[6], b[10], b[14], b[6], c[10], c[6], c[14], a[7], a[15],
b[7], b[15], c[19], c[18], c[7], c[15], a[6], b[2], b[17], b[14], b[6],
c[14], c[6], c[2], c[17], a[15], b[15], c[3], c[13], c[7], c[15], a[15],
b[15], c[18], c[7], c[15], a[6], b[1], b[17], b[6], c[17], c[6], c[1], a[6],
a[17], a[5], b[18], b[1], b[17], b[16], b[6], b[5], c[16], c[5], c[6],
c[17], c[18], c[1], a[5], a[6], a[14], b[14], b[9], b[10], b[4], b[6], b[5],
c[6], c[9], c[10], c[5], c[4], c[14], a[11], a[15], a[13], b[11], b[15],
b[13], c[4], c[13], c[14], c[5], c[11], c[15], a[15], b[15], c[13], c[4],
c[11], c[15], b[17], b[6], c[6], c[17], a[5], a[11], a[4], b[5], b[11],
b[4], b[13], b[15], c[14], c[4], c[13], c[6], c[15], c[5], c[11], b[14],
b[6], c[14], c[6], c[13], c[15], a[6], b[16], b[17], b[6], b[5], c[5], c[6],
c[16], c[17], c[7], c[15], b[5], b[6], c[5], c[6], a[6], b[11], b[6], b[5],
c[6], c[11], c[5], u[3], a[15], a[4], a[11], a[13], a[9], a[5], b[4], b[13],
b[5], b[9], b[11], b[15], c[5], c[11], c[10], c[9], c[15], c[14], c[4],
c[13], u[2], a[11], a[14], a[5], a[4], a[10], a[6], b[14], b[4], b[6],
b[10], b[9], b[13], b[5], b[11], c[6], c[5], c[10], c[9], c[11], c[13],
c[14], c[4], a[15], b[15], c[7], c[16], c[15], c[11], b[6], c[6], c[15],
a[11], b[11], b[15], c[5], c[11], c[15], c[6], a[5], b[15], b[5], b[11],
c[6], c[5], c[15], c[11], a[15], b[15], c[11], c[15], c[5], c[15], c[11],
a[13], a[15], a[11], b[13], b[11], b[15], c[11], c[15], c[9], c[10], c[4],
c[13], a[1], a[17], a[19], b[19], b[1], b[17], c[17], c[19], c[1], u[1],
a[8], a[12], a[9], a[3], a[18], a[13], a[19], a[7], b[8], b[12], b[9],
b[18], b[3], b[19], b[13], b[7], c[13], c[7], c[19], c[8], c[12], c[9],
c[3], c[18], a[6], b[6], b[4], b[14], b[5], c[4], c[14], c[5], c[6], a[6],
a[5], a[14], b[6], b[5], b[13], b[14], b[4], b[11], c[14], c[13], c[4],
c[11], c[6], c[5], a[12], a[19], b[19], b[12], c[12], c[19], u[2], a[16],
a[6], a[5], a[14], a[2], a[1], a[17], a[4], b[17], b[6], b[1], b[12], b[2],
b[18], b[3], b[14], b[4], b[16], b[5], c[17], c[3], c[5], c[4], c[16],
c[14], c[2], c[12], c[18], c[1], c[6], u[1], a[1], a[0], a[8], a[12], a[19],
a[10], a[2], b[19], b[0], b[8], b[12], b[10], b[2], b[1], c[10], c[2], c[1],
c[8], c[12], c[0], c[19], a[19], b[19], c[19], a[15], a[13], b[15], b[13],
c[13], c[15], c[0], c[9], a[16], a[11], a[15], a[7], a[18], b[16], b[18],
b[11], b[7], b[15], c[7], c[15], c[19], c[18], c[1], c[16], c[11], a[11],
a[15], a[7], b[11], b[7], b[15], c[15], c[16], c[7], c[17], c[11], c[5],
u[3], a[4], a[11], a[15], a[3], a[9], a[7], a[13], a[16], b[9], b[4], b[11],
b[13], b[3], b[16], b[7], b[15], c[16], c[13], c[15], c[7], c[8], c[9],
c[10], c[2], c[3], c[4], c[11], a[2], a[1], a[3], a[18], a[12], a[19], a[4],
a[16], b[2], b[19], b[1], b[12], b[3], b[18], b[16], b[4], c[4], c[16],
c[19], c[18], c[12], c[3], c[2], c[1], a[5], a[14], a[17], a[6], b[6],
b[17], b[3], b[2], b[14], b[16], b[4], b[5], c[6], c[4], c[5], c[14], c[3],
c[2], c[16], c[17], u[1], a[17], a[5], a[11], a[16], a[1], a[18], a[19],
a[7], b[17], b[1], b[5], b[19], b[18], b[16], b[7], b[11], c[7], c[16],
c[18], c[11], c[19], c[1], c[17], c[5], u[2], a[4], a[16], a[6], a[5],
a[17], a[10], a[2], a[14], b[6], b[14], b[2], b[8], b[10], b[3], b[9],
b[17], b[4], b[16], b[5], c[14], c[9], c[4], c[5], c[10], c[17], c[8],
c[16], c[3], c[2], c[6], u[1], a[18], a[14], a[17], a[4], a[16], a[2],
a[12], a[19], a[1], a[5], a[3], b[14], b[1], b[17], b[19], b[12], b[2],
b[3], b[18], b[4], b[16], b[5], c[5], c[1], c[16], c[3], c[18], c[2], c[12],
c[4], c[19], c[14], c[17], a[17], a[16], a[1], a[19], a[5], a[18], b[17],
b[19], b[1], b[18], b[16], b[5], c[5], c[18], c[1], c[19], c[16], c[17],
u[1], a[10], a[2], a[1], a[9], a[3], a[18], a[8], a[19], a[12], a[4], a[16],
b[10], b[1], b[12], b[2], b[19], b[8], b[9], b[3], b[18], b[4], b[16], c[4],
c[16], c[12], c[3], c[8], c[18], c[9], c[19], c[10], c[2], c[1], a[1],
a[16], a[7], a[18], a[19], a[11], b[1], b[19], b[16], b[18], b[7], b[11],
c[11], c[18], c[7], c[19], c[1], c[16], a[6], a[5], a[17], a[1], a[16],
b[6], b[19], b[1], b[18], b[17], b[16], b[5], c[18], c[16], c[17], c[1],
c[5], c[19], c[6], a[11], a[15], a[7], b[11], b[7], b[15], c[15], c[18],
c[1], c[7], c[16], c[11], u[1], a[2], a[1], a[4], a[16], a[13], a[7], a[3],
a[19], a[12], a[18], a[11], b[2], b[12], b[1], b[4], b[18], b[16], b[19],
b[3], b[13], b[7], b[11], c[11], c[18], c[7], c[3], c[13], c[12], c[19],
c[2], c[1], c[4], c[16], u[3], a[5], a[15], a[16], a[4], a[13], a[7], a[3],
a[11], b[4], b[5], b[11], b[16], b[7], b[3], b[13], b[15], c[11], c[15],
c[13], c[2], c[3], c[4], c[14], c[17], c[16], c[7], c[5], u[2], a[6], a[11],
a[17], a[14], a[4], a[16], a[2], a[5], b[14], b[6], b[5], b[17], b[16],
b[2], b[3], b[4], b[7], b[13], b[11], c[5], c[13], c[11], c[4], c[2], c[3],
c[14], c[7], c[17], c[16], c[6], a[1], a[18], a[19], a[16], b[1], b[19],
b[18], b[16], c[16], c[19], c[18], c[1], u[3], a[5], a[11], a[16], a[7],
a[18], a[15], b[5], b[16], b[18], b[7], b[11], b[15], c[15], c[11], c[7],
c[1], c[18], c[16], c[17], c[5], u[3], a[4], a[16], a[11], a[15], a[13],
a[18], a[3], a[7], b[4], b[3], b[16], b[7], b[11], b[18], b[13], b[15],
c[7], c[15], c[13], c[12], c[3], c[2], c[1], c[18], c[4], c[16], c[11],
a[5], a[11], a[16], b[5], b[16], b[7], b[11], b[15], c[15], c[11], c[17],
c[16], c[7], c[5], c[6], a[11], a[7], a[13], a[15], b[13], b[11], b[15],
b[7], c[15], c[3], c[2], c[13], c[4], c[16], c[7], c[11], a[6], a[5], a[17],
b[6], b[7], b[17], b[16], b[5], b[11], c[11], c[5], c[17], c[7], c[16],
c[6], a[15], b[15], c[15], c[9], c[13], a[8], a[12], a[19], a[10], a[2],
a[1], b[8], b[12], b[19], b[2], b[10], b[1], c[10], c[2], c[1], c[12],
c[19], c[8], a[12], a[19], a[2], a[1], b[12], b[19], b[1], b[2], c[2], c[1],
c[19], c[12], a[19], a[1], b[19], b[1], c[1], c[19], u[3], a[9], a[13],
a[7], a[15], a[3], b[7], b[9], b[13], b[3], b[15], c[15], c[3], c[7], c[0],
c[8], c[9], c[13], u[3], a[9], a[3], a[13], a[7], a[18], a[15], b[9], b[3],
b[7], b[13], b[18], b[15], c[15], c[18], c[8], c[12], c[9], c[3], c[13],
c[7], a[3], a[18], a[13], a[7], a[15], b[3], b[18], b[13], b[7], b[15],
c[15], c[12], c[19], c[3], c[18], c[13], c[7], a[18], a[7], a[15], b[18],
b[7], b[15], c[15], c[19], c[18], c[7], a[19], a[0], a[8], a[12], b[8],
b[0], b[12], b[19], c[0], c[8], c[12], c[19], u[2], a[6], a[5], a[17],
a[16], a[1], a[11], b[6], b[17], b[1], b[18], b[16], b[7], b[5], b[11],
c[7], c[11], c[5], c[16], c[1], c[18], c[17], c[6], u[2], a[4], a[6], a[14],
a[10], a[5], b[6], b[10], b[0], b[9], b[14], b[4], b[5], c[6], c[14], c[0],
c[4], c[9], c[10], c[5], u[1], a[19], a[12], a[0], a[8], b[0], b[8], b[19],
b[12], c[0], c[8], c[12], c[19], u[1], a[0], a[8], a[12], a[19], a[18],
a[9], a[3], b[19], b[0], b[12], b[8], b[9], b[3], b[18], c[9], c[3], c[18],
c[19], c[0], c[8], c[12], a[8], a[12], a[19], a[9], a[3], a[18], b[8],
b[19], b[12], b[3], b[9], b[18], c[9], c[3], c[18], c[8], c[12], c[19],
a[12], a[19], a[3], a[18], b[12], b[19], b[18], b[3], c[3], c[18], c[12],
c[19], a[19], a[18], b[19], b[18], c[18], c[19], u[1], a[12], a[19], a[10],
a[2], a[1], a[14], a[8], a[17], b[8], b[12], b[19], b[10], b[2], b[1],
b[14], b[17], c[14], c[17], c[2], c[8], c[12], c[1], c[10], c[19], a[19],
a[2], a[1], a[14], a[17], a[12], b[12], b[19], b[2], b[1], b[17], b[14],
c[14], c[17], c[1], c[12], c[19], c[2], a[12], a[19], a[3], a[18], a[13],
a[7], b[12], b[19], b[3], b[18], b[7], b[13], c[13], c[7], c[12], c[19],
c[3], c[18], a[19], a[18], a[7], b[19], b[18], b[7], c[7], c[19], c[18]
};
for (int i = 0; i < 1968; i++)
macaulay_matrix[indices[i]] = values[i];
}
#endif
// Transforms a 3 - vector in a 3x9 matrix such that :
// R * v = leftMultiplyMatrix(v) * vec(R)
// Where R is a rotation matrix and vec(R) converts R to a 9x1 vector.
Matx<double, 3, 9> leftMultiplyMatrix(const Vec3d& v) const {
Matx<double, 3, 9> left_mult_mat = Matx<double, 3, 9>::zeros();
left_mult_mat(0,0) = v[0]; left_mult_mat(0,1) = v[1]; left_mult_mat(0,2) = v[2];
left_mult_mat(1,3) = v[0]; left_mult_mat(1,4) = v[1]; left_mult_mat(1,5) = v[2];
left_mult_mat(2,6) = v[0]; left_mult_mat(2,7) = v[1]; left_mult_mat(2,8) = v[2];
return left_mult_mat;
}
// Extracts the coefficients of the Jacobians of the LS cost function (which is
// parameterized by the 3 rotation coefficients s1, s2, s3).
void extractJacobianCoefficients(const double * const D,
double f1_coeff[20], double f2_coeff[20], double f3_coeff[20]) const {
f1_coeff[0] =
2 * D[5] - 2 * D[7] + 2 * D[41] - 2 * D[43] + 2 * D[45] +
2 * D[49] + 2 * D[53] - 2 * D[63] - 2 * D[67] - 2 * D[71] +
2 * D[77] - 2 * D[79]; // constant term
f1_coeff[1] =
(6 * D[1] + 6 * D[3] + 6 * D[9] - 6 * D[13] - 6 * D[17] +
6 * D[27] - 6 * D[31] - 6 * D[35] - 6 * D[37] - 6 * D[39] -
6 * D[73] - 6 * D[75]); // s1^2 * s2
f1_coeff[2] =
(4 * D[6] - 4 * D[2] + 8 * D[14] - 8 * D[16] - 4 * D[18] +
4 * D[22] + 4 * D[26] + 8 * D[32] - 8 * D[34] + 4 * D[38] -
4 * D[42] + 8 * D[46] + 8 * D[48] + 4 * D[54] - 4 * D[58] -
4 * D[62] - 8 * D[64] - 8 * D[66] + 4 * D[74] -
4 * D[78]); // s1 * s2
f1_coeff[3] =
(4 * D[1] - 4 * D[3] + 4 * D[9] - 4 * D[13] - 4 * D[17] +
8 * D[23] - 8 * D[25] - 4 * D[27] + 4 * D[31] + 4 * D[35] -
4 * D[37] + 4 * D[39] + 8 * D[47] + 8 * D[51] + 8 * D[59] -
8 * D[61] - 8 * D[65] - 8 * D[69] - 4 * D[73] +
4 * D[75]); // s1 * s3
f1_coeff[4] = (8 * D[10] - 8 * D[20] - 8 * D[30] + 8 * D[50] +
8 * D[60] - 8 * D[70]); // s2 * s3
f1_coeff[5] =
(4 * D[14] - 2 * D[6] - 2 * D[2] + 4 * D[16] - 2 * D[18] +
2 * D[22] - 2 * D[26] + 4 * D[32] + 4 * D[34] + 2 * D[38] +
2 * D[42] + 4 * D[46] + 4 * D[48] - 2 * D[54] + 2 * D[58] -
2 * D[62] + 4 * D[64] + 4 * D[66] - 2 * D[74] -
2 * D[78]); // s2^2 * s3
f1_coeff[6] = (2 * D[13] - 2 * D[3] - 2 * D[9] - 2 * D[1] -
2 * D[17] - 2 * D[27] + 2 * D[31] - 2 * D[35] +
2 * D[37] + 2 * D[39] - 2 * D[73] - 2 * D[75]); // s2^3
f1_coeff[7] =
(4 * D[8] - 4 * D[0] + 8 * D[20] + 8 * D[24] + 4 * D[40] +
8 * D[56] + 8 * D[60] + 4 * D[72] - 4 * D[80]); // s1 * s3^2
f1_coeff[8] =
(4 * D[0] - 4 * D[40] - 4 * D[44] + 8 * D[50] - 8 * D[52] -
8 * D[68] + 8 * D[70] - 4 * D[76] - 4 * D[80]); // s1
f1_coeff[9] = (2 * D[2] + 2 * D[6] + 4 * D[14] - 4 * D[16] +
2 * D[18] + 2 * D[22] + 2 * D[26] - 4 * D[32] +
4 * D[34] + 2 * D[38] + 2 * D[42] + 4 * D[46] -
4 * D[48] + 2 * D[54] + 2 * D[58] + 2 * D[62] -
4 * D[64] + 4 * D[66] + 2 * D[74] + 2 * D[78]); // s3
f1_coeff[10] = (2 * D[1] + 2 * D[3] + 2 * D[9] + 2 * D[13] +
2 * D[17] - 4 * D[23] + 4 * D[25] + 2 * D[27] +
2 * D[31] + 2 * D[35] + 2 * D[37] + 2 * D[39] -
4 * D[47] + 4 * D[51] + 4 * D[59] - 4 * D[61] +
4 * D[65] - 4 * D[69] + 2 * D[73] + 2 * D[75]); // s2
f1_coeff[11] =
(2 * D[17] - 2 * D[3] - 2 * D[9] - 2 * D[13] - 2 * D[1] +
4 * D[23] + 4 * D[25] - 2 * D[27] - 2 * D[31] + 2 * D[35] -
2 * D[37] - 2 * D[39] + 4 * D[47] + 4 * D[51] + 4 * D[59] +
4 * D[61] + 4 * D[65] + 4 * D[69] + 2 * D[73] +
2 * D[75]); // s2 * s3^2
f1_coeff[12] =
(6 * D[5] - 6 * D[7] - 6 * D[41] + 6 * D[43] + 6 * D[45] -
6 * D[49] - 6 * D[53] - 6 * D[63] + 6 * D[67] + 6 * D[71] -
6 * D[77] + 6 * D[79]); // s1^2
f1_coeff[13] =
(2 * D[7] - 2 * D[5] + 4 * D[11] + 4 * D[15] + 4 * D[19] -
4 * D[21] - 4 * D[29] - 4 * D[33] - 2 * D[41] + 2 * D[43] -
2 * D[45] - 2 * D[49] + 2 * D[53] + 4 * D[55] - 4 * D[57] +
2 * D[63] + 2 * D[67] - 2 * D[71] + 2 * D[77] -
2 * D[79]); // s3^2
f1_coeff[14] =
(2 * D[7] - 2 * D[5] - 4 * D[11] + 4 * D[15] - 4 * D[19] -
4 * D[21] - 4 * D[29] + 4 * D[33] + 2 * D[41] - 2 * D[43] -
2 * D[45] + 2 * D[49] - 2 * D[53] + 4 * D[55] + 4 * D[57] +
2 * D[63] - 2 * D[67] + 2 * D[71] - 2 * D[77] +
2 * D[79]); // s2^2
f1_coeff[15] =
(2 * D[26] - 2 * D[6] - 2 * D[18] - 2 * D[22] - 2 * D[2] -
2 * D[38] - 2 * D[42] - 2 * D[54] - 2 * D[58] + 2 * D[62] +
2 * D[74] + 2 * D[78]); // s3^3
f1_coeff[16] =
(4 * D[5] + 4 * D[7] + 8 * D[11] + 8 * D[15] + 8 * D[19] +
8 * D[21] + 8 * D[29] + 8 * D[33] - 4 * D[41] - 4 * D[43] +
4 * D[45] - 4 * D[49] - 4 * D[53] + 8 * D[55] + 8 * D[57] +
4 * D[63] - 4 * D[67] - 4 * D[71] - 4 * D[77] -
4 * D[79]); // s1 * s2 * s3
f1_coeff[17] =
(4 * D[4] - 4 * D[0] + 8 * D[10] + 8 * D[12] + 8 * D[28] +
8 * D[30] + 4 * D[36] - 4 * D[40] + 4 * D[80]); // s1 * s2^2
f1_coeff[18] =
(6 * D[2] + 6 * D[6] + 6 * D[18] - 6 * D[22] - 6 * D[26] -
6 * D[38] - 6 * D[42] + 6 * D[54] - 6 * D[58] - 6 * D[62] -
6 * D[74] - 6 * D[78]); // s1^2 * s3
f1_coeff[19] =
(4 * D[0] - 4 * D[4] - 4 * D[8] - 4 * D[36] + 4 * D[40] +
4 * D[44] - 4 * D[72] + 4 * D[76] + 4 * D[80]); // s1^3
f2_coeff[0] =
-2 * D[2] + 2 * D[6] - 2 * D[18] - 2 * D[22] - 2 * D[26] -
2 * D[38] + 2 * D[42] + 2 * D[54] + 2 * D[58] + 2 * D[62] -
2 * D[74] + 2 * D[78]; // constant term
f2_coeff[1] =
(4 * D[4] - 4 * D[0] + 8 * D[10] + 8 * D[12] + 8 * D[28] +
8 * D[30] + 4 * D[36] - 4 * D[40] + 4 * D[80]); // s1^2 * s2
f2_coeff[2] =
(4 * D[7] - 4 * D[5] - 8 * D[11] + 8 * D[15] - 8 * D[19] -
8 * D[21] - 8 * D[29] + 8 * D[33] + 4 * D[41] - 4 * D[43] -
4 * D[45] + 4 * D[49] - 4 * D[53] + 8 * D[55] + 8 * D[57] +
4 * D[63] - 4 * D[67] + 4 * D[71] - 4 * D[77] +
4 * D[79]); // s1 * s2
f2_coeff[3] = (8 * D[10] - 8 * D[20] - 8 * D[30] + 8 * D[50] +
8 * D[60] - 8 * D[70]); // s1 * s3
f2_coeff[4] =
(4 * D[3] - 4 * D[1] - 4 * D[9] + 4 * D[13] - 4 * D[17] -
8 * D[23] - 8 * D[25] + 4 * D[27] - 4 * D[31] + 4 * D[35] +
4 * D[37] - 4 * D[39] - 8 * D[47] + 8 * D[51] + 8 * D[59] +
8 * D[61] - 8 * D[65] + 8 * D[69] - 4 * D[73] +
4 * D[75]); // s2 * s3
f2_coeff[5] =
(6 * D[41] - 6 * D[7] - 6 * D[5] + 6 * D[43] - 6 * D[45] +
6 * D[49] - 6 * D[53] - 6 * D[63] + 6 * D[67] - 6 * D[71] -
6 * D[77] - 6 * D[79]); // s2^2 * s3
f2_coeff[6] =
(4 * D[0] - 4 * D[4] + 4 * D[8] - 4 * D[36] + 4 * D[40] -
4 * D[44] + 4 * D[72] - 4 * D[76] + 4 * D[80]); // s2^3
f2_coeff[7] =
(2 * D[17] - 2 * D[3] - 2 * D[9] - 2 * D[13] - 2 * D[1] +
4 * D[23] + 4 * D[25] - 2 * D[27] - 2 * D[31] + 2 * D[35] -
2 * D[37] - 2 * D[39] + 4 * D[47] + 4 * D[51] + 4 * D[59] +
4 * D[61] + 4 * D[65] + 4 * D[69] + 2 * D[73] +
2 * D[75]); // s1 * s3^2
f2_coeff[8] = (2 * D[1] + 2 * D[3] + 2 * D[9] + 2 * D[13] +
2 * D[17] - 4 * D[23] + 4 * D[25] + 2 * D[27] +
2 * D[31] + 2 * D[35] + 2 * D[37] + 2 * D[39] -
4 * D[47] + 4 * D[51] + 4 * D[59] - 4 * D[61] +
4 * D[65] - 4 * D[69] + 2 * D[73] + 2 * D[75]); // s1
f2_coeff[9] = (2 * D[5] + 2 * D[7] - 4 * D[11] + 4 * D[15] -
4 * D[19] + 4 * D[21] + 4 * D[29] - 4 * D[33] +
2 * D[41] + 2 * D[43] + 2 * D[45] + 2 * D[49] +
2 * D[53] + 4 * D[55] - 4 * D[57] + 2 * D[63] +
2 * D[67] + 2 * D[71] + 2 * D[77] + 2 * D[79]); // s3
f2_coeff[10] =
(8 * D[20] - 4 * D[8] - 4 * D[0] - 8 * D[24] + 4 * D[40] -
8 * D[56] + 8 * D[60] - 4 * D[72] - 4 * D[80]); // s2
f2_coeff[11] =
(4 * D[0] - 4 * D[40] + 4 * D[44] + 8 * D[50] + 8 * D[52] +
8 * D[68] + 8 * D[70] + 4 * D[76] - 4 * D[80]); // s2 * s3^2
f2_coeff[12] =
(2 * D[6] - 2 * D[2] + 4 * D[14] - 4 * D[16] - 2 * D[18] +
2 * D[22] + 2 * D[26] + 4 * D[32] - 4 * D[34] + 2 * D[38] -
2 * D[42] + 4 * D[46] + 4 * D[48] + 2 * D[54] - 2 * D[58] -
2 * D[62] - 4 * D[64] - 4 * D[66] + 2 * D[74] -
2 * D[78]); // s1^2
f2_coeff[13] =
(2 * D[2] - 2 * D[6] + 4 * D[14] + 4 * D[16] + 2 * D[18] +
2 * D[22] - 2 * D[26] - 4 * D[32] - 4 * D[34] + 2 * D[38] -
2 * D[42] + 4 * D[46] - 4 * D[48] - 2 * D[54] - 2 * D[58] +
2 * D[62] + 4 * D[64] - 4 * D[66] - 2 * D[74] +
2 * D[78]); // s3^2
f2_coeff[14] =
(6 * D[2] - 6 * D[6] + 6 * D[18] - 6 * D[22] + 6 * D[26] -
6 * D[38] + 6 * D[42] - 6 * D[54] + 6 * D[58] - 6 * D[62] +
6 * D[74] - 6 * D[78]); // s2^2
f2_coeff[15] =
(2 * D[53] - 2 * D[7] - 2 * D[41] - 2 * D[43] - 2 * D[45] -
2 * D[49] - 2 * D[5] - 2 * D[63] - 2 * D[67] + 2 * D[71] +
2 * D[77] + 2 * D[79]); // s3^3
f2_coeff[16] =
(8 * D[14] - 4 * D[6] - 4 * D[2] + 8 * D[16] - 4 * D[18] +
4 * D[22] - 4 * D[26] + 8 * D[32] + 8 * D[34] + 4 * D[38] +
4 * D[42] + 8 * D[46] + 8 * D[48] - 4 * D[54] + 4 * D[58] -
4 * D[62] + 8 * D[64] + 8 * D[66] - 4 * D[74] -
4 * D[78]); // s1 * s2 * s3
f2_coeff[17] =
(6 * D[13] - 6 * D[3] - 6 * D[9] - 6 * D[1] - 6 * D[17] -
6 * D[27] + 6 * D[31] - 6 * D[35] + 6 * D[37] + 6 * D[39] -
6 * D[73] - 6 * D[75]); // s1 * s2^2
f2_coeff[18] =
(2 * D[5] + 2 * D[7] + 4 * D[11] + 4 * D[15] + 4 * D[19] +
4 * D[21] + 4 * D[29] + 4 * D[33] - 2 * D[41] - 2 * D[43] +
2 * D[45] - 2 * D[49] - 2 * D[53] + 4 * D[55] + 4 * D[57] +
2 * D[63] - 2 * D[67] - 2 * D[71] - 2 * D[77] -
2 * D[79]); // s1^2 * s3
f2_coeff[19] =
(2 * D[1] + 2 * D[3] + 2 * D[9] - 2 * D[13] - 2 * D[17] +
2 * D[27] - 2 * D[31] - 2 * D[35] - 2 * D[37] - 2 * D[39] -
2 * D[73] - 2 * D[75]); // s1^3
f3_coeff[0] =
2 * D[1] - 2 * D[3] + 2 * D[9] + 2 * D[13] + 2 * D[17] -
2 * D[27] - 2 * D[31] - 2 * D[35] + 2 * D[37] - 2 * D[39] +
2 * D[73] - 2 * D[75]; // constant term
f3_coeff[1] =
(2 * D[5] + 2 * D[7] + 4 * D[11] + 4 * D[15] + 4 * D[19] +
4 * D[21] + 4 * D[29] + 4 * D[33] - 2 * D[41] - 2 * D[43] +
2 * D[45] - 2 * D[49] - 2 * D[53] + 4 * D[55] + 4 * D[57] +
2 * D[63] - 2 * D[67] - 2 * D[71] - 2 * D[77] -
2 * D[79]); // s1^2 * s2
f3_coeff[2] = (8 * D[10] - 8 * D[20] - 8 * D[30] + 8 * D[50] +
8 * D[60] - 8 * D[70]); // s1 * s2
f3_coeff[3] =
(4 * D[7] - 4 * D[5] + 8 * D[11] + 8 * D[15] + 8 * D[19] -
8 * D[21] - 8 * D[29] - 8 * D[33] - 4 * D[41] + 4 * D[43] -
4 * D[45] - 4 * D[49] + 4 * D[53] + 8 * D[55] - 8 * D[57] +
4 * D[63] + 4 * D[67] - 4 * D[71] + 4 * D[77] -
4 * D[79]); // s1 * s3
f3_coeff[4] =
(4 * D[2] - 4 * D[6] + 8 * D[14] + 8 * D[16] + 4 * D[18] +
4 * D[22] - 4 * D[26] - 8 * D[32] - 8 * D[34] + 4 * D[38] -
4 * D[42] + 8 * D[46] - 8 * D[48] - 4 * D[54] - 4 * D[58] +
4 * D[62] + 8 * D[64] - 8 * D[66] - 4 * D[74] +
4 * D[78]); // s2 * s3
f3_coeff[5] =
(4 * D[0] - 4 * D[40] + 4 * D[44] + 8 * D[50] + 8 * D[52] +
8 * D[68] + 8 * D[70] + 4 * D[76] - 4 * D[80]); // s2^2 * s3
f3_coeff[6] = (2 * D[41] - 2 * D[7] - 2 * D[5] + 2 * D[43] -
2 * D[45] + 2 * D[49] - 2 * D[53] - 2 * D[63] +
2 * D[67] - 2 * D[71] - 2 * D[77] - 2 * D[79]); // s2^3
f3_coeff[7] =
(6 * D[26] - 6 * D[6] - 6 * D[18] - 6 * D[22] - 6 * D[2] -
6 * D[38] - 6 * D[42] - 6 * D[54] - 6 * D[58] + 6 * D[62] +
6 * D[74] + 6 * D[78]); // s1 * s3^2
f3_coeff[8] = (2 * D[2] + 2 * D[6] + 4 * D[14] - 4 * D[16] +
2 * D[18] + 2 * D[22] + 2 * D[26] - 4 * D[32] +
4 * D[34] + 2 * D[38] + 2 * D[42] + 4 * D[46] -
4 * D[48] + 2 * D[54] + 2 * D[58] + 2 * D[62] -
4 * D[64] + 4 * D[66] + 2 * D[74] + 2 * D[78]); // s1
f3_coeff[9] =
(8 * D[10] - 4 * D[4] - 4 * D[0] - 8 * D[12] - 8 * D[28] +
8 * D[30] - 4 * D[36] - 4 * D[40] + 4 * D[80]); // s3
f3_coeff[10] = (2 * D[5] + 2 * D[7] - 4 * D[11] + 4 * D[15] -
4 * D[19] + 4 * D[21] + 4 * D[29] - 4 * D[33] +
2 * D[41] + 2 * D[43] + 2 * D[45] + 2 * D[49] +
2 * D[53] + 4 * D[55] - 4 * D[57] + 2 * D[63] +
2 * D[67] + 2 * D[71] + 2 * D[77] + 2 * D[79]); // s2
f3_coeff[11] =
(6 * D[53] - 6 * D[7] - 6 * D[41] - 6 * D[43] - 6 * D[45] -
6 * D[49] - 6 * D[5] - 6 * D[63] - 6 * D[67] + 6 * D[71] +
6 * D[77] + 6 * D[79]); // s2 * s3^2
f3_coeff[12] =
(2 * D[1] - 2 * D[3] + 2 * D[9] - 2 * D[13] - 2 * D[17] +
4 * D[23] - 4 * D[25] - 2 * D[27] + 2 * D[31] + 2 * D[35] -
2 * D[37] + 2 * D[39] + 4 * D[47] + 4 * D[51] + 4 * D[59] -
4 * D[61] - 4 * D[65] - 4 * D[69] - 2 * D[73] +
2 * D[75]); // s1^2
f3_coeff[13] =
(6 * D[3] - 6 * D[1] - 6 * D[9] - 6 * D[13] + 6 * D[17] +
6 * D[27] + 6 * D[31] - 6 * D[35] - 6 * D[37] + 6 * D[39] +
6 * D[73] - 6 * D[75]); // s3^2
f3_coeff[14] =
(2 * D[3] - 2 * D[1] - 2 * D[9] + 2 * D[13] - 2 * D[17] -
4 * D[23] - 4 * D[25] + 2 * D[27] - 2 * D[31] + 2 * D[35] +
2 * D[37] - 2 * D[39] - 4 * D[47] + 4 * D[51] + 4 * D[59] +
4 * D[61] - 4 * D[65] + 4 * D[69] - 2 * D[73] +
2 * D[75]); // s2^2
f3_coeff[15] =
(4 * D[0] + 4 * D[4] - 4 * D[8] + 4 * D[36] + 4 * D[40] -
4 * D[44] - 4 * D[72] - 4 * D[76] + 4 * D[80]); // s3^3
f3_coeff[16] =
(4 * D[17] - 4 * D[3] - 4 * D[9] - 4 * D[13] - 4 * D[1] +
8 * D[23] + 8 * D[25] - 4 * D[27] - 4 * D[31] + 4 * D[35] -
4 * D[37] - 4 * D[39] + 8 * D[47] + 8 * D[51] + 8 * D[59] +
8 * D[61] + 8 * D[65] + 8 * D[69] + 4 * D[73] +
4 * D[75]); // s1 * s2 * s3
f3_coeff[17] =
(4 * D[14] - 2 * D[6] - 2 * D[2] + 4 * D[16] - 2 * D[18] +
2 * D[22] - 2 * D[26] + 4 * D[32] + 4 * D[34] + 2 * D[38] +
2 * D[42] + 4 * D[46] + 4 * D[48] - 2 * D[54] + 2 * D[58] -
2 * D[62] + 4 * D[64] + 4 * D[66] - 2 * D[74] -
2 * D[78]); // s1 * s2^2
f3_coeff[18] =
(4 * D[8] - 4 * D[0] + 8 * D[20] + 8 * D[24] + 4 * D[40] +
8 * D[56] + 8 * D[60] + 4 * D[72] - 4 * D[80]); // s1^2 * s3
f3_coeff[19] =
(2 * D[2] + 2 * D[6] + 2 * D[18] - 2 * D[22] - 2 * D[26] -
2 * D[38] - 2 * D[42] + 2 * D[54] - 2 * D[58] - 2 * D[62] -
2 * D[74] - 2 * D[78]); // s1^3
}
};
Ptr<DLSPnP> DLSPnP::create(const Mat &points_, const Mat &calib_norm_pts, const Mat &K) {
return makePtr<DLSPnPImpl>(points_, calib_norm_pts, K);
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#if defined(HAVE_EIGEN)
#include <Eigen/Eigen>
#elif defined(HAVE_LAPACK)
#include "opencv_lapack.h"
#endif
namespace cv { namespace usac {
// Essential matrix solver:
/*
* H. Stewenius, C. Engels, and D. Nister. Recent developments on direct relative orientation.
* ISPRS J. of Photogrammetry and Remote Sensing, 60:284,294, 2006
* http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.61.9329&rep=rep1&type=pdf
*/
class EssentialMinimalSolverStewenius5ptsImpl : public EssentialMinimalSolverStewenius5pts {
private:
// Points must be calibrated K^-1 x
const Mat * points_mat;
#if defined(HAVE_EIGEN) || defined(HAVE_LAPACK)
const float * const pts;
#endif
public:
explicit EssentialMinimalSolverStewenius5ptsImpl (const Mat &points_) :
points_mat(&points_)
#if defined(HAVE_EIGEN) || defined(HAVE_LAPACK)
, pts((float*)points_.data)
#endif
{}
#if defined(HAVE_LAPACK) || defined(HAVE_EIGEN)
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
// (1) Extract 4 null vectors from linear equations of epipolar constraint
std::vector<double> coefficients(45); // 5 pts=rows, 9 columns
auto *coefficients_ = &coefficients[0];
for (int i = 0; i < 5; i++) {
const int smpl = 4 * sample[i];
const auto x1 = pts[smpl], y1 = pts[smpl+1], x2 = pts[smpl+2], y2 = pts[smpl+3];
(*coefficients_++) = x2 * x1;
(*coefficients_++) = x2 * y1;
(*coefficients_++) = x2;
(*coefficients_++) = y2 * x1;
(*coefficients_++) = y2 * y1;
(*coefficients_++) = y2;
(*coefficients_++) = x1;
(*coefficients_++) = y1;
(*coefficients_++) = 1;
}
const int num_cols = 9, num_e_mat = 4;
double ee[36]; // 9*4
// eliminate linear equations
Math::eliminateUpperTriangular(coefficients, 5, num_cols);
for (int i = 0; i < num_e_mat; i++)
for (int j = 5; j < num_cols; j++)
ee[num_cols * i + j] = (i + 5 == j) ? 1 : 0;
// use back-substitution
for (int e = 0; e < num_e_mat; e++) {
const int curr_e = num_cols * e;
// start from the last row
for (int i = 4; i >= 0; i--) {
const int row_i = i * num_cols;
double acc = 0;
for (int j = i + 1; j < num_cols; j++)
acc -= coefficients[row_i + j] * ee[curr_e + j];
ee[curr_e + i] = acc / coefficients[row_i + i];
// due to numerical errors return 0 solutions
if (std::isnan(ee[curr_e + i]))
return 0;
}
}
const Matx<double, 4, 9> null_space(ee);
const Matx<double, 4, 1> null_space_mat[3][3] = {
{null_space.col(0), null_space.col(3), null_space.col(6)},
{null_space.col(1), null_space.col(4), null_space.col(7)},
{null_space.col(2), null_space.col(5), null_space.col(8)}};
// (2) Use the rank constraint and the trace constraint to build ten third-order polynomial
// equations in the three unknowns. The monomials are ordered in GrLex order and
// represented in a 10×20 matrix, where each row corresponds to an equation and each column
// corresponds to a monomial
Matx<double, 1, 10> eet[3][3];
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
// compute EE Transpose
// Shorthand for multiplying the Essential matrix with its transpose.
eet[i][j] = 2 * (multPolysDegOne(null_space_mat[i][0].val, null_space_mat[j][0].val) +
multPolysDegOne(null_space_mat[i][1].val, null_space_mat[j][1].val) +
multPolysDegOne(null_space_mat[i][2].val, null_space_mat[j][2].val));
const Matx<double, 1, 10> trace = eet[0][0] + eet[1][1] + eet[2][2];
Mat_<double> constraint_mat(10, 20);
// Trace constraint
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
Mat(multPolysDegOneAndTwo(eet[i][0].val, null_space_mat[0][j].val) +
multPolysDegOneAndTwo(eet[i][1].val, null_space_mat[1][j].val) +
multPolysDegOneAndTwo(eet[i][2].val, null_space_mat[2][j].val) -
0.5 * multPolysDegOneAndTwo(trace.val, null_space_mat[i][j].val))
.copyTo(constraint_mat.row(3 * i + j));
// Rank = zero determinant constraint
Mat(multPolysDegOneAndTwo(
(multPolysDegOne(null_space_mat[0][1].val, null_space_mat[1][2].val) -
multPolysDegOne(null_space_mat[0][2].val, null_space_mat[1][1].val)).val,
null_space_mat[2][0].val) +
multPolysDegOneAndTwo(
(multPolysDegOne(null_space_mat[0][2].val, null_space_mat[1][0].val) -
multPolysDegOne(null_space_mat[0][0].val, null_space_mat[1][2].val)).val,
null_space_mat[2][1].val) +
multPolysDegOneAndTwo(
(multPolysDegOne(null_space_mat[0][0].val, null_space_mat[1][1].val) -
multPolysDegOne(null_space_mat[0][1].val, null_space_mat[1][0].val)).val,
null_space_mat[2][2].val)).copyTo(constraint_mat.row(9));
#ifdef HAVE_EIGEN
const Eigen::Matrix<double, 10, 20, Eigen::RowMajor> constraint_mat_eig((double *) constraint_mat.data);
// (3) Compute the Gröbner basis. This turns out to be as simple as performing a
// Gauss-Jordan elimination on the 10×20 matrix
const Eigen::Matrix<double, 10, 10> eliminated_mat_eig = constraint_mat_eig.block<10, 10>(0, 0)
.fullPivLu().solve(constraint_mat_eig.block<10, 10>(0, 10));
// (4) Compute the 10×10 action matrix for multiplication by one of the un-knowns.
// This is a simple matter of extracting the correct elements fromthe eliminated
// 10×20 matrix and organising them to form the action matrix.
Eigen::Matrix<double, 10, 10> action_mat_eig = Eigen::Matrix<double, 10, 10>::Zero();
action_mat_eig.block<3, 10>(0, 0) = eliminated_mat_eig.block<3, 10>(0, 0);
action_mat_eig.block<2, 10>(3, 0) = eliminated_mat_eig.block<2, 10>(4, 0);
action_mat_eig.row(5) = eliminated_mat_eig.row(7);
action_mat_eig(6, 0) = -1.0;
action_mat_eig(7, 1) = -1.0;
action_mat_eig(8, 3) = -1.0;
action_mat_eig(9, 6) = -1.0;
// (5) Compute the left eigenvectors of the action matrix
Eigen::EigenSolver<Eigen::Matrix<double, 10, 10>> eigensolver(action_mat_eig);
const Eigen::VectorXcd &eigenvalues = eigensolver.eigenvalues();
const auto * const eig_vecs_ = (double *) eigensolver.eigenvectors().real().data();
#else
Matx<double, 10, 10> A = constraint_mat.colRange(0, 10),
B = constraint_mat.colRange(10, 20), eliminated_mat;
if (!solve(A, B, eliminated_mat, DECOMP_LU)) return 0;
Mat eliminated_mat_dyn = Mat(eliminated_mat);
Mat action_mat = Mat_<double>::zeros(10, 10);
eliminated_mat_dyn.rowRange(0,3).copyTo(action_mat.rowRange(0,3));
eliminated_mat_dyn.rowRange(4,6).copyTo(action_mat.rowRange(3,5));
eliminated_mat_dyn.row(7).copyTo(action_mat.row(5));
auto * action_mat_data = (double *) action_mat.data;
action_mat_data[60] = -1.0; // 6 row, 0 col
action_mat_data[71] = -1.0; // 7 row, 1 col
action_mat_data[83] = -1.0; // 8 row, 3 col
action_mat_data[96] = -1.0; // 9 row, 6 col
int mat_order = 10, info, lda = 10, ldvl = 10, ldvr = 1, lwork = 100;
double wr[10], wi[10] = {0}, eig_vecs[100], work[100]; // 10 = mat_order, 100 = lwork
char jobvl = 'V', jobvr = 'N'; // only left eigen vectors are computed
dgeev_(&jobvl, &jobvr, &mat_order, action_mat_data, &lda, wr, wi, eig_vecs, &ldvl,
nullptr, &ldvr, work, &lwork, &info);
if (info != 0) return 0;
#endif
models = std::vector<Mat>(); models.reserve(10);
// Read off the values for the three unknowns at all the solution points and
// back-substitute to obtain the solutions for the essential matrix.
for (int i = 0; i < 10; i++)
// process only real solutions
#ifdef HAVE_EIGEN
if (eigenvalues(i).imag() == 0) {
Mat_<double> model(3, 3);
auto * model_data = (double *) model.data;
const int eig_i = 20 * i + 12; // eigen stores imaginary values too
for (int j = 0; j < 9; j++)
model_data[j] = ee[j ] * eig_vecs_[eig_i ] + ee[j+9 ] * eig_vecs_[eig_i+2] +
ee[j+18] * eig_vecs_[eig_i+4] + ee[j+27] * eig_vecs_[eig_i+6];
#else
if (wi[i] == 0) {
Mat_<double> model (3,3);
auto * model_data = (double *) model.data;
const int eig_i = 10 * i + 6;
for (int j = 0; j < 9; j++)
model_data[j] = ee[j ]*eig_vecs[eig_i ] + ee[j+9 ]*eig_vecs[eig_i+1] +
ee[j+18]*eig_vecs[eig_i+2] + ee[j+27]*eig_vecs[eig_i+3];
#endif
models.emplace_back(model);
}
return static_cast<int>(models.size());
#else
int estimate (const std::vector<int> &/*sample*/, std::vector<Mat> &/*models*/) const override {
CV_Error(cv::Error::StsNotImplemented, "To use essential matrix solver LAPACK or Eigen has to be installed!");
#endif
}
// number of possible solutions is 0,2,4,6,8,10
int getMaxNumberOfSolutions () const override { return 10; }
int getSampleSize() const override { return 5; }
Ptr<MinimalSolver> clone () const override {
return makePtr<EssentialMinimalSolverStewenius5ptsImpl>(*points_mat);
}
private:
/*
* Multiply two polynomials of degree one with unknowns x y z
* @p = (p1 x + p2 y + p3 z + p4) [p1 p2 p3 p4]
* @q = (q1 x + q2 y + q3 z + q4) [q1 q2 q3 a4]
* @result is a new polynomial in x^2 xy y^2 xz yz z^2 x y z 1 of size 10
*/
static inline Matx<double,1,10> multPolysDegOne(const double * const p,
const double * const q) {
return
{p[0]*q[0], p[0]*q[1]+p[1]*q[0], p[1]*q[1], p[0]*q[2]+p[2]*q[0], p[1]*q[2]+p[2]*q[1],
p[2]*q[2], p[0]*q[3]+p[3]*q[0], p[1]*q[3]+p[3]*q[1], p[2]*q[3]+p[3]*q[2], p[3]*q[3]};
}
/*
* Multiply two polynomials with unknowns x y z
* @p is of size 10 and @q is of size 4
* @p = (p1 x^2 + p2 xy + p3 y^2 + p4 xz + p5 yz + p6 z^2 + p7 x + p8 y + p9 z + p10)
* @q = (q1 x + q2 y + q3 z + a4) [q1 q2 q3 q4]
* @result is a new polynomial of size 20
* x^3 x^2y xy^2 y^3 x^2z xyz y^2z xz^2 yz^2 z^3 x^2 xy y^2 xz yz z^2 x y z 1
*/
static inline Matx<double, 1, 20> multPolysDegOneAndTwo(const double * const p,
const double * const q) {
return Matx<double, 1, 20>
({p[0]*q[0], p[0]*q[1]+p[1]*q[0], p[1]*q[1]+p[2]*q[0], p[2]*q[1], p[0]*q[2]+p[3]*q[0],
p[1]*q[2]+p[3]*q[1]+p[4]*q[0], p[2]*q[2]+p[4]*q[1], p[3]*q[2]+p[5]*q[0],
p[4]*q[2]+p[5]*q[1], p[5]*q[2], p[0]*q[3]+p[6]*q[0], p[1]*q[3]+p[6]*q[1]+p[7]*q[0],
p[2]*q[3]+p[7]*q[1], p[3]*q[3]+p[6]*q[2]+p[8]*q[0], p[4]*q[3]+p[7]*q[2]+p[8]*q[1],
p[5]*q[3]+p[8]*q[2], p[6]*q[3]+p[9]*q[0], p[7]*q[3]+p[9]*q[1], p[8]*q[3]+p[9]*q[2],
p[9]*q[3]});
}
};
Ptr<EssentialMinimalSolverStewenius5pts> EssentialMinimalSolverStewenius5pts::create
(const Mat &points_) {
return makePtr<EssentialMinimalSolverStewenius5ptsImpl>(points_);
}
class EssentialNonMinimalSolverImpl : public EssentialNonMinimalSolver {
private:
const Mat * points_mat;
const Ptr<FundamentalNonMinimalSolver> non_min_fundamental;
public:
/*
* Input calibrated points K^-1 x.
* Linear 8 points algorithm is used for estimation.
*/
explicit EssentialNonMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), non_min_fundamental(FundamentalNonMinimalSolver::create(points_)) {}
int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat>
&models, const std::vector<double> &weights) const override {
return non_min_fundamental->estimate(sample, sample_size, models, weights);
}
int getMinimumRequiredSampleSize() const override {
return non_min_fundamental->getMinimumRequiredSampleSize();
}
int getMaxNumberOfSolutions () const override {
return non_min_fundamental->getMaxNumberOfSolutions();
}
Ptr<NonMinimalSolver> clone () const override {
return makePtr<EssentialNonMinimalSolverImpl>(*points_mat);
}
};
Ptr<EssentialNonMinimalSolver> EssentialNonMinimalSolver::create (const Mat &points_) {
return makePtr<EssentialNonMinimalSolverImpl>(points_);
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
namespace cv { namespace usac {
class HomographyEstimatorImpl : public HomographyEstimator {
private:
const Ptr<MinimalSolver> min_solver;
const Ptr<NonMinimalSolver> non_min_solver;
const Ptr<Degeneracy> degeneracy;
public:
HomographyEstimatorImpl (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) :
min_solver (min_solver_), non_min_solver (non_min_solver_), degeneracy (degeneracy_) {}
inline int estimateModels (const std::vector<int> &sample, std::vector<Mat> &models) const override {
if (! degeneracy->isSampleGood(sample)) return 0;
return min_solver->estimate (sample, models);
}
int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
return non_min_solver->estimate (sample, sample_size, models, weights);
};
int getMaxNumSolutions () const override {
return min_solver->getMaxNumberOfSolutions();
}
int getMaxNumSolutionsNonMinimal () const override {
return non_min_solver->getMaxNumberOfSolutions();
}
int getMinimalSampleSize () const override {
return min_solver->getSampleSize();
}
int getNonMinimalSampleSize () const override {
return non_min_solver->getMinimumRequiredSampleSize();
}
Ptr<Estimator> clone() const override {
return makePtr<HomographyEstimatorImpl>(min_solver->clone(), non_min_solver->clone(),
degeneracy->clone(0 /*we don't need state here*/));
}
};
Ptr<HomographyEstimator> HomographyEstimator::create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) {
return makePtr<HomographyEstimatorImpl>(min_solver_, non_min_solver_, degeneracy_);
}
/////////////////////////////////////////////////////////////////////////
class FundamentalEstimatorImpl : public FundamentalEstimator {
private:
const Ptr<MinimalSolver> min_solver;
const Ptr<NonMinimalSolver> non_min_solver;
const Ptr<Degeneracy> degeneracy;
public:
FundamentalEstimatorImpl (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) :
min_solver (min_solver_), non_min_solver (non_min_solver_), degeneracy (degeneracy_) {}
inline int
estimateModels(const std::vector<int> &sample, std::vector<Mat> &models) const override {
std::vector<Mat> F;
const int models_count = min_solver->estimate(sample, F);
int valid_models_count = 0;
for (int i = 0; i < models_count; i++)
if (degeneracy->isModelValid(F[i], sample))
models[valid_models_count++] = F[i];
return valid_models_count;
}
int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
std::vector<Mat> Fs;
const int num_est_models = non_min_solver->estimate(sample, sample_size, Fs, weights);
int valid_models_count = 0;
for (int i = 0; i < num_est_models; i++)
if (degeneracy->isModelValid (Fs[i], sample, sample_size))
models[valid_models_count++] = Fs[i];
return valid_models_count;
}
int getMaxNumSolutions () const override {
return min_solver->getMaxNumberOfSolutions();
}
int getMinimalSampleSize () const override {
return min_solver->getSampleSize();
}
int getNonMinimalSampleSize () const override {
return non_min_solver->getMinimumRequiredSampleSize();
}
int getMaxNumSolutionsNonMinimal () const override {
return non_min_solver->getMaxNumberOfSolutions();
}
Ptr<Estimator> clone() const override {
return makePtr<FundamentalEstimatorImpl>(min_solver->clone(), non_min_solver->clone(),
degeneracy->clone(0));
}
};
Ptr<FundamentalEstimator> FundamentalEstimator::create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) {
return makePtr<FundamentalEstimatorImpl>(min_solver_, non_min_solver_, degeneracy_);
}
/////////////////////////////////////////////////////////////////////////
class EssentialEstimatorImpl : public EssentialEstimator {
private:
const Ptr<MinimalSolver> min_solver;
const Ptr<NonMinimalSolver> non_min_solver;
const Ptr<Degeneracy> degeneracy;
public:
explicit EssentialEstimatorImpl (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) :
min_solver (min_solver_), non_min_solver (non_min_solver_), degeneracy (degeneracy_) {}
inline int
estimateModels(const std::vector<int> &sample, std::vector<Mat> &models) const override {
std::vector<Mat> E;
const int models_count = min_solver->estimate(sample, E);
int valid_models_count = 0;
for (int i = 0; i < models_count; i++)
if (degeneracy->isModelValid (E[i], sample))
models[valid_models_count++] = E[i];
return valid_models_count;
}
int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
std::vector<Mat> Es;
const int num_est_models = non_min_solver->estimate(sample, sample_size, Es, weights);
int valid_models_count = 0;
for (int i = 0; i < num_est_models; i++)
if (degeneracy->isModelValid (Es[i], sample, sample_size))
models[valid_models_count++] = Es[i];
return valid_models_count;
};
int getMaxNumSolutions () const override {
return min_solver->getMaxNumberOfSolutions();
}
int getMinimalSampleSize () const override {
return min_solver->getSampleSize();
}
int getNonMinimalSampleSize () const override {
return non_min_solver->getMinimumRequiredSampleSize();
}
int getMaxNumSolutionsNonMinimal () const override {
return non_min_solver->getMaxNumberOfSolutions();
}
Ptr<Estimator> clone() const override {
return makePtr<EssentialEstimatorImpl>(min_solver->clone(), non_min_solver->clone(),
degeneracy->clone(0));
}
};
Ptr<EssentialEstimator> EssentialEstimator::create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_, const Ptr<Degeneracy> &degeneracy_) {
return makePtr<EssentialEstimatorImpl>(min_solver_, non_min_solver_, degeneracy_);
}
/////////////////////////////////////////////////////////////////////////
class AffineEstimatorImpl : public AffineEstimator {
private:
const Ptr<MinimalSolver> min_solver;
const Ptr<NonMinimalSolver> non_min_solver;
public:
explicit AffineEstimatorImpl (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_) :
min_solver (min_solver_), non_min_solver (non_min_solver_) {}
int estimateModels(const std::vector<int> &sample, std::vector<Mat> &models) const override {
return min_solver->estimate(sample, models);
}
int estimateModelNonMinimalSample (const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
return non_min_solver->estimate(sample, sample_size, models, weights);
}
int getMinimalSampleSize() const override {
return min_solver->getSampleSize(); // 3 points required
}
int getNonMinimalSampleSize() const override {
return non_min_solver->getMinimumRequiredSampleSize();
}
int getMaxNumSolutions () const override {
return min_solver->getMaxNumberOfSolutions();
}
int getMaxNumSolutionsNonMinimal () const override {
return non_min_solver->getMaxNumberOfSolutions();
}
Ptr<Estimator> clone() const override {
return makePtr<AffineEstimatorImpl>(min_solver->clone(), non_min_solver->clone());
}
};
Ptr<AffineEstimator> AffineEstimator::create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_) {
return makePtr<AffineEstimatorImpl>(min_solver_, non_min_solver_);
}
/////////////////////////////////////////////////////////////////////////
class PnPEstimatorImpl : public PnPEstimator {
private:
const Ptr<MinimalSolver> min_solver;
const Ptr<NonMinimalSolver> non_min_solver;
public:
explicit PnPEstimatorImpl (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_) :
min_solver(min_solver_), non_min_solver(non_min_solver_) {}
int estimateModels (const std::vector<int> &sample, std::vector<Mat> &models) const override {
return min_solver->estimate(sample, models);
}
int estimateModelNonMinimalSample (const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
return non_min_solver->estimate(sample, sample_size, models, weights);
}
int getMinimalSampleSize() const override {
return min_solver->getSampleSize();
}
int getNonMinimalSampleSize() const override {
return non_min_solver->getMinimumRequiredSampleSize();
}
int getMaxNumSolutions () const override {
return min_solver->getMaxNumberOfSolutions();
}
int getMaxNumSolutionsNonMinimal () const override {
return non_min_solver->getMaxNumberOfSolutions();
}
Ptr<Estimator> clone() const override {
return makePtr<PnPEstimatorImpl>(min_solver->clone(), non_min_solver->clone());
}
};
Ptr<PnPEstimator> PnPEstimator::create (const Ptr<MinimalSolver> &min_solver_,
const Ptr<NonMinimalSolver> &non_min_solver_) {
return makePtr<PnPEstimatorImpl>(min_solver_, non_min_solver_);
}
///////////////////////////////////////////// ERROR /////////////////////////////////////////
// Symmetric Reprojection Error
class ReprojectedErrorSymmetricImpl : public ReprojectionErrorSymmetric {
private:
const Mat * points_mat;
const float * const points;
float m11, m12, m13, m21, m22, m23, m31, m32, m33;
float minv11, minv12, minv13, minv21, minv22, minv23, minv31, minv32, minv33;
std::vector<float> errors;
public:
explicit ReprojectedErrorSymmetricImpl (const Mat &points_) :
points_mat(&points_), points ((float *) points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const m = (double *) model.data;
m11=static_cast<float>(m[0]); m12=static_cast<float>(m[1]); m13=static_cast<float>(m[2]);
m21=static_cast<float>(m[3]); m22=static_cast<float>(m[4]); m23=static_cast<float>(m[5]);
m31=static_cast<float>(m[6]); m32=static_cast<float>(m[7]); m33=static_cast<float>(m[8]);
const Mat model_inv = model.inv();
const auto * const minv = (double *) model_inv.data;
minv11=(float)minv[0]; minv12=(float)minv[1]; minv13=(float)minv[2];
minv21=(float)minv[3]; minv22=(float)minv[4]; minv23=(float)minv[5];
minv31=(float)minv[6]; minv32=(float)minv[7]; minv33=(float)minv[8];
}
inline float getError (int point_idx) const override {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float est_z2 = 1 / (m31 * x1 + m32 * y1 + m33),
dx2 = x2 - (m11 * x1 + m12 * y1 + m13) * est_z2,
dy2 = y2 - (m21 * x1 + m22 * y1 + m23) * est_z2;
const float est_z1 = 1 / (minv31 * x2 + minv32 * y2 + minv33),
dx1 = x1 - (minv11 * x2 + minv12 * y2 + minv13) * est_z1,
dy1 = y1 - (minv21 * x2 + minv22 * y2 + minv23) * est_z1;
return (dx2 * dx2 + dy2 * dy2 + dx1 * dx1 + dy1 * dy1) * .5f;
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float est_z2 = 1 / (m31 * x1 + m32 * y1 + m33),
dx2 = x2 - (m11 * x1 + m12 * y1 + m13) * est_z2,
dy2 = y2 - (m21 * x1 + m22 * y1 + m23) * est_z2;
const float est_z1 = 1 / (minv31 * x2 + minv32 * y2 + minv33),
dx1 = x1 - (minv11 * x2 + minv12 * y2 + minv13) * est_z1,
dy1 = y1 - (minv21 * x2 + minv22 * y2 + minv23) * est_z1;
errors[point_idx] = (dx2 * dx2 + dy2 * dy2 + dx1 * dx1 + dy1 * dy1) * .5f;
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<ReprojectedErrorSymmetricImpl>(*points_mat);
}
};
Ptr<ReprojectionErrorSymmetric>
ReprojectionErrorSymmetric::create(const Mat &points) {
return makePtr<ReprojectedErrorSymmetricImpl>(points);
}
// Forward Reprojection Error
class ReprojectedErrorForwardImpl : public ReprojectionErrorForward {
private:
const Mat * points_mat;
const float * const points;
float m11, m12, m13, m21, m22, m23, m31, m32, m33;
std::vector<float> errors;
public:
explicit ReprojectedErrorForwardImpl (const Mat &points_)
: points_mat(&points_), points ((float *)points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const m = (double *) model.data;
m11=static_cast<float>(m[0]); m12=static_cast<float>(m[1]); m13=static_cast<float>(m[2]);
m21=static_cast<float>(m[3]); m22=static_cast<float>(m[4]); m23=static_cast<float>(m[5]);
m31=static_cast<float>(m[6]); m32=static_cast<float>(m[7]); m33=static_cast<float>(m[8]);
}
inline float getError (int point_idx) const override {
const int smpl = 4*point_idx;
const float x1 = points[smpl], y1 = points[smpl+1], x2 = points[smpl+2], y2 = points[smpl+3];
const float est_z2 = 1 / (m31 * x1 + m32 * y1 + m33),
dx2 = x2 - (m11 * x1 + m12 * y1 + m13) * est_z2,
dy2 = y2 - (m21 * x1 + m22 * y1 + m23) * est_z2;
return dx2 * dx2 + dy2 * dy2;
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float est_z2 = 1 / (m31 * x1 + m32 * y1 + m33),
dx2 = x2 - (m11 * x1 + m12 * y1 + m13) * est_z2,
dy2 = y2 - (m21 * x1 + m22 * y1 + m23) * est_z2;
errors[point_idx] = dx2 * dx2 + dy2 * dy2;
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<ReprojectedErrorForwardImpl>(*points_mat);
}
};
Ptr<ReprojectionErrorForward>
ReprojectionErrorForward::create(const Mat &points) {
return makePtr<ReprojectedErrorForwardImpl>(points);
}
class SampsonErrorImpl : public SampsonError {
private:
const Mat * points_mat;
const float * const points;
float m11, m12, m13, m21, m22, m23, m31, m32, m33;
std::vector<float> errors;
public:
explicit SampsonErrorImpl (const Mat &points_) :
points_mat(&points_), points ((float *) points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const m = (double *) model.data;
m11=static_cast<float>(m[0]); m12=static_cast<float>(m[1]); m13=static_cast<float>(m[2]);
m21=static_cast<float>(m[3]); m22=static_cast<float>(m[4]); m23=static_cast<float>(m[5]);
m31=static_cast<float>(m[6]); m32=static_cast<float>(m[7]); m33=static_cast<float>(m[8]);
}
/*
* (pt2^t * F * pt1)^2)
* Sampson error = ------------------------------------------------------------------------
* (((F⋅pt1)(0))^2 + ((F⋅pt1)(1))^2 + ((F^t⋅pt2)(0))^2 + ((F^t⋅pt2)(1))^2)
*
* [ x2 y2 1 ] * [ F(1,1) F(1,2) F(1,3) ] [ x1 ]
* [ F(2,1) F(2,2) F(2,3) ] * [ y1 ]
* [ F(3,1) F(3,2) F(3,3) ] [ 1 ]
*
*/
inline float getError (int point_idx) const override {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float F_pt1_x = m11 * x1 + m12 * y1 + m13,
F_pt1_y = m21 * x1 + m22 * y1 + m23;
const float pt2_F_x = x2 * m11 + y2 * m21 + m31,
pt2_F_y = x2 * m12 + y2 * m22 + m32;
const float pt2_F_pt1 = x2 * F_pt1_x + y2 * F_pt1_y + m31 * x1 + m32 * y1 + m33;
return pt2_F_pt1 * pt2_F_pt1 / (F_pt1_x * F_pt1_x + F_pt1_y * F_pt1_y +
pt2_F_x * pt2_F_x + pt2_F_y * pt2_F_y);
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float F_pt1_x = m11 * x1 + m12 * y1 + m13,
F_pt1_y = m21 * x1 + m22 * y1 + m23;
const float pt2_F_x = x2 * m11 + y2 * m21 + m31,
pt2_F_y = x2 * m12 + y2 * m22 + m32;
const float pt2_F_pt1 = x2 * F_pt1_x + y2 * F_pt1_y + m31 * x1 + m32 * y1 + m33;
errors[point_idx] = pt2_F_pt1 * pt2_F_pt1 / (F_pt1_x * F_pt1_x + F_pt1_y * F_pt1_y +
pt2_F_x * pt2_F_x + pt2_F_y * pt2_F_y);
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<SampsonErrorImpl>(*points_mat);
}
};
Ptr<SampsonError>
SampsonError::create(const Mat &points) {
return makePtr<SampsonErrorImpl>(points);
}
class SymmetricGeometricDistanceImpl : public SymmetricGeometricDistance {
private:
const Mat * points_mat;
const float * const points;
float m11, m12, m13, m21, m22, m23, m31, m32, m33;
std::vector<float> errors;
public:
explicit SymmetricGeometricDistanceImpl (const Mat &points_) :
points_mat(&points_), points ((float *) points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const m = (double *) model.data;
m11=static_cast<float>(m[0]); m12=static_cast<float>(m[1]); m13=static_cast<float>(m[2]);
m21=static_cast<float>(m[3]); m22=static_cast<float>(m[4]); m23=static_cast<float>(m[5]);
m31=static_cast<float>(m[6]); m32=static_cast<float>(m[7]); m33=static_cast<float>(m[8]);
}
inline float getError (int point_idx) const override {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
// pt2^T * E, line 1 = [l1 l2]
const float l1 = x2 * m11 + y2 * m21 + m31,
l2 = x2 * m12 + y2 * m22 + m32;
// E * pt1, line 2 = [t1 t2]
const float t1 = m11 * x1 + m12 * y1 + m13,
t2 = m21 * x1 + m22 * y1 + m23;
float p2Ep1 = l1 * x1 + l2 * y1 + x2 * m13 + y2 * m23 + m33;
p2Ep1 *= p2Ep1;
return p2Ep1 / (l1 * l1 + l2 * l2) // distance from pt1 to line 1
+
p2Ep1 / (t1 * t1 + t2 * t2); // distance from pt2 to line 2
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float l1 = x2 * m11 + y2 * m21 + m31, t1 = m11 * x1 + m12 * y1 + m13,
l2 = x2 * m12 + y2 * m22 + m32, t2 = m21 * x1 + m22 * y1 + m23;
float p2Ep1 = l1 * x1 + l2 * y1 + x2 * m13 + y2 * m23 + m33;
p2Ep1 *= p2Ep1;
errors[point_idx] = p2Ep1 / (l1 * l1 + l2 * l2) + p2Ep1 / (t1 * t1 + t2 * t2);
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<SymmetricGeometricDistanceImpl>(*points_mat);
}
};
Ptr<SymmetricGeometricDistance>
SymmetricGeometricDistance::create(const Mat &points) {
return makePtr<SymmetricGeometricDistanceImpl>(points);
}
class ReprojectionErrorPmatrixImpl : public ReprojectionErrorPmatrix {
private:
const Mat * points_mat;
const float * const points;
float p11, p12, p13, p14, p21, p22, p23, p24, p31, p32, p33, p34;
std::vector<float> errors;
public:
explicit ReprojectionErrorPmatrixImpl (const Mat &points_) :
points_mat(&points_), points ((float *) points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const p = (double *) model.data;
p11 = (float)p[0]; p12 = (float)p[1]; p13 = (float)p[2]; p14 = (float)p[3];
p21 = (float)p[4]; p22 = (float)p[5]; p23 = (float)p[6]; p24 = (float)p[7];
p31 = (float)p[8]; p32 = (float)p[9]; p33 = (float)p[10]; p34 = (float)p[11];
}
inline float getError (int point_idx) const override {
const int smpl = 5*point_idx;
const float u = points[smpl ], v = points[smpl+1],
x = points[smpl+2], y = points[smpl+3], z = points[smpl+4];
const float depth = 1 / (p31 * x + p32 * y + p33 * z + p34);
const float du = u - (p11 * x + p12 * y + p13 * z + p14) * depth;
const float dv = v - (p21 * x + p22 * y + p23 * z + p24) * depth;
return du * du + dv * dv;
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 5*point_idx;
const float u = points[smpl ], v = points[smpl+1],
x = points[smpl+2], y = points[smpl+3], z = points[smpl+4];
const float depth = 1 / (p31 * x + p32 * y + p33 * z + p34);
const float du = u - (p11 * x + p12 * y + p13 * z + p14) * depth;
const float dv = v - (p21 * x + p22 * y + p23 * z + p24) * depth;
errors[point_idx] = du * du + dv * dv;
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<ReprojectionErrorPmatrixImpl>(*points_mat);
}
};
Ptr<ReprojectionErrorPmatrix> ReprojectionErrorPmatrix::create(const Mat &points) {
return makePtr<ReprojectionErrorPmatrixImpl>(points);
}
///////////////////////////////////////////////////////////////////////////////////////////////////
// Computes forward reprojection error for affine transformation.
class ReprojectedDistanceAffineImpl : public ReprojectionErrorAffine {
private:
/*
* m11 m12 m13
* m21 m22 m23
* 0 0 1
*/
const Mat * points_mat;
const float * const points;
float m11, m12, m13, m21, m22, m23;
std::vector<float> errors;
public:
explicit ReprojectedDistanceAffineImpl (const Mat &points_) :
points_mat(&points_), points ((float*)points_.data), errors(points_.rows) {}
inline void setModelParameters (const Mat &model) override {
const auto * const m = (double *) model.data;
m11 = (float)m[0]; m12 = (float)m[1]; m13 = (float)m[2];
m21 = (float)m[3]; m22 = (float)m[4]; m23 = (float)m[5];
}
inline float getError (int point_idx) const override {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float dx2 = x2 - (m11 * x1 + m12 * y1 + m13), dy2 = y2 - (m21 * x1 + m22 * y1 + m23);
return dx2 * dx2 + dy2 * dy2;
}
const std::vector<float> &getErrors (const Mat &model) override {
setModelParameters(model);
for (int point_idx = 0; point_idx < points_mat->rows; point_idx++) {
const int smpl = 4*point_idx;
const float x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
const float dx2 = x2 - (m11 * x1 + m12 * y1 + m13), dy2 = y2 - (m21 * x1 + m22 * y1 + m23);
errors[point_idx] = dx2 * dx2 + dy2 * dy2;
}
return errors;
}
Ptr<Error> clone () const override {
return makePtr<ReprojectedDistanceAffineImpl>(*points_mat);
}
};
Ptr<ReprojectionErrorAffine>
ReprojectionErrorAffine::create(const Mat &points) {
return makePtr<ReprojectedDistanceAffineImpl>(points);
}
////////////////////////////////////// NORMALIZING TRANSFORMATION /////////////////////////
class NormTransformImpl : public NormTransform {
private:
const float * const points;
public:
explicit NormTransformImpl (const Mat &points_) : points((float*)points_.data) {}
// Compute normalized points and transformation matrices.
void getNormTransformation (Mat& norm_points, const std::vector<int> &sample,
int sample_size, Matx33d &T1, Matx33d &T2) const override {
double mean_pts1_x = 0, mean_pts1_y = 0, mean_pts2_x = 0, mean_pts2_y = 0;
// find average of each coordinate of points.
int smpl;
for (int i = 0; i < sample_size; i++) {
smpl = 4 * sample[i];
mean_pts1_x += points[smpl ];
mean_pts1_y += points[smpl + 1];
mean_pts2_x += points[smpl + 2];
mean_pts2_y += points[smpl + 3];
}
mean_pts1_x /= sample_size; mean_pts1_y /= sample_size;
mean_pts2_x /= sample_size; mean_pts2_y /= sample_size;
double avg_dist1 = 0, avg_dist2 = 0, x1_m, y1_m, x2_m, y2_m;
for (int i = 0; i < sample_size; i++) {
smpl = 4 * sample[i];
/*
* Compute a similarity transform T that takes points xi
* to a new set of points x̃i such that the centroid of
* the points x̃i is the coordinate origin and their
* average distance from the origin is √2
*
* sqrt(x̃*x̃ + ỹ*ỹ) = sqrt(2)
* ax*ax + by*by = 2
*/
x1_m = points[smpl ] - mean_pts1_x;
y1_m = points[smpl + 1] - mean_pts1_y;
x2_m = points[smpl + 2] - mean_pts2_x;
y2_m = points[smpl + 3] - mean_pts2_y;
avg_dist1 += sqrt (x1_m * x1_m + y1_m * y1_m);
avg_dist2 += sqrt (x2_m * x2_m + y2_m * y2_m);
}
// scale
avg_dist1 = M_SQRT2 / (avg_dist1 / sample_size);
avg_dist2 = M_SQRT2 / (avg_dist2 / sample_size);
const double transl_x1 = -mean_pts1_x * avg_dist1, transl_y1 = -mean_pts1_y * avg_dist1;
const double transl_x2 = -mean_pts2_x * avg_dist2, transl_y2 = -mean_pts2_y * avg_dist2;
// transformation matrices
T1 = Matx33d (avg_dist1, 0, transl_x1,0, avg_dist1, transl_y1,0, 0, 1);
T2 = Matx33d (avg_dist2, 0, transl_x2,0, avg_dist2, transl_y2,0, 0, 1);
norm_points = Mat_<float>(sample_size, 4); // normalized points Nx4 matrix
auto * norm_points_ptr = (float *) norm_points.data;
// Normalize points: Npts = T*pts 3x3 * 3xN
const float avg_dist1f = (float)avg_dist1, avg_dist2f = (float)avg_dist2;
const float transl_x1f = (float)transl_x1, transl_y1f = (float)transl_y1;
const float transl_x2f = (float)transl_x2, transl_y2f = (float)transl_y2;
for (int i = 0; i < sample_size; i++) {
smpl = 4 * sample[i];
(*norm_points_ptr++) = avg_dist1f * points[smpl ] + transl_x1f;
(*norm_points_ptr++) = avg_dist1f * points[smpl + 1] + transl_y1f;
(*norm_points_ptr++) = avg_dist2f * points[smpl + 2] + transl_x2f;
(*norm_points_ptr++) = avg_dist2f * points[smpl + 3] + transl_y2f;
}
}
};
Ptr<NormTransform> NormTransform::create (const Mat &points) {
return makePtr<NormTransformImpl>(points);
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#ifdef HAVE_EIGEN
#include <Eigen/Eigen>
#endif
namespace cv { namespace usac {
// Fundamental Matrix Solver:
class FundamentalMinimalSolver7ptsImpl: public FundamentalMinimalSolver7pts {
private:
const Mat * points_mat;
const float * const points;
public:
explicit FundamentalMinimalSolver7ptsImpl (const Mat &points_) :
points_mat (&points_), points ((float *) points_.data) {}
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
const int m = 7, n = 9; // rows, cols
std::vector<double> a(m*n);
auto * a_ = &a[0];
for (int i = 0; i < m; i++ ) {
const int smpl = 4*sample[i];
const auto x1 = points[smpl ], y1 = points[smpl+1],
x2 = points[smpl+2], y2 = points[smpl+3];
(*a_++) = x2*x1;
(*a_++) = x2*y1;
(*a_++) = x2;
(*a_++) = y2*x1;
(*a_++) = y2*y1;
(*a_++) = y2;
(*a_++) = x1;
(*a_++) = y1;
(*a_++) = 1;
}
Math::eliminateUpperTriangular(a, m, n);
/*
[a11 a12 a13 a14 a15 a16 a17 a18 a19]
[ 0 a22 a23 a24 a25 a26 a27 a28 a29]
[ 0 0 a33 a34 a35 a36 a37 a38 a39]
[ 0 0 0 a44 a45 a46 a47 a48 a49]
[ 0 0 0 0 a55 a56 a57 a58 a59]
[ 0 0 0 0 0 a66 a67 a68 a69]
[ 0 0 0 0 0 0 a77 a78 a79]
f9 = 1
*/
double f1[9], f2[9];
f1[8] = 1.;
f1[7] = 0.;
f1[6] = -a[6*n+8] / a[6*n+6];
f2[8] = 1.;
f2[7] = -a[6*n+8] / a[6*n+7];
f2[6] = 0.;
// start from the last row
for (int i = m-2; i >= 0; i--) {
const int row_i = i*n;
double acc1 = 0, acc2 = 0;
for (int j = i+1; j < n; j++) {
acc1 -= a[row_i + j] * f1[j];
acc2 -= a[row_i + j] * f2[j];
}
f1[i] = acc1 / a[row_i + i];
f2[i] = acc2 / a[row_i + i];
// due to numerical errors return 0 solutions
if (std::isnan(f1[i]) || std::isnan(f2[i]))
return 0;
}
// OpenCV:
double c[4], r[3];
double t0, t1, t2;
Mat_<double> coeffs (1, 4, c);
Mat_<double> roots (1, 3, r);
for (int i = 0; i < 9; i++)
f1[i] -= f2[i];
t0 = f2[4]*f2[8] - f2[5]*f2[7];
t1 = f2[3]*f2[8] - f2[5]*f2[6];
t2 = f2[3]*f2[7] - f2[4]*f2[6];
c[3] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2;
c[2] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2 -
f1[3]*(f2[1]*f2[8] - f2[2]*f2[7]) +
f1[4]*(f2[0]*f2[8] - f2[2]*f2[6]) -
f1[5]*(f2[0]*f2[7] - f2[1]*f2[6]) +
f1[6]*(f2[1]*f2[5] - f2[2]*f2[4]) -
f1[7]*(f2[0]*f2[5] - f2[2]*f2[3]) +
f1[8]*(f2[0]*f2[4] - f2[1]*f2[3]);
t0 = f1[4]*f1[8] - f1[5]*f1[7];
t1 = f1[3]*f1[8] - f1[5]*f1[6];
t2 = f1[3]*f1[7] - f1[4]*f1[6];
c[1] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2 -
f2[3]*(f1[1]*f1[8] - f1[2]*f1[7]) +
f2[4]*(f1[0]*f1[8] - f1[2]*f1[6]) -
f2[5]*(f1[0]*f1[7] - f1[1]*f1[6]) +
f2[6]*(f1[1]*f1[5] - f1[2]*f1[4]) -
f2[7]*(f1[0]*f1[5] - f1[2]*f1[3]) +
f2[8]*(f1[0]*f1[4] - f1[1]*f1[3]);
c[0] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2;
// solve the cubic equation; there can be 1 to 3 roots ...
int nroots = solveCubic (coeffs, roots);
if (nroots < 1) return 0;
models = std::vector<Mat>(nroots);
for (int k = 0; k < nroots; k++) {
models[k] = Mat_<double>(3,3);
auto * F_ptr = (double *) models[k].data;
// for each root form the fundamental matrix
double lambda = r[k], mu = 1;
double s = f1[8]*lambda + f2[8];
// normalize each matrix, so that F(3,3) (~F[8]) == 1
if (fabs(s) > FLT_EPSILON) {
mu = 1/s;
lambda *= mu;
F_ptr[8] = 1;
} else
F_ptr[8] = 0;
for (int i = 0; i < 8; i++)
F_ptr[i] = f1[i] * lambda + f2[i] * mu;
}
return nroots;
}
int getMaxNumberOfSolutions () const override { return 3; }
int getSampleSize() const override { return 7; }
Ptr<MinimalSolver> clone () const override {
return makePtr<FundamentalMinimalSolver7ptsImpl>(*points_mat);
}
};
Ptr<FundamentalMinimalSolver7pts> FundamentalMinimalSolver7pts::create(const Mat &points_) {
return makePtr<FundamentalMinimalSolver7ptsImpl>(points_);
}
class FundamentalMinimalSolver8ptsImpl : public FundamentalMinimalSolver8pts {
private:
const Mat * points_mat;
const float * const points;
public:
explicit FundamentalMinimalSolver8ptsImpl (const Mat &points_) :
points_mat (&points_), points ((float*) points_.data) {}
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
const int m = 8, n = 9; // rows, cols
std::vector<double> a(m*n);
auto * a_ = &a[0];
for (int i = 0; i < m; i++ ) {
const int smpl = 4*sample[i];
const auto x1 = points[smpl ], y1 = points[smpl+1],
x2 = points[smpl+2], y2 = points[smpl+3];
(*a_++) = x2*x1;
(*a_++) = x2*y1;
(*a_++) = x2;
(*a_++) = y2*x1;
(*a_++) = y2*y1;
(*a_++) = y2;
(*a_++) = x1;
(*a_++) = y1;
(*a_++) = 1;
}
Math::eliminateUpperTriangular(a, m, n);
/*
[a11 a12 a13 a14 a15 a16 a17 a18 a19]
[ 0 a22 a23 a24 a25 a26 a27 a28 a29]
[ 0 0 a33 a34 a35 a36 a37 a38 a39]
[ 0 0 0 a44 a45 a46 a47 a48 a49]
[ 0 0 0 0 a55 a56 a57 a58 a59]
[ 0 0 0 0 0 a66 a67 a68 a69]
[ 0 0 0 0 0 0 a77 a78 a79]
[ 0 0 0 0 0 0 0 a88 a89]
f9 = 1
f8 = (-a89*f9) / a88
f7 = (-a79*f9 - a78*f8) / a77
f6 = (-a69*f9 - a68*f8 - a69*f9) / a66
...
*/
models = std::vector<Mat>{ Mat_<double>(3,3) };
auto * f = (double *) models[0].data;
f[8] = 1.;
// start from the last row
for (int i = m-1; i >= 0; i--) {
double acc = 0;
for (int j = i+1; j < n; j++)
acc -= a[i*n+j]*f[j];
f[i] = acc / a[i*n+i];
// due to numerical errors return 0 solutions
if (std::isnan(f[i]))
return 0;
}
return 1;
}
int getMaxNumberOfSolutions () const override { return 1; }
int getSampleSize() const override { return 8; }
Ptr<MinimalSolver> clone () const override {
return makePtr<FundamentalMinimalSolver8ptsImpl>(*points_mat);
}
};
Ptr<FundamentalMinimalSolver8pts> FundamentalMinimalSolver8pts::create(const Mat &points_) {
return makePtr<FundamentalMinimalSolver8ptsImpl>(points_);
}
class FundamentalNonMinimalSolverImpl : public FundamentalNonMinimalSolver {
private:
const Mat * points_mat;
const Ptr<NormTransform> normTr;
public:
explicit FundamentalNonMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), normTr (NormTransform::create(points_)) {}
int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat>
&models, const std::vector<double> &weights) const override {
if (sample_size < getMinimumRequiredSampleSize())
return 0;
Matx33d T1, T2;
Mat norm_points;
normTr->getNormTransformation(norm_points, sample, sample_size, T1, T2);
const auto * const norm_pts = (float *) norm_points.data;
// ------- 8 points algorithm with Eigen and covariance matrix --------------
double a[9] = {0, 0, 0, 0, 0, 0, 0, 0, 1};
double AtA[81] = {0}; // 9x9
if (weights.empty()) {
for (int i = 0; i < sample_size; i++) {
const int norm_points_idx = 4*i;
const double x1 = norm_pts[norm_points_idx ], y1 = norm_pts[norm_points_idx+1],
x2 = norm_pts[norm_points_idx+2], y2 = norm_pts[norm_points_idx+3];
a[0] = x2*x1;
a[1] = x2*y1;
a[2] = x2;
a[3] = y2*x1;
a[4] = y2*y1;
a[5] = y2;
a[6] = x1;
a[7] = y1;
// calculate covariance for eigen
for (int row = 0; row < 9; row++)
for (int col = row; col < 9; col++)
AtA[row*9+col] += a[row]*a[col];
}
} else {
for (int i = 0; i < sample_size; i++) {
const int smpl = 4*i;
const double weight = weights[i];
const double x1 = norm_pts[smpl ], y1 = norm_pts[smpl+1],
x2 = norm_pts[smpl+2], y2 = norm_pts[smpl+3];
const double weight_times_x2 = weight * x2,
weight_times_y2 = weight * y2;
a[0] = weight_times_x2 * x1;
a[1] = weight_times_x2 * y1;
a[2] = weight_times_x2;
a[3] = weight_times_y2 * x1;
a[4] = weight_times_y2 * y1;
a[5] = weight_times_y2;
a[6] = weight * x1;
a[7] = weight * y1;
a[8] = weight;
// calculate covariance for eigen
for (int row = 0; row < 9; row++)
for (int col = row; col < 9; col++)
AtA[row*9+col] += a[row]*a[col];
}
}
// copy symmetric part of covariance matrix
for (int j = 1; j < 9; j++)
for (int z = 0; z < j; z++)
AtA[j*9+z] = AtA[z*9+j];
#ifdef HAVE_EIGEN
models = std::vector<Mat>{ Mat_<double>(3,3) };
const Eigen::JacobiSVD<Eigen::Matrix<double, 9, 9>> svd((Eigen::Matrix<double, 9, 9>(AtA)),
Eigen::ComputeFullV);
// extract the last nullspace
Eigen::Map<Eigen::Matrix<double, 9, 1>>((double *)models[0].data) = svd.matrixV().col(8);
#else
Matx<double, 9, 9> AtA_(AtA), U, Vt;
Vec<double, 9> W;
SVD::compute(AtA_, W, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
models = std::vector<Mat> { Mat(Vt.row(8).reshape<3,3>()) };
#endif
// Transpose T2 (in T2 the lower diagonal is zero)
T2(2, 0) = T2(0, 2); T2(2, 1) = T2(1, 2);
T2(0, 2) = 0; T2(1, 2) = 0;
models[0] = T2 * models[0] * T1;
FundamentalDegeneracy::recoverRank(models[0]);
return 1;
}
int getMinimumRequiredSampleSize() const override { return 8; }
int getMaxNumberOfSolutions () const override { return 1; }
Ptr<NonMinimalSolver> clone () const override {
return makePtr<FundamentalNonMinimalSolverImpl>(*points_mat);
}
};
Ptr<FundamentalNonMinimalSolver> FundamentalNonMinimalSolver::create(const Mat &points_) {
return makePtr<FundamentalNonMinimalSolverImpl>(points_);
}
}}

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modules/calib3d/src/usac/gamma_values.hpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
constexpr int stored_gamma_number = 2999;
constexpr int stored_incomplete_gamma_number = 3999;
constexpr double scale_of_stored_gammas_n4 = 1647.8;
constexpr double scale_of_stored_incomplete_gammas_n4 = 603.64;
constexpr double stored_complete_gamma_values_n4[] = {0.88623,0.88618,0.8861,0.88599,0.88587,0.88573,0.88557,0.8854,0.88522,0.88502,0.88482,0.8846,0.88438,0.88415,0.8839,0.88365,0.8834,0.88313,0.88285,0.88257,0.88229,0.88199,0.88169,0.88138,0.88107,0.88075,0.88042,0.88009,0.87975,0.87941,0.87906,0.8787,0.87834,0.87798,0.87761,0.87724,0.87686,0.87647,0.87609,0.87569,0.8753,0.8749,0.87449,0.87408,0.87367,0.87325,0.87283,0.8724,0.87197,0.87154,0.8711,0.87066,0.87022,0.86977,0.86932,0.86886,0.8684,0.86794,0.86748,0.86701,0.86654,0.86606,0.86559,0.86511,0.86462,0.86414,0.86365,0.86315,0.86266,0.86216,0.86166,0.86116,0.86065,0.86014,0.85963,0.85911,0.8586,0.85808,0.85755,0.85703,0.8565,0.85597,0.85544,0.85491,0.85437,0.85383,0.85329,0.85275,0.8522,0.85165,0.8511,0.85055,0.85,0.84944,0.84888,0.84832,0.84776,0.8472,0.84663,0.84606,
0.84549,0.84492,0.84434,0.84377,0.84319,0.84261,0.84203,0.84145,0.84086,0.84027,0.83969,0.83909,0.8385,0.83791,0.83731,0.83672,0.83612,0.83552,0.83492,0.83431,0.83371,0.8331,0.8325,0.83189,0.83128,0.83066,0.83005,0.82943,0.82882,0.8282,0.82758,0.82696,0.82634,0.82572,0.82509,0.82447,0.82384,0.82321,0.82258,0.82195,0.82132,0.82068,0.82005,0.81941,0.81878,0.81814,0.8175,0.81686,0.81622,0.81558,0.81493,0.81429,0.81364,0.813,0.81235,0.8117,0.81105,0.8104,0.80975,0.80909,0.80844,0.80779,0.80713,0.80647,0.80582,0.80516,0.8045,0.80384,0.80318,0.80251,0.80185,0.80119,0.80052,0.79986,0.79919,0.79852,0.79786,0.79719,0.79652,0.79585,0.79518,0.7945,0.79383,0.79316,0.79248,0.79181,0.79113,0.79046,0.78978,0.7891,0.78843,0.78775,0.78707,0.78639,0.78571,0.78503,0.78434,0.78366,0.78298,0.78229,
0.78161,0.78093,0.78024,0.77955,0.77887,0.77818,0.77749,0.7768,0.77612,0.77543,0.77474,0.77405,0.77336,0.77266,0.77197,0.77128,0.77059,0.76989,0.7692,0.76851,0.76781,0.76712,0.76642,0.76573,0.76503,0.76433,0.76364,0.76294,0.76224,0.76154,0.76085,0.76015,0.75945,0.75875,0.75805,0.75735,0.75665,0.75595,0.75525,0.75454,0.75384,0.75314,0.75244,0.75174,0.75103,0.75033,0.74963,0.74892,0.74822,0.74751,0.74681,0.74611,0.7454,0.7447,0.74399,0.74328,0.74258,0.74187,0.74117,0.74046,0.73975,0.73905,0.73834,0.73763,0.73692,0.73622,0.73551,0.7348,0.73409,0.73339,0.73268,0.73197,0.73126,0.73055,0.72984,0.72913,0.72842,0.72772,0.72701,0.7263,0.72559,0.72488,0.72417,0.72346,0.72275,0.72204,0.72133,0.72062,0.71991,0.7192,0.71849,0.71778,0.71707,0.71636,0.71565,0.71494,0.71423,0.71352,0.71281,0.71209,
0.71138,0.71067,0.70996,0.70925,0.70854,0.70783,0.70712,0.70641,0.7057,0.70499,0.70428,0.70357,0.70286,0.70215,0.70144,0.70073,0.70002,0.69931,0.6986,0.69789,0.69718,0.69647,0.69576,0.69505,0.69434,0.69363,0.69292,0.69221,0.6915,0.69079,0.69008,0.68937,0.68867,0.68796,0.68725,0.68654,0.68583,0.68512,0.68441,0.68371,0.683,0.68229,0.68158,0.68088,0.68017,0.67946,0.67875,0.67805,0.67734,0.67663,0.67593,0.67522,0.67451,0.67381,0.6731,0.6724,0.67169,0.67099,0.67028,0.66958,0.66887,0.66817,0.66746,0.66676,0.66605,0.66535,0.66465,0.66394,0.66324,0.66254,0.66183,0.66113,0.66043,0.65973,0.65903,0.65832,0.65762,0.65692,0.65622,0.65552,0.65482,0.65412,0.65342,0.65272,0.65202,0.65132,0.65062,0.64992,0.64922,0.64853,0.64783,0.64713,0.64643,0.64574,0.64504,0.64434,0.64365,0.64295,0.64225,0.64156,
0.64086,0.64017,0.63947,0.63878,0.63808,0.63739,0.6367,0.636,0.63531,0.63462,0.63393,0.63323,0.63254,0.63185,0.63116,0.63047,0.62978,0.62909,0.6284,0.62771,0.62702,0.62633,0.62564,0.62495,0.62427,0.62358,0.62289,0.6222,0.62152,0.62083,0.62014,0.61946,0.61877,0.61809,0.6174,0.61672,0.61604,0.61535,0.61467,0.61399,0.6133,0.61262,0.61194,0.61126,0.61058,0.6099,0.60922,0.60854,0.60786,0.60718,0.6065,0.60582,0.60514,0.60446,0.60379,0.60311,0.60243,0.60176,0.60108,0.60041,0.59973,0.59906,0.59838,0.59771,0.59703,0.59636,0.59569,0.59501,0.59434,0.59367,0.593,0.59233,0.59166,0.59099,0.59032,0.58965,0.58898,0.58831,0.58764,0.58698,0.58631,0.58564,0.58498,0.58431,0.58365,0.58298,0.58232,0.58165,0.58099,0.58032,0.57966,0.579,0.57834,0.57767,0.57701,0.57635,0.57569,0.57503,0.57437,0.57371,
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0.00789,0.00788,0.00787,0.00785,0.00784,0.00783,0.00782,0.00781,0.00779,0.00778,0.00777,0.00776,0.00775,0.00773,0.00772,0.00771,0.0077,0.00769,0.00767,0.00766,0.00765,0.00764,0.00763,0.00762,0.0076,0.00759,0.00758,0.00757,0.00756,0.00755,0.00753,0.00752,0.00751,0.0075,0.00749,0.00748,0.00747,0.00745,0.00744,0.00743,0.00742,0.00741,0.0074,0.00739,0.00737,0.00736,0.00735,0.00734,0.00733,0.00732,0.00731,0.0073,0.00728,0.00727,0.00726,0.00725,0.00724,0.00723,0.00722,0.00721,0.0072,0.00718,0.00717,0.00716,0.00715,0.00714,0.00713,0.00712,0.00711,0.0071,0.00709,0.00707,0.00706,0.00705,0.00704,0.00703,0.00702,0.00701,0.007,0.00699,0.00698,0.00697,0.00696,0.00695,0.00693,0.00692,0.00691,0.0069,0.00689,0.00688,0.00687,0.00686,0.00685,0.00684,0.00683,0.00682,0.00681,0.0068,0.00679,0.00678,
0.00677,0.00676,0.00675,0.00674,0.00673,0.00671,0.0067,0.00669,0.00668,0.00667,0.00666,0.00665,0.00664,0.00663,0.00662,0.00661,0.0066,0.00659,0.00658,0.00657,0.00656,0.00655,0.00654,0.00653,0.00652,0.00651,0.0065,0.00649,0.00648,0.00647,0.00646,0.00645,0.00644,0.00643,0.00642,0.00641,0.0064,0.00639,0.00638,0.00637,0.00636,0.00635,0.00634,0.00633,0.00632,0.00631,0.0063,0.00629,0.00629,0.00628,0.00627,0.00626,0.00625,0.00624,0.00623,0.00622,0.00621,0.0062,0.00619,0.00618,0.00617,0.00616,0.00615,0.00614,0.00613,0.00612,0.00611,0.0061,0.00609,0.00609,0.00608,0.00607,0.00606,0.00605,0.00604,0.00603,0.00602,0.00601,0.006,0.00599,0.00598,0.00597,0.00596,0.00596,0.00595,0.00594,0.00593,0.00592,0.00591,0.0059,0.00589,0.00588,0.00587,0.00586,0.00586,0.00585,0.00584,0.00583,0.00582,0.00581,
0.0058,0.00579,0.00578,0.00578,0.00577,0.00576,0.00575,0.00574,0.00573,0.00572,0.00571,0.0057,0.0057,0.00569,0.00568,0.00567,0.00566,0.00565,0.00564,0.00563,0.00563,0.00562,0.00561,0.0056,0.00559,0.00558,0.00557,0.00557,0.00556,0.00555,0.00554,0.00553,0.00552,0.00551,0.00551,0.0055,0.00549,0.00548,0.00547,0.00546,0.00546,0.00545,0.00544,0.00543,0.00542,0.00541,0.00541,0.0054,0.00539,0.00538,0.00537,0.00536,0.00536,0.00535,0.00534,0.00533,0.00532,0.00531,0.00531,0.0053,0.00529,0.00528,0.00527,0.00527,0.00526,0.00525,0.00524,0.00523,0.00522,0.00522,0.00521,0.0052,0.00519,0.00518,0.00518,0.00517,0.00516,0.00515,0.00515,0.00514,0.00513,0.00512,0.00511,0.00511,0.0051,0.00509,0.00508,0.00507,0.00507,0.00506,0.00505,0.00504,0.00504,0.00503,0.00502,0.00501,0.005,0.005,0.00499,0.00498,
0.00497,0.00497,0.00496,0.00495,0.00494,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00487,0.00486,0.00485,0.00484,0.00484,0.00483,0.00482,0.00481,0.00481,0.0048,0.00479,0.00479,0.00478,0.00477,0.00476,0.00476,0.00475,0.00474,0.00473,0.00473,0.00472,0.00471,0.0047,0.0047,0.00469,0.00468,0.00468,0.00467,0.00466,0.00465,0.00465,0.00464,0.00463,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459,0.00458,0.00458,0.00457,0.00456,0.00455,0.00455,0.00454,0.00453,0.00453,0.00452,0.00451,0.00451,0.0045,0.00449,0.00448,0.00448,0.00447,0.00446,0.00446,0.00445,0.00444,0.00444,0.00443,0.00442,0.00442,0.00441,0.0044,0.0044,0.00439,0.00438,0.00438,0.00437,0.00436,0.00436,0.00435,0.00434,0.00434,0.00433,0.00432,0.00432,0.00431,0.0043,0.0043,0.00429,0.00428,0.00428,0.00427,
0.00426,0.00426,0.00425,0.00424,0.00424,0.00423,0.00422,0.00422,0.00421,0.0042,0.0042,0.00419,0.00418,0.00418,0.00417,0.00416,0.00416,0.00415,0.00415,0.00414,0.00413,0.00413,0.00412,0.00411,0.00411,0.0041,0.00409,0.00409,0.00408,0.00408,0.00407,0.00406,0.00406,0.00405,0.00404,0.00404,0.00403,0.00403,0.00402,0.00401,0.00401,0.004,0.00399,0.00399,0.00398,0.00398,0.00397,0.00396,0.00396,0.00395,0.00395,0.00394,0.00393,0.00393,0.00392,0.00391,0.00391,0.0039,0.0039,0.00389,0.00388,0.00388,0.00387,0.00387,0.00386,0.00385,0.00385,0.00384,0.00384,0.00383,0.00383,0.00382,0.00381,0.00381,0.0038,0.0038,0.00379,0.00378,0.00378,0.00377,0.00377,0.00376,0.00375,0.00375,0.00374,0.00374,0.00373,0.00373,0.00372,0.00371,0.00371,0.0037,0.0037,0.00369,0.00369,0.00368,0.00367,0.00367,0.00366,0.00366};
constexpr double stored_lower_incomplete_gamma_values_n4[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,3e-05,3e-05,4e-05,4e-05,5e-05,6e-05,7e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00014,0.00015,0.00016,0.00018,0.0002,0.00021,0.00023,0.00025,0.00027,0.00029,0.00031,0.00033,0.00036,0.00038,0.00041,0.00043,0.00046,0.00049,0.00051,0.00054,0.00058,0.00061,0.00064,0.00067,0.00071,0.00074,0.00078,0.00082,0.00086,0.0009,0.00094,0.00098,0.00102,0.00107,0.00111,0.00116,0.00121,0.00126,0.00131,0.00136,0.00141,0.00146,0.00152,0.00157,0.00163,0.00169,0.00175,0.00181,0.00187,0.00193,0.00199,0.00206,0.00212,0.00219,0.00226,0.00233,0.0024,0.00247,0.00254,0.00262,0.00269,0.00277,0.00285,0.00293,0.00301,0.00309,0.00317,0.00325,0.00334,0.00343,0.00351,0.0036,0.00369,0.00379,0.00388,
0.00397,0.00407,0.00416,0.00426,0.00436,0.00446,0.00456,0.00467,0.00477,0.00488,0.00498,0.00509,0.0052,0.00531,0.00542,0.00554,0.00565,0.00577,0.00588,0.006,0.00612,0.00624,0.00636,0.00649,0.00661,0.00674,0.00687,0.007,0.00713,0.00726,0.00739,0.00752,0.00766,0.0078,0.00793,0.00807,0.00821,0.00836,0.0085,0.00864,0.00879,0.00894,0.00909,0.00924,0.00939,0.00954,0.0097,0.00985,0.01001,0.01017,0.01032,0.01049,0.01065,0.01081,0.01098,0.01114,0.01131,0.01148,0.01165,0.01182,0.01199,0.01217,0.01234,0.01252,0.0127,0.01288,0.01306,0.01324,0.01342,0.01361,0.01379,0.01398,0.01417,0.01436,0.01455,0.01474,0.01494,0.01513,0.01533,0.01553,0.01573,0.01593,0.01613,0.01633,0.01654,0.01675,0.01695,0.01716,0.01737,0.01758,0.0178,0.01801,0.01823,0.01844,0.01866,0.01888,0.0191,0.01932,0.01955,0.01977,
0.02,0.02023,0.02046,0.02069,0.02092,0.02115,0.02138,0.02162,0.02186,0.02209,0.02233,0.02257,0.02282,0.02306,0.0233,0.02355,0.0238,0.02405,0.0243,0.02455,0.0248,0.02505,0.02531,0.02556,0.02582,0.02608,0.02634,0.0266,0.02687,0.02713,0.0274,0.02766,0.02793,0.0282,0.02847,0.02874,0.02902,0.02929,0.02957,0.02984,0.03012,0.0304,0.03068,0.03097,0.03125,0.03153,0.03182,0.03211,0.0324,0.03269,0.03298,0.03327,0.03356,0.03386,0.03415,0.03445,0.03475,0.03505,0.03535,0.03565,0.03596,0.03626,0.03657,0.03688,0.03719,0.0375,0.03781,0.03812,0.03843,0.03875,0.03906,0.03938,0.0397,0.04002,0.04034,0.04066,0.04099,0.04131,0.04164,0.04197,0.04229,0.04262,0.04296,0.04329,0.04362,0.04396,0.04429,0.04463,0.04497,0.04531,0.04565,0.04599,0.04633,0.04668,0.04702,0.04737,0.04772,0.04806,0.04841,0.04877,
0.04912,0.04947,0.04983,0.05018,0.05054,0.0509,0.05126,0.05162,0.05198,0.05234,0.05271,0.05307,0.05344,0.05381,0.05418,0.05455,0.05492,0.05529,0.05566,0.05604,0.05641,0.05679,0.05717,0.05755,0.05793,0.05831,0.05869,0.05908,0.05946,0.05985,0.06023,0.06062,0.06101,0.0614,0.06179,0.06219,0.06258,0.06297,0.06337,0.06377,0.06417,0.06456,0.06496,0.06537,0.06577,0.06617,0.06658,0.06698,0.06739,0.0678,0.06821,0.06862,0.06903,0.06944,0.06985,0.07027,0.07068,0.0711,0.07152,0.07194,0.07236,0.07278,0.0732,0.07362,0.07405,0.07447,0.0749,0.07532,0.07575,0.07618,0.07661,0.07704,0.07747,0.07791,0.07834,0.07878,0.07921,0.07965,0.08009,0.08053,0.08097,0.08141,0.08185,0.0823,0.08274,0.08319,0.08363,0.08408,0.08453,0.08498,0.08543,0.08588,0.08633,0.08679,0.08724,0.08769,0.08815,0.08861,0.08907,0.08953,
0.08999,0.09045,0.09091,0.09137,0.09184,0.0923,0.09277,0.09323,0.0937,0.09417,0.09464,0.09511,0.09558,0.09605,0.09653,0.097,0.09748,0.09795,0.09843,0.09891,0.09939,0.09987,0.10035,0.10083,0.10131,0.1018,0.10228,0.10277,0.10325,0.10374,0.10423,0.10472,0.10521,0.1057,0.10619,0.10668,0.10718,0.10767,0.10817,0.10866,0.10916,0.10966,0.11015,0.11065,0.11115,0.11166,0.11216,0.11266,0.11316,0.11367,0.11418,0.11468,0.11519,0.1157,0.11621,0.11672,0.11723,0.11774,0.11825,0.11876,0.11928,0.11979,0.12031,0.12082,0.12134,0.12186,0.12238,0.1229,0.12342,0.12394,0.12446,0.12498,0.12551,0.12603,0.12656,0.12708,0.12761,0.12814,0.12867,0.1292,0.12973,0.13026,0.13079,0.13132,0.13185,0.13239,0.13292,0.13346,0.13399,0.13453,0.13507,0.13561,0.13614,0.13668,0.13723,0.13777,0.13831,0.13885,0.1394,0.13994,
0.14049,0.14103,0.14158,0.14212,0.14267,0.14322,0.14377,0.14432,0.14487,0.14542,0.14598,0.14653,0.14708,0.14764,0.14819,0.14875,0.14931,0.14986,0.15042,0.15098,0.15154,0.1521,0.15266,0.15322,0.15378,0.15435,0.15491,0.15547,0.15604,0.1566,0.15717,0.15774,0.1583,0.15887,0.15944,0.16001,0.16058,0.16115,0.16172,0.16229,0.16287,0.16344,0.16401,0.16459,0.16516,0.16574,0.16632,0.16689,0.16747,0.16805,0.16863,0.16921,0.16979,0.17037,0.17095,0.17153,0.17211,0.1727,0.17328,0.17387,0.17445,0.17504,0.17562,0.17621,0.1768,0.17739,0.17797,0.17856,0.17915,0.17974,0.18033,0.18093,0.18152,0.18211,0.1827,0.1833,0.18389,0.18449,0.18508,0.18568,0.18628,0.18687,0.18747,0.18807,0.18867,0.18927,0.18987,0.19047,0.19107,0.19167,0.19227,0.19287,0.19348,0.19408,0.19469,0.19529,0.1959,0.1965,0.19711,0.19771,
0.19832,0.19893,0.19954,0.20015,0.20076,0.20137,0.20198,0.20259,0.2032,0.20381,0.20442,0.20504,0.20565,0.20626,0.20688,0.20749,0.20811,0.20872,0.20934,0.20996,0.21057,0.21119,0.21181,0.21243,0.21305,0.21367,0.21429,0.21491,0.21553,0.21615,0.21677,0.21739,0.21802,0.21864,0.21926,0.21989,0.22051,0.22114,0.22176,0.22239,0.22301,0.22364,0.22427,0.22489,0.22552,0.22615,0.22678,0.22741,0.22804,0.22867,0.2293,0.22993,0.23056,0.23119,0.23182,0.23246,0.23309,0.23372,0.23436,0.23499,0.23563,0.23626,0.2369,0.23753,0.23817,0.2388,0.23944,0.24008,0.24071,0.24135,0.24199,0.24263,0.24327,0.24391,0.24455,0.24519,0.24583,0.24647,0.24711,0.24775,0.24839,0.24904,0.24968,0.25032,0.25096,0.25161,0.25225,0.2529,0.25354,0.25419,0.25483,0.25548,0.25612,0.25677,0.25742,0.25806,0.25871,0.25936,0.26001,0.26065,
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1.27516,1.27523,1.2753,1.27537,1.27544,1.27551,1.27558,1.27565,1.27572,1.27579,1.27586,1.27593,1.27599,1.27606,1.27613,1.2762,1.27627,1.27634,1.27641,1.27648,1.27654,1.27661,1.27668,1.27675,1.27682,1.27689,1.27695,1.27702,1.27709,1.27716,1.27723,1.27729,1.27736,1.27743,1.27749,1.27756,1.27763,1.2777,1.27776,1.27783,1.2779,1.27796,1.27803,1.2781,1.27816,1.27823,1.2783,1.27836,1.27843,1.27849,1.27856,1.27863,1.27869,1.27876,1.27882,1.27889,1.27896,1.27902,1.27909,1.27915,1.27922,1.27928,1.27935,1.27941,1.27948,1.27954,1.27961,1.27967,1.27974,1.2798,1.27986,1.27993,1.27999,1.28006,1.28012,1.28018,1.28025,1.28031,1.28038,1.28044,1.2805,1.28057,1.28063,1.28069,1.28076,1.28082,1.28088,1.28095,1.28101,1.28107,1.28114,1.2812,1.28126,1.28132,1.28139,1.28145,1.28151,1.28157,1.28164,1.2817,
1.28176,1.28182,1.28188,1.28194,1.28201,1.28207,1.28213,1.28219,1.28225,1.28231,1.28238,1.28244,1.2825,1.28256,1.28262,1.28268,1.28274,1.2828,1.28286,1.28292,1.28298,1.28304,1.2831,1.28317,1.28323,1.28329,1.28335,1.28341,1.28347,1.28353,1.28359,1.28364,1.2837,1.28376,1.28382,1.28388,1.28394,1.284,1.28406,1.28412,1.28418,1.28424,1.2843,1.28436,1.28441,1.28447,1.28453,1.28459,1.28465,1.28471,1.28477,1.28482,1.28488,1.28494,1.285,1.28506,1.28511,1.28517,1.28523,1.28529,1.28534,1.2854,1.28546,1.28552,1.28557,1.28563,1.28569,1.28575,1.2858,1.28586,1.28592,1.28597,1.28603,1.28609,1.28614,1.2862,1.28626,1.28631,1.28637,1.28643,1.28648,1.28654,1.28659,1.28665,1.28671,1.28676,1.28682,1.28687,1.28693,1.28698,1.28704,1.28709,1.28715,1.28721,1.28726,1.28732,1.28737,1.28743,1.28748,1.28754,
1.28759,1.28764,1.2877,1.28775,1.28781,1.28786,1.28792,1.28797,1.28803,1.28808,1.28813,1.28819,1.28824,1.2883,1.28835,1.2884,1.28846,1.28851,1.28856,1.28862,1.28867,1.28872,1.28878,1.28883,1.28888,1.28894,1.28899,1.28904,1.2891,1.28915,1.2892,1.28925,1.28931,1.28936,1.28941,1.28946,1.28952,1.28957,1.28962,1.28967,1.28973,1.28978,1.28983,1.28988,1.28993,1.28999,1.29004,1.29009,1.29014,1.29019,1.29024,1.29029,1.29035,1.2904,1.29045,1.2905,1.29055,1.2906,1.29065,1.2907,1.29075,1.29081,1.29086,1.29091,1.29096,1.29101,1.29106,1.29111,1.29116,1.29121,1.29126,1.29131,1.29136,1.29141,1.29146,1.29151,1.29156,1.29161,1.29166,1.29171,1.29176,1.29181,1.29186,1.29191,1.29195,1.292,1.29205,1.2921,1.29215,1.2922,1.29225,1.2923,1.29235,1.2924,1.29244,1.29249,1.29254,1.29259,1.29264,1.29269,
1.29274,1.29278,1.29283,1.29288,1.29293,1.29298,1.29302,1.29307,1.29312,1.29317,1.29321,1.29326,1.29331,1.29336,1.29341,1.29345,1.2935,1.29355,1.29359,1.29364,1.29369,1.29374,1.29378,1.29383,1.29388,1.29392,1.29397,1.29402,1.29406,1.29411,1.29416,1.2942,1.29425,1.2943,1.29434,1.29439,1.29443,1.29448,1.29453,1.29457,1.29462,1.29466,1.29471,1.29476,1.2948,1.29485,1.29489,1.29494,1.29498,1.29503,1.29507,1.29512,1.29517,1.29521,1.29526,1.2953,1.29535,1.29539,1.29544,1.29548,1.29552,1.29557,1.29561,1.29566,1.2957,1.29575,1.29579,1.29584,1.29588,1.29593,1.29597,1.29601,1.29606,1.2961,1.29615,1.29619,1.29623,1.29628,1.29632,1.29637,1.29641,1.29645,1.2965,1.29654,1.29658,1.29663,1.29667,1.29671,1.29676,1.2968,1.29684,1.29689,1.29693,1.29697,1.29701,1.29706,1.2971,1.29714,1.29719,1.29723,
1.29727,1.29731,1.29736,1.2974,1.29744,1.29748,1.29752,1.29757,1.29761,1.29765,1.29769,1.29774,1.29778,1.29782,1.29786,1.2979,1.29794,1.29799,1.29803,1.29807,1.29811,1.29815,1.29819,1.29823,1.29828,1.29832,1.29836,1.2984,1.29844,1.29848,1.29852,1.29856,1.2986,1.29865,1.29869,1.29873,1.29877,1.29881,1.29885,1.29889,1.29893,1.29897,1.29901,1.29905,1.29909,1.29913,1.29917,1.29921,1.29925,1.29929,1.29933,1.29937,1.29941,1.29945,1.29949,1.29953,1.29957,1.29961,1.29965,1.29969,1.29973,1.29977,1.29981,1.29985,1.29988,1.29992,1.29996,1.3,1.30004,1.30008,1.30012,1.30016,1.3002,1.30024,1.30027,1.30031,1.30035,1.30039,1.30043,1.30047,1.30051,1.30054,1.30058,1.30062,1.30066,1.3007,1.30074,1.30077,1.30081,1.30085,1.30089,1.30093,1.30096,1.301,1.30104,1.30108,1.30111,1.30115,1.30119,1.30123};
constexpr double stored_gamma_values_n4[] = {0.88623,0.88622,0.8862,0.88618,0.88615,0.88612,0.88608,0.88604,0.886,0.88596,0.88591,0.88586,0.88581,0.88576,0.88571,0.88565,0.88559,0.88553,0.88547,0.88541,0.88534,0.88528,0.88521,0.88514,0.88507,0.88499,0.88492,0.88484,0.88477,0.88469,0.88461,0.88453,0.88444,0.88436,0.88428,0.88419,0.8841,0.88401,0.88392,0.88383,0.88374,0.88365,0.88356,0.88346,0.88336,0.88327,0.88317,0.88307,0.88297,0.88287,0.88277,0.88266,0.88256,0.88245,0.88235,0.88224,0.88213,0.88203,0.88192,0.88181,0.88169,0.88158,0.88147,0.88136,0.88124,0.88113,0.88101,0.88089,0.88077,0.88066,0.88054,0.88042,0.8803,0.88017,0.88005,0.87993,0.8798,0.87968,0.87955,0.87943,0.8793,0.87917,0.87904,0.87891,0.87878,0.87865,0.87852,0.87839,0.87826,0.87812,0.87799,0.87786,0.87772,0.87758,0.87745,0.87731,0.87717,0.87703,0.8769,0.87676,
0.87662,0.87647,0.87633,0.87619,0.87605,0.8759,0.87576,0.87562,0.87547,0.87532,0.87518,0.87503,0.87488,0.87474,0.87459,0.87444,0.87429,0.87414,0.87399,0.87384,0.87368,0.87353,0.87338,0.87322,0.87307,0.87292,0.87276,0.8726,0.87245,0.87229,0.87213,0.87198,0.87182,0.87166,0.8715,0.87134,0.87118,0.87102,0.87086,0.8707,0.87053,0.87037,0.87021,0.87004,0.86988,0.86972,0.86955,0.86938,0.86922,0.86905,0.86889,0.86872,0.86855,0.86838,0.86821,0.86804,0.86787,0.8677,0.86753,0.86736,0.86719,0.86702,0.86685,0.86667,0.8665,0.86633,0.86615,0.86598,0.8658,0.86563,0.86545,0.86528,0.8651,0.86492,0.86475,0.86457,0.86439,0.86421,0.86403,0.86386,0.86368,0.8635,0.86332,0.86313,0.86295,0.86277,0.86259,0.86241,0.86222,0.86204,0.86186,0.86167,0.86149,0.86131,0.86112,0.86094,0.86075,0.86056,0.86038,0.86019,
0.86,0.85982,0.85963,0.85944,0.85925,0.85906,0.85887,0.85868,0.85849,0.8583,0.85811,0.85792,0.85773,0.85754,0.85735,0.85716,0.85696,0.85677,0.85658,0.85638,0.85619,0.856,0.8558,0.85561,0.85541,0.85522,0.85502,0.85482,0.85463,0.85443,0.85423,0.85404,0.85384,0.85364,0.85344,0.85324,0.85304,0.85285,0.85265,0.85245,0.85225,0.85205,0.85185,0.85164,0.85144,0.85124,0.85104,0.85084,0.85064,0.85043,0.85023,0.85003,0.84982,0.84962,0.84941,0.84921,0.84901,0.8488,0.8486,0.84839,0.84818,0.84798,0.84777,0.84757,0.84736,0.84715,0.84694,0.84674,0.84653,0.84632,0.84611,0.8459,0.84569,0.84549,0.84528,0.84507,0.84486,0.84465,0.84444,0.84423,0.84401,0.8438,0.84359,0.84338,0.84317,0.84296,0.84274,0.84253,0.84232,0.8421,0.84189,0.84168,0.84146,0.84125,0.84104,0.84082,0.84061,0.84039,0.84018,0.83996,
0.83974,0.83953,0.83931,0.8391,0.83888,0.83866,0.83845,0.83823,0.83801,0.83779,0.83757,0.83736,0.83714,0.83692,0.8367,0.83648,0.83626,0.83604,0.83582,0.8356,0.83538,0.83516,0.83494,0.83472,0.8345,0.83428,0.83406,0.83384,0.83361,0.83339,0.83317,0.83295,0.83273,0.8325,0.83228,0.83206,0.83183,0.83161,0.83139,0.83116,0.83094,0.83071,0.83049,0.83026,0.83004,0.82981,0.82959,0.82936,0.82914,0.82891,0.82869,0.82846,0.82823,0.82801,0.82778,0.82755,0.82733,0.8271,0.82687,0.82664,0.82641,0.82619,0.82596,0.82573,0.8255,0.82527,0.82504,0.82481,0.82458,0.82436,0.82413,0.8239,0.82367,0.82344,0.82321,0.82298,0.82274,0.82251,0.82228,0.82205,0.82182,0.82159,0.82136,0.82113,0.82089,0.82066,0.82043,0.8202,0.81996,0.81973,0.8195,0.81926,0.81903,0.8188,0.81856,0.81833,0.8181,0.81786,0.81763,0.81739,
0.81716,0.81693,0.81669,0.81646,0.81622,0.81599,0.81575,0.81551,0.81528,0.81504,0.81481,0.81457,0.81433,0.8141,0.81386,0.81363,0.81339,0.81315,0.81291,0.81268,0.81244,0.8122,0.81196,0.81173,0.81149,0.81125,0.81101,0.81077,0.81054,0.8103,0.81006,0.80982,0.80958,0.80934,0.8091,0.80886,0.80862,0.80838,0.80814,0.8079,0.80766,0.80742,0.80718,0.80694,0.8067,0.80646,0.80622,0.80598,0.80574,0.8055,0.80526,0.80501,0.80477,0.80453,0.80429,0.80405,0.80381,0.80356,0.80332,0.80308,0.80284,0.80259,0.80235,0.80211,0.80187,0.80162,0.80138,0.80114,0.80089,0.80065,0.80041,0.80016,0.79992,0.79967,0.79943,0.79919,0.79894,0.7987,0.79845,0.79821,0.79796,0.79772,0.79747,0.79723,0.79698,0.79674,0.79649,0.79625,0.796,0.79576,0.79551,0.79526,0.79502,0.79477,0.79453,0.79428,0.79403,0.79379,0.79354,0.79329,
0.79305,0.7928,0.79255,0.79231,0.79206,0.79181,0.79156,0.79132,0.79107,0.79082,0.79057,0.79033,0.79008,0.78983,0.78958,0.78933,0.78909,0.78884,0.78859,0.78834,0.78809,0.78784,0.7876,0.78735,0.7871,0.78685,0.7866,0.78635,0.7861,0.78585,0.7856,0.78535,0.7851,0.78485,0.7846,0.78435,0.7841,0.78385,0.7836,0.78335,0.7831,0.78285,0.7826,0.78235,0.7821,0.78185,0.7816,0.78135,0.7811,0.78085,0.7806,0.78034,0.78009,0.77984,0.77959,0.77934,0.77909,0.77884,0.77858,0.77833,0.77808,0.77783,0.77758,0.77732,0.77707,0.77682,0.77657,0.77632,0.77606,0.77581,0.77556,0.77531,0.77505,0.7748,0.77455,0.77429,0.77404,0.77379,0.77354,0.77328,0.77303,0.77278,0.77252,0.77227,0.77202,0.77176,0.77151,0.77126,0.771,0.77075,0.77049,0.77024,0.76999,0.76973,0.76948,0.76922,0.76897,0.76872,0.76846,0.76821,
0.76795,0.7677,0.76744,0.76719,0.76693,0.76668,0.76642,0.76617,0.76592,0.76566,0.76541,0.76515,0.7649,0.76464,0.76438,0.76413,0.76387,0.76362,0.76336,0.76311,0.76285,0.7626,0.76234,0.76209,0.76183,0.76157,0.76132,0.76106,0.76081,0.76055,0.7603,0.76004,0.75978,0.75953,0.75927,0.75901,0.75876,0.7585,0.75825,0.75799,0.75773,0.75748,0.75722,0.75696,0.75671,0.75645,0.75619,0.75594,0.75568,0.75542,0.75517,0.75491,0.75465,0.75439,0.75414,0.75388,0.75362,0.75337,0.75311,0.75285,0.75259,0.75234,0.75208,0.75182,0.75156,0.75131,0.75105,0.75079,0.75053,0.75028,0.75002,0.74976,0.7495,0.74925,0.74899,0.74873,0.74847,0.74821,0.74796,0.7477,0.74744,0.74718,0.74692,0.74667,0.74641,0.74615,0.74589,0.74563,0.74538,0.74512,0.74486,0.7446,0.74434,0.74408,0.74383,0.74357,0.74331,0.74305,0.74279,0.74253,
0.74227,0.74202,0.74176,0.7415,0.74124,0.74098,0.74072,0.74046,0.7402,0.73994,0.73969,0.73943,0.73917,0.73891,0.73865,0.73839,0.73813,0.73787,0.73761,0.73735,0.7371,0.73684,0.73658,0.73632,0.73606,0.7358,0.73554,0.73528,0.73502,0.73476,0.7345,0.73424,0.73398,0.73372,0.73347,0.73321,0.73295,0.73269,0.73243,0.73217,0.73191,0.73165,0.73139,0.73113,0.73087,0.73061,0.73035,0.73009,0.72983,0.72957,0.72931,0.72905,0.72879,0.72853,0.72827,0.72801,0.72775,0.72749,0.72723,0.72697,0.72671,0.72645,0.72619,0.72593,0.72567,0.72541,0.72515,0.72489,0.72463,0.72437,0.72412,0.72386,0.7236,0.72334,0.72307,0.72281,0.72255,0.72229,0.72203,0.72177,0.72151,0.72125,0.72099,0.72073,0.72047,0.72021,0.71995,0.71969,0.71943,0.71917,0.71891,0.71865,0.71839,0.71813,0.71787,0.71761,0.71735,0.71709,0.71683,0.71657,
0.71631,0.71605,0.71579,0.71553,0.71527,0.71501,0.71475,0.71449,0.71423,0.71397,0.71371,0.71345,0.71319,0.71293,0.71267,0.71241,0.71215,0.71189,0.71163,0.71137,0.71111,0.71085,0.71059,0.71033,0.71007,0.70981,0.70954,0.70928,0.70902,0.70876,0.7085,0.70824,0.70798,0.70772,0.70746,0.7072,0.70694,0.70668,0.70642,0.70616,0.7059,0.70564,0.70538,0.70512,0.70486,0.7046,0.70434,0.70408,0.70382,0.70356,0.7033,0.70304,0.70278,0.70252,0.70226,0.702,0.70174,0.70148,0.70122,0.70096,0.7007,0.70044,0.70018,0.69992,0.69966,0.6994,0.69914,0.69888,0.69862,0.69836,0.6981,0.69784,0.69758,0.69732,0.69706,0.6968,0.69654,0.69628,0.69602,0.69576,0.6955,0.69524,0.69498,0.69472,0.69446,0.6942,0.69394,0.69368,0.69342,0.69316,0.6929,0.69264,0.69238,0.69212,0.69186,0.6916,0.69134,0.69108,0.69082,0.69056,
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0.37654,0.37637,0.37619,0.37601,0.37583,0.37566,0.37548,0.3753,0.37513,0.37495,0.37477,0.3746,0.37442,0.37424,0.37407,0.37389,0.37371,0.37354,0.37336,0.37318,0.37301,0.37283,0.37266,0.37248,0.3723,0.37213,0.37195,0.37178,0.3716,0.37142,0.37125,0.37107,0.3709,0.37072,0.37055,0.37037,0.3702,0.37002,0.36985,0.36967,0.3695,0.36932,0.36915,0.36897,0.3688,0.36862,0.36845,0.36828,0.3681,0.36793,0.36775,0.36758,0.36741,0.36723,0.36706,0.36688,0.36671,0.36654,0.36636,0.36619,0.36602,0.36584,0.36567,0.3655,0.36532,0.36515,0.36498,0.3648,0.36463,0.36446,0.36428,0.36411,0.36394,0.36377,0.36359,0.36342,0.36325,0.36308,0.36291,0.36273,0.36256,0.36239,0.36222,0.36205,0.36187,0.3617,0.36153,0.36136,0.36119,0.36102,0.36084,0.36067,0.3605,0.36033,0.36016,0.35999,0.35982,0.35965,0.35948,0.3593,
0.35913,0.35896,0.35879,0.35862,0.35845,0.35828,0.35811,0.35794,0.35777,0.3576,0.35743,0.35726,0.35709,0.35692,0.35675,0.35658,0.35641,0.35624,0.35607,0.3559,0.35573,0.35556,0.35539,0.35523,0.35506,0.35489,0.35472,0.35455,0.35438,0.35421,0.35404,0.35387,0.35371,0.35354,0.35337,0.3532,0.35303,0.35286,0.3527,0.35253,0.35236,0.35219,0.35202,0.35186,0.35169,0.35152,0.35135,0.35119,0.35102,0.35085,0.35068,0.35052,0.35035,0.35018,0.35002,0.34985,0.34968,0.34951,0.34935,0.34918,0.34901,0.34885,0.34868,0.34851,0.34835,0.34818,0.34802,0.34785,0.34768,0.34752,0.34735,0.34719,0.34702,0.34685,0.34669,0.34652,0.34636,0.34619,0.34603,0.34586,0.3457,0.34553,0.34536,0.3452,0.34503,0.34487,0.3447,0.34454,0.34437,0.34421,0.34405,0.34388,0.34372,0.34355,0.34339,0.34322,0.34306,0.34289,0.34273,0.34257,
0.3424,0.34224,0.34207,0.34191,0.34175,0.34158,0.34142,0.34126,0.34109,0.34093,0.34077,0.3406,0.34044,0.34028,0.34011,0.33995,0.33979,0.33963,0.33946,0.3393,0.33914,0.33897,0.33881,0.33865,0.33849,0.33832,0.33816,0.338,0.33784,0.33768,0.33751,0.33735,0.33719,0.33703,0.33687,0.33671,0.33654,0.33638,0.33622,0.33606,0.3359,0.33574,0.33558,0.33541,0.33525,0.33509,0.33493,0.33477,0.33461,0.33445,0.33429,0.33413,0.33397,0.33381,0.33365,0.33349,0.33333,0.33317,0.33301,0.33285,0.33269,0.33253,0.33237,0.33221,0.33205,0.33189,0.33173,0.33157,0.33141,0.33125,0.33109,0.33093,0.33077,0.33061,0.33045,0.33029,0.33013,0.32998,0.32982,0.32966,0.3295,0.32934,0.32918,0.32902,0.32886,0.32871,0.32855,0.32839,0.32823,0.32807,0.32792,0.32776,0.3276,0.32744,0.32728,0.32713,0.32697,0.32681,0.32665,0.3265,
0.32634,0.32618,0.32602,0.32587,0.32571,0.32555,0.3254,0.32524,0.32508,0.32493,0.32477,0.32461,0.32446,0.3243,0.32414,0.32399,0.32383,0.32367,0.32352,0.32336,0.3232,0.32305,0.32289,0.32274,0.32258,0.32243,0.32227,0.32211,0.32196,0.3218,0.32165,0.32149,0.32134,0.32118,0.32103,0.32087,0.32072,0.32056,0.32041,0.32025,0.3201,0.31994,0.31979,0.31963,0.31948,0.31932,0.31917,0.31902,0.31886,0.31871,0.31855,0.3184,0.31824,0.31809,0.31794,0.31778,0.31763,0.31748,0.31732,0.31717,0.31701,0.31686,0.31671,0.31655,0.3164,0.31625,0.31609,0.31594,0.31579,0.31564,0.31548,0.31533,0.31518,0.31502,0.31487,0.31472,0.31457,0.31441,0.31426,0.31411,0.31396,0.31381,0.31365,0.3135,0.31335,0.3132,0.31305,0.31289,0.31274,0.31259,0.31244,0.31229,0.31214,0.31199,0.31183,0.31168,0.31153,0.31138,0.31123,0.31108,
0.31093,0.31078,0.31063,0.31047,0.31032,0.31017,0.31002,0.30987,0.30972,0.30957,0.30942,0.30927,0.30912,0.30897,0.30882,0.30867,0.30852,0.30837,0.30822,0.30807,0.30792,0.30777,0.30762,0.30747,0.30732,0.30717,0.30702,0.30688,0.30673,0.30658,0.30643,0.30628,0.30613,0.30598,0.30583,0.30568,0.30554,0.30539,0.30524,0.30509,0.30494,0.30479,0.30464,0.3045,0.30435,0.3042,0.30405,0.3039,0.30376,0.30361,0.30346,0.30331,0.30317,0.30302,0.30287,0.30272,0.30258,0.30243,0.30228,0.30213,0.30199,0.30184,0.30169,0.30155,0.3014,0.30125,0.30111,0.30096,0.30081,0.30067,0.30052,0.30037,0.30023,0.30008,0.29993,0.29979,0.29964,0.29949,0.29935,0.2992,0.29906,0.29891,0.29877,0.29862,0.29847,0.29833,0.29818,0.29804,0.29789,0.29775,0.2976,0.29746,0.29731,0.29717,0.29702,0.29688,0.29673,0.29659,0.29644,0.2963,
0.29615,0.29601,0.29586,0.29572,0.29557,0.29543,0.29529,0.29514,0.295,0.29485,0.29471,0.29456,0.29442,0.29428,0.29413,0.29399,0.29385,0.2937,0.29356,0.29341,0.29327,0.29313,0.29298,0.29284,0.2927,0.29256,0.29241,0.29227,0.29213,0.29198,0.29184,0.2917,0.29156,0.29141,0.29127,0.29113,0.29099,0.29084,0.2907,0.29056,0.29042,0.29027,0.29013,0.28999,0.28985,0.28971,0.28956,0.28942,0.28928,0.28914,0.289,0.28886,0.28871,0.28857,0.28843,0.28829,0.28815,0.28801,0.28787,0.28773,0.28758,0.28744,0.2873,0.28716,0.28702,0.28688,0.28674,0.2866,0.28646,0.28632,0.28618,0.28604,0.2859,0.28576,0.28562,0.28548,0.28534,0.2852,0.28506,0.28492,0.28478,0.28464,0.2845,0.28436,0.28422,0.28408,0.28394,0.2838,0.28366,0.28352,0.28338,0.28324,0.28311,0.28297,0.28283,0.28269,0.28255,0.28241,0.28227,0.28213,
0.282,0.28186,0.28172,0.28158,0.28144,0.2813,0.28117,0.28103,0.28089,0.28075,0.28061,0.28048,0.28034,0.2802,0.28006,0.27992,0.27979,0.27965,0.27951,0.27937,0.27924,0.2791,0.27896,0.27883,0.27869,0.27855,0.27841,0.27828,0.27814,0.278,0.27787,0.27773,0.27759,0.27746,0.27732,0.27718,0.27705,0.27691,0.27678,0.27664,0.2765,0.27637,0.27623,0.27609,0.27596,0.27582,0.27569,0.27555,0.27542,0.27528,0.27514,0.27501,0.27487,0.27474,0.2746,0.27447,0.27433,0.2742,0.27406,0.27393,0.27379,0.27366,0.27352,0.27339,0.27325,0.27312,0.27298,0.27285,0.27271,0.27258,0.27245,0.27231,0.27218,0.27204,0.27191,0.27177,0.27164,0.27151,0.27137,0.27124,0.2711,0.27097,0.27084,0.2707,0.27057,0.27044,0.2703,0.27017,0.27004,0.2699,0.26977,0.26964,0.2695,0.26937,0.26924,0.26911,0.26897,0.26884,0.26871,0.26857};
constexpr double scale_of_stored_gammas_n5 = 1545.88;
constexpr double scale_of_stored_incomplete_gammas_n5 = 531.27;
constexpr double stored_complete_gamma_values_n5[] = {1.0,1.0,0.99999,0.99998,0.99997,0.99996,0.99994,0.99991,0.99989,0.99986,0.99983,0.99979,0.99975,0.99971,0.99966,0.99961,0.99956,0.9995,0.99944,0.99938,0.99931,0.99924,0.99917,0.99909,0.99901,0.99893,0.99884,0.99875,0.99866,0.99856,0.99846,0.99836,0.99826,0.99815,0.99804,0.99792,0.99781,0.99768,0.99756,0.99743,0.9973,0.99717,0.99704,0.9969,0.99675,0.99661,0.99646,0.99631,0.99616,0.996,0.99584,0.99568,0.99551,0.99534,0.99517,0.995,0.99482,0.99464,0.99446,0.99427,0.99408,0.99389,0.9937,0.9935,0.9933,0.9931,0.99289,0.99269,0.99248,0.99226,0.99205,0.99183,0.99161,0.99138,0.99115,0.99093,0.99069,0.99046,0.99022,0.98998,0.98974,0.98949,0.98925,0.989,0.98874,0.98849,0.98823,0.98797,0.98771,0.98744,0.98717,0.9869,0.98663,0.98635,0.98608,0.9858,0.98551,0.98523,0.98494,0.98465,
0.98436,0.98406,0.98377,0.98347,0.98317,0.98286,0.98256,0.98225,0.98194,0.98162,0.98131,0.98099,0.98067,0.98035,0.98002,0.97969,0.97936,0.97903,0.9787,0.97836,0.97803,0.97769,0.97734,0.977,0.97665,0.9763,0.97595,0.9756,0.97524,0.97489,0.97453,0.97416,0.9738,0.97343,0.97307,0.9727,0.97232,0.97195,0.97157,0.9712,0.97082,0.97043,0.97005,0.96966,0.96928,0.96889,0.96849,0.9681,0.9677,0.96731,0.96691,0.9665,0.9661,0.9657,0.96529,0.96488,0.96447,0.96405,0.96364,0.96322,0.9628,0.96238,0.96196,0.96154,0.96111,0.96068,0.96026,0.95982,0.95939,0.95896,0.95852,0.95808,0.95764,0.9572,0.95676,0.95631,0.95586,0.95542,0.95497,0.95451,0.95406,0.9536,0.95315,0.95269,0.95223,0.95177,0.9513,0.95084,0.95037,0.9499,0.94943,0.94896,0.94849,0.94801,0.94754,0.94706,0.94658,0.9461,0.94562,0.94513,
0.94465,0.94416,0.94367,0.94318,0.94269,0.9422,0.9417,0.94121,0.94071,0.94021,0.93971,0.93921,0.9387,0.9382,0.93769,0.93719,0.93668,0.93617,0.93566,0.93514,0.93463,0.93411,0.9336,0.93308,0.93256,0.93204,0.93151,0.93099,0.93046,0.92994,0.92941,0.92888,0.92835,0.92782,0.92728,0.92675,0.92621,0.92568,0.92514,0.9246,0.92406,0.92352,0.92297,0.92243,0.92188,0.92134,0.92079,0.92024,0.91969,0.91914,0.91859,0.91803,0.91748,0.91692,0.91636,0.91581,0.91525,0.91469,0.91412,0.91356,0.913,0.91243,0.91186,0.9113,0.91073,0.91016,0.90959,0.90902,0.90844,0.90787,0.9073,0.90672,0.90614,0.90556,0.90498,0.9044,0.90382,0.90324,0.90266,0.90207,0.90149,0.9009,0.90032,0.89973,0.89914,0.89855,0.89796,0.89737,0.89677,0.89618,0.89558,0.89499,0.89439,0.89379,0.8932,0.8926,0.892,0.89139,0.89079,0.89019,
0.88959,0.88898,0.88838,0.88777,0.88716,0.88655,0.88594,0.88533,0.88472,0.88411,0.8835,0.88289,0.88227,0.88166,0.88104,0.88043,0.87981,0.87919,0.87857,0.87795,0.87733,0.87671,0.87609,0.87547,0.87484,0.87422,0.87359,0.87297,0.87234,0.87171,0.87109,0.87046,0.86983,0.8692,0.86857,0.86794,0.8673,0.86667,0.86604,0.8654,0.86477,0.86413,0.8635,0.86286,0.86222,0.86158,0.86095,0.86031,0.85967,0.85903,0.85838,0.85774,0.8571,0.85646,0.85581,0.85517,0.85452,0.85388,0.85323,0.85258,0.85194,0.85129,0.85064,0.84999,0.84934,0.84869,0.84804,0.84739,0.84674,0.84608,0.84543,0.84478,0.84412,0.84347,0.84281,0.84216,0.8415,0.84085,0.84019,0.83953,0.83887,0.83821,0.83755,0.8369,0.83623,0.83557,0.83491,0.83425,0.83359,0.83293,0.83226,0.8316,0.83094,0.83027,0.82961,0.82894,0.82828,0.82761,0.82694,0.82628,
0.82561,0.82494,0.82427,0.82361,0.82294,0.82227,0.8216,0.82093,0.82026,0.81959,0.81892,0.81824,0.81757,0.8169,0.81623,0.81555,0.81488,0.81421,0.81353,0.81286,0.81218,0.81151,0.81083,0.81016,0.80948,0.8088,0.80813,0.80745,0.80677,0.8061,0.80542,0.80474,0.80406,0.80338,0.8027,0.80202,0.80134,0.80066,0.79998,0.7993,0.79862,0.79794,0.79726,0.79658,0.7959,0.79521,0.79453,0.79385,0.79317,0.79248,0.7918,0.79112,0.79043,0.78975,0.78906,0.78838,0.78769,0.78701,0.78632,0.78564,0.78495,0.78427,0.78358,0.7829,0.78221,0.78152,0.78084,0.78015,0.77946,0.77878,0.77809,0.7774,0.77671,0.77602,0.77534,0.77465,0.77396,0.77327,0.77258,0.77189,0.77121,0.77052,0.76983,0.76914,0.76845,0.76776,0.76707,0.76638,0.76569,0.765,0.76431,0.76362,0.76293,0.76224,0.76155,0.76086,0.76017,0.75947,0.75878,0.75809,
0.7574,0.75671,0.75602,0.75533,0.75464,0.75394,0.75325,0.75256,0.75187,0.75118,0.75049,0.74979,0.7491,0.74841,0.74772,0.74703,0.74633,0.74564,0.74495,0.74426,0.74356,0.74287,0.74218,0.74149,0.7408,0.7401,0.73941,0.73872,0.73803,0.73733,0.73664,0.73595,0.73526,0.73456,0.73387,0.73318,0.73249,0.73179,0.7311,0.73041,0.72972,0.72902,0.72833,0.72764,0.72695,0.72625,0.72556,0.72487,0.72418,0.72349,0.72279,0.7221,0.72141,0.72072,0.72003,0.71933,0.71864,0.71795,0.71726,0.71657,0.71588,0.71519,0.71449,0.7138,0.71311,0.71242,0.71173,0.71104,0.71035,0.70966,0.70897,0.70827,0.70758,0.70689,0.7062,0.70551,0.70482,0.70413,0.70344,0.70275,0.70206,0.70137,0.70068,0.69999,0.69931,0.69862,0.69793,0.69724,0.69655,0.69586,0.69517,0.69448,0.6938,0.69311,0.69242,0.69173,0.69104,0.69036,0.68967,0.68898,
0.68829,0.68761,0.68692,0.68623,0.68555,0.68486,0.68417,0.68349,0.6828,0.68212,0.68143,0.68074,0.68006,0.67937,0.67869,0.678,0.67732,0.67664,0.67595,0.67527,0.67458,0.6739,0.67322,0.67253,0.67185,0.67117,0.67048,0.6698,0.66912,0.66844,0.66775,0.66707,0.66639,0.66571,0.66503,0.66435,0.66367,0.66299,0.66231,0.66163,0.66095,0.66027,0.65959,0.65891,0.65823,0.65755,0.65687,0.65619,0.65551,0.65484,0.65416,0.65348,0.6528,0.65213,0.65145,0.65077,0.6501,0.64942,0.64875,0.64807,0.6474,0.64672,0.64605,0.64537,0.6447,0.64402,0.64335,0.64268,0.642,0.64133,0.64066,0.63998,0.63931,0.63864,0.63797,0.6373,0.63663,0.63596,0.63529,0.63462,0.63394,0.63328,0.63261,0.63194,0.63127,0.6306,0.62993,0.62926,0.62859,0.62793,0.62726,0.62659,0.62593,0.62526,0.62459,0.62393,0.62326,0.6226,0.62193,0.62127,
0.6206,0.61994,0.61928,0.61861,0.61795,0.61729,0.61662,0.61596,0.6153,0.61464,0.61398,0.61332,0.61266,0.612,0.61134,0.61068,0.61002,0.60936,0.6087,0.60804,0.60738,0.60673,0.60607,0.60541,0.60476,0.6041,0.60344,0.60279,0.60213,0.60148,0.60082,0.60017,0.59951,0.59886,0.59821,0.59755,0.5969,0.59625,0.5956,0.59494,0.59429,0.59364,0.59299,0.59234,0.59169,0.59104,0.59039,0.58974,0.5891,0.58845,0.5878,0.58715,0.5865,0.58586,0.58521,0.58457,0.58392,0.58327,0.58263,0.58199,0.58134,0.5807,0.58005,0.57941,0.57877,0.57813,0.57748,0.57684,0.5762,0.57556,0.57492,0.57428,0.57364,0.573,0.57236,0.57172,0.57108,0.57045,0.56981,0.56917,0.56853,0.5679,0.56726,0.56663,0.56599,0.56536,0.56472,0.56409,0.56345,0.56282,0.56219,0.56156,0.56092,0.56029,0.55966,0.55903,0.5584,0.55777,0.55714,0.55651,
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0.00887,0.00886,0.00884,0.00883,0.00881,0.0088,0.00878,0.00877,0.00875,0.00874,0.00873,0.00871,0.0087,0.00868,0.00867,0.00865,0.00864,0.00863,0.00861,0.0086,0.00858,0.00857,0.00856,0.00854,0.00853,0.00851,0.0085,0.00849,0.00847,0.00846,0.00844,0.00843,0.00842,0.0084,0.00839,0.00837,0.00836,0.00835,0.00833,0.00832,0.00831,0.00829,0.00828,0.00827,0.00825,0.00824,0.00822,0.00821,0.0082,0.00818,0.00817,0.00816,0.00814,0.00813,0.00812,0.0081,0.00809,0.00808,0.00806,0.00805,0.00804,0.00802,0.00801,0.008,0.00798,0.00797,0.00796,0.00795,0.00793,0.00792,0.00791,0.00789,0.00788,0.00787,0.00785,0.00784,0.00783,0.00782,0.0078,0.00779,0.00778,0.00776,0.00775,0.00774,0.00773,0.00771,0.0077,0.00769,0.00768,0.00766,0.00765,0.00764,0.00763,0.00761,0.0076,0.00759,0.00758,0.00756,0.00755,0.00754,
0.00753,0.00751,0.0075,0.00749,0.00748,0.00746,0.00745,0.00744,0.00743,0.00742,0.0074,0.00739,0.00738,0.00737,0.00735,0.00734,0.00733,0.00732,0.00731,0.00729,0.00728,0.00727,0.00726,0.00725,0.00723,0.00722,0.00721,0.0072,0.00719,0.00717,0.00716,0.00715,0.00714,0.00713,0.00712,0.0071,0.00709,0.00708,0.00707,0.00706,0.00705,0.00703,0.00702,0.00701,0.007,0.00699,0.00698,0.00697,0.00695,0.00694,0.00693,0.00692,0.00691,0.0069,0.00689,0.00687,0.00686,0.00685,0.00684,0.00683,0.00682,0.00681,0.00679,0.00678,0.00677,0.00676,0.00675,0.00674,0.00673,0.00672,0.00671,0.00669,0.00668,0.00667,0.00666,0.00665,0.00664,0.00663,0.00662,0.00661,0.0066,0.00659,0.00657,0.00656,0.00655,0.00654,0.00653,0.00652,0.00651,0.0065,0.00649,0.00648,0.00647,0.00646,0.00645,0.00643,0.00642,0.00641,0.0064,0.00639,
0.00638,0.00637,0.00636,0.00635,0.00634,0.00633,0.00632,0.00631,0.0063,0.00629,0.00628,0.00627,0.00626,0.00625,0.00624,0.00623,0.00622,0.00621,0.00619,0.00618,0.00617,0.00616,0.00615,0.00614,0.00613,0.00612,0.00611,0.0061,0.00609,0.00608,0.00607,0.00606,0.00605,0.00604,0.00603,0.00602,0.00601,0.006,0.00599,0.00598,0.00597,0.00596,0.00595,0.00594,0.00593,0.00592,0.00591,0.0059,0.0059,0.00589,0.00588,0.00587,0.00586,0.00585,0.00584,0.00583,0.00582,0.00581,0.0058,0.00579,0.00578,0.00577,0.00576,0.00575,0.00574,0.00573,0.00572,0.00571,0.0057,0.00569,0.00568,0.00568,0.00567,0.00566,0.00565,0.00564,0.00563,0.00562,0.00561,0.0056,0.00559,0.00558,0.00557,0.00556,0.00555,0.00555,0.00554,0.00553,0.00552,0.00551,0.0055,0.00549,0.00548,0.00547,0.00546,0.00545,0.00544,0.00544,0.00543,0.00542,
0.00541,0.0054,0.00539,0.00538,0.00537,0.00536,0.00536,0.00535,0.00534,0.00533,0.00532,0.00531,0.0053,0.00529,0.00528,0.00528,0.00527,0.00526,0.00525,0.00524,0.00523,0.00522,0.00522,0.00521,0.0052,0.00519,0.00518,0.00517,0.00516,0.00516,0.00515,0.00514,0.00513,0.00512,0.00511,0.0051,0.0051,0.00509,0.00508,0.00507,0.00506,0.00505,0.00505,0.00504,0.00503,0.00502,0.00501,0.005,0.005,0.00499,0.00498,0.00497,0.00496,0.00495,0.00495,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00486,0.00486,0.00485,0.00484,0.00483,0.00482,0.00482,0.00481,0.0048,0.00479,0.00478,0.00478,0.00477,0.00476,0.00475,0.00474,0.00474,0.00473,0.00472,0.00471,0.00471,0.0047,0.00469,0.00468,0.00467,0.00467,0.00466,0.00465,0.00464,0.00464,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459};
constexpr double stored_lower_incomplete_gamma_values_n5[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,2e-05,3e-05,3e-05,3e-05,4e-05,4e-05,5e-05,5e-05,6e-05,6e-05,7e-05,8e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00012,0.00013,0.00014,0.00016,0.00017,0.00018,0.00019,0.0002,0.00022,0.00023,0.00024,0.00026,0.00027,0.00029,0.00031,0.00032,0.00034,0.00036,0.00038,0.0004,0.00042,0.00044,0.00046,0.00049,0.00051,0.00053,0.00056,0.00058,0.00061,0.00064,0.00066,0.00069,0.00072,0.00075,0.00078,0.00081,0.00084,0.00088,0.00091,0.00095,0.00098,0.00102,0.00105,0.00109,0.00113,0.00117,0.00121,0.00125,0.0013,0.00134,0.00138,0.00143,0.00147,0.00152,0.00157,0.00162,0.00167,0.00172,0.00177,0.00182,0.00188,
0.00193,0.00199,0.00204,0.0021,0.00216,0.00222,0.00228,0.00234,0.00241,0.00247,0.00254,0.0026,0.00267,0.00274,0.00281,0.00288,0.00295,0.00302,0.00309,0.00317,0.00325,0.00332,0.0034,0.00348,0.00356,0.00364,0.00373,0.00381,0.0039,0.00398,0.00407,0.00416,0.00425,0.00434,0.00443,0.00453,0.00462,0.00472,0.00481,0.00491,0.00501,0.00511,0.00522,0.00532,0.00542,0.00553,0.00564,0.00575,0.00586,0.00597,0.00608,0.00619,0.00631,0.00643,0.00654,0.00666,0.00678,0.0069,0.00703,0.00715,0.00728,0.0074,0.00753,0.00766,0.00779,0.00793,0.00806,0.00819,0.00833,0.00847,0.00861,0.00875,0.00889,0.00903,0.00918,0.00932,0.00947,0.00962,0.00977,0.00992,0.01008,0.01023,0.01039,0.01055,0.0107,0.01086,0.01103,0.01119,0.01135,0.01152,0.01169,0.01186,0.01203,0.0122,0.01237,0.01255,0.01272,0.0129,0.01308,0.01326,
0.01345,0.01363,0.01381,0.014,0.01419,0.01438,0.01457,0.01476,0.01496,0.01515,0.01535,0.01555,0.01575,0.01595,0.01616,0.01636,0.01657,0.01677,0.01698,0.0172,0.01741,0.01762,0.01784,0.01805,0.01827,0.01849,0.01872,0.01894,0.01916,0.01939,0.01962,0.01985,0.02008,0.02031,0.02055,0.02078,0.02102,0.02126,0.0215,0.02174,0.02198,0.02223,0.02248,0.02273,0.02298,0.02323,0.02348,0.02373,0.02399,0.02425,0.02451,0.02477,0.02503,0.0253,0.02556,0.02583,0.0261,0.02637,0.02664,0.02692,0.02719,0.02747,0.02775,0.02803,0.02831,0.02859,0.02888,0.02917,0.02945,0.02974,0.03004,0.03033,0.03062,0.03092,0.03122,0.03152,0.03182,0.03212,0.03243,0.03273,0.03304,0.03335,0.03366,0.03397,0.03429,0.03461,0.03492,0.03524,0.03556,0.03589,0.03621,0.03654,0.03686,0.03719,0.03752,0.03785,0.03819,0.03852,0.03886,0.0392,
0.03954,0.03988,0.04023,0.04057,0.04092,0.04127,0.04162,0.04197,0.04232,0.04268,0.04303,0.04339,0.04375,0.04411,0.04448,0.04484,0.04521,0.04558,0.04595,0.04632,0.04669,0.04707,0.04744,0.04782,0.0482,0.04858,0.04896,0.04935,0.04973,0.05012,0.05051,0.0509,0.0513,0.05169,0.05209,0.05248,0.05288,0.05328,0.05369,0.05409,0.0545,0.0549,0.05531,0.05572,0.05613,0.05655,0.05696,0.05738,0.0578,0.05822,0.05864,0.05907,0.05949,0.05992,0.06035,0.06078,0.06121,0.06164,0.06208,0.06251,0.06295,0.06339,0.06383,0.06427,0.06472,0.06516,0.06561,0.06606,0.06651,0.06697,0.06742,0.06788,0.06833,0.06879,0.06925,0.06971,0.07018,0.07064,0.07111,0.07158,0.07205,0.07252,0.07299,0.07347,0.07395,0.07442,0.0749,0.07539,0.07587,0.07635,0.07684,0.07733,0.07782,0.07831,0.0788,0.07929,0.07979,0.08028,0.08078,0.08128,
0.08179,0.08229,0.08279,0.0833,0.08381,0.08432,0.08483,0.08534,0.08586,0.08637,0.08689,0.08741,0.08793,0.08845,0.08897,0.0895,0.09003,0.09055,0.09108,0.09162,0.09215,0.09268,0.09322,0.09376,0.09429,0.09484,0.09538,0.09592,0.09647,0.09701,0.09756,0.09811,0.09866,0.09921,0.09977,0.10032,0.10088,0.10144,0.102,0.10256,0.10312,0.10369,0.10426,0.10482,0.10539,0.10596,0.10654,0.10711,0.10768,0.10826,0.10884,0.10942,0.11,0.11058,0.11117,0.11175,0.11234,0.11293,0.11352,0.11411,0.1147,0.1153,0.11589,0.11649,0.11709,0.11769,0.11829,0.11889,0.1195,0.1201,0.12071,0.12132,0.12193,0.12254,0.12316,0.12377,0.12439,0.125,0.12562,0.12624,0.12687,0.12749,0.12811,0.12874,0.12937,0.13,0.13063,0.13126,0.13189,0.13253,0.13316,0.1338,0.13444,0.13508,0.13572,0.13636,0.13701,0.13765,0.1383,0.13895,
0.1396,0.14025,0.1409,0.14156,0.14221,0.14287,0.14353,0.14418,0.14485,0.14551,0.14617,0.14684,0.1475,0.14817,0.14884,0.14951,0.15018,0.15085,0.15153,0.1522,0.15288,0.15356,0.15424,0.15492,0.1556,0.15628,0.15697,0.15766,0.15834,0.15903,0.15972,0.16041,0.16111,0.1618,0.1625,0.16319,0.16389,0.16459,0.16529,0.16599,0.16669,0.1674,0.1681,0.16881,0.16952,0.17023,0.17094,0.17165,0.17237,0.17308,0.1738,0.17451,0.17523,0.17595,0.17667,0.17739,0.17812,0.17884,0.17957,0.18029,0.18102,0.18175,0.18248,0.18321,0.18395,0.18468,0.18542,0.18615,0.18689,0.18763,0.18837,0.18911,0.18986,0.1906,0.19135,0.19209,0.19284,0.19359,0.19434,0.19509,0.19584,0.1966,0.19735,0.19811,0.19886,0.19962,0.20038,0.20114,0.2019,0.20267,0.20343,0.2042,0.20496,0.20573,0.2065,0.20727,0.20804,0.20881,0.20958,0.21036,
0.21113,0.21191,0.21269,0.21347,0.21425,0.21503,0.21581,0.21659,0.21738,0.21816,0.21895,0.21974,0.22053,0.22132,0.22211,0.2229,0.22369,0.22449,0.22528,0.22608,0.22688,0.22767,0.22847,0.22928,0.23008,0.23088,0.23168,0.23249,0.23329,0.2341,0.23491,0.23572,0.23653,0.23734,0.23815,0.23897,0.23978,0.24059,0.24141,0.24223,0.24305,0.24387,0.24469,0.24551,0.24633,0.24715,0.24798,0.2488,0.24963,0.25046,0.25129,0.25212,0.25295,0.25378,0.25461,0.25544,0.25628,0.25711,0.25795,0.25879,0.25963,0.26046,0.2613,0.26215,0.26299,0.26383,0.26467,0.26552,0.26637,0.26721,0.26806,0.26891,0.26976,0.27061,0.27146,0.27231,0.27317,0.27402,0.27488,0.27573,0.27659,0.27745,0.2783,0.27916,0.28002,0.28089,0.28175,0.28261,0.28348,0.28434,0.28521,0.28607,0.28694,0.28781,0.28868,0.28955,0.29042,0.29129,0.29217,0.29304,
0.29391,0.29479,0.29567,0.29654,0.29742,0.2983,0.29918,0.30006,0.30094,0.30182,0.30271,0.30359,0.30448,0.30536,0.30625,0.30713,0.30802,0.30891,0.3098,0.31069,0.31158,0.31247,0.31337,0.31426,0.31515,0.31605,0.31695,0.31784,0.31874,0.31964,0.32054,0.32144,0.32234,0.32324,0.32414,0.32504,0.32595,0.32685,0.32776,0.32866,0.32957,0.33048,0.33138,0.33229,0.3332,0.33411,0.33502,0.33594,0.33685,0.33776,0.33867,0.33959,0.3405,0.34142,0.34234,0.34326,0.34417,0.34509,0.34601,0.34693,0.34785,0.34877,0.3497,0.35062,0.35154,0.35247,0.35339,0.35432,0.35525,0.35617,0.3571,0.35803,0.35896,0.35989,0.36082,0.36175,0.36268,0.36361,0.36455,0.36548,0.36641,0.36735,0.36828,0.36922,0.37016,0.37109,0.37203,0.37297,0.37391,0.37485,0.37579,0.37673,0.37767,0.37862,0.37956,0.3805,0.38145,0.38239,0.38334,0.38428,
0.38523,0.38618,0.38712,0.38807,0.38902,0.38997,0.39092,0.39187,0.39282,0.39377,0.39473,0.39568,0.39663,0.39759,0.39854,0.3995,0.40045,0.40141,0.40236,0.40332,0.40428,0.40524,0.4062,0.40716,0.40811,0.40908,0.41004,0.411,0.41196,0.41292,0.41388,0.41485,0.41581,0.41678,0.41774,0.41871,0.41967,0.42064,0.42161,0.42257,0.42354,0.42451,0.42548,0.42645,0.42742,0.42839,0.42936,0.43033,0.4313,0.43227,0.43325,0.43422,0.43519,0.43617,0.43714,0.43812,0.43909,0.44007,0.44104,0.44202,0.443,0.44398,0.44495,0.44593,0.44691,0.44789,0.44887,0.44985,0.45083,0.45181,0.45279,0.45377,0.45476,0.45574,0.45672,0.4577,0.45869,0.45967,0.46066,0.46164,0.46263,0.46361,0.4646,0.46559,0.46657,0.46756,0.46855,0.46953,0.47052,0.47151,0.4725,0.47349,0.47448,0.47547,0.47646,0.47745,0.47844,0.47943,0.48043,0.48142,
0.48241,0.4834,0.4844,0.48539,0.48638,0.48738,0.48837,0.48937,0.49036,0.49136,0.49235,0.49335,0.49435,0.49534,0.49634,0.49734,0.49834,0.49933,0.50033,0.50133,0.50233,0.50333,0.50433,0.50533,0.50633,0.50733,0.50833,0.50933,0.51033,0.51133,0.51233,0.51333,0.51434,0.51534,0.51634,0.51735,0.51835,0.51935,0.52036,0.52136,0.52236,0.52337,0.52437,0.52538,0.52638,0.52739,0.52839,0.5294,0.53041,0.53141,0.53242,0.53343,0.53443,0.53544,0.53645,0.53746,0.53846,0.53947,0.54048,0.54149,0.5425,0.54351,0.54452,0.54552,0.54653,0.54754,0.54855,0.54956,0.55057,0.55159,0.5526,0.55361,0.55462,0.55563,0.55664,0.55765,0.55866,0.55968,0.56069,0.5617,0.56271,0.56372,0.56474,0.56575,0.56676,0.56778,0.56879,0.5698,0.57082,0.57183,0.57284,0.57386,0.57487,0.57589,0.5769,0.57792,0.57893,0.57995,0.58096,0.58198,
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1.91935,1.91946,1.91957,1.91968,1.9198,1.91991,1.92002,1.92013,1.92024,1.92035,1.92046,1.92058,1.92069,1.9208,1.92091,1.92102,1.92113,1.92124,1.92135,1.92146,1.92157,1.92168,1.92179,1.9219,1.922,1.92211,1.92222,1.92233,1.92244,1.92255,1.92266,1.92276,1.92287,1.92298,1.92309,1.9232,1.9233,1.92341,1.92352,1.92362,1.92373,1.92384,1.92394,1.92405,1.92416,1.92426,1.92437,1.92447,1.92458,1.92469,1.92479,1.9249,1.925,1.92511,1.92521,1.92532,1.92542,1.92552,1.92563,1.92573,1.92584,1.92594,1.92604,1.92615,1.92625,1.92636,1.92646,1.92656,1.92666,1.92677,1.92687,1.92697,1.92707,1.92718,1.92728,1.92738,1.92748,1.92758,1.92769,1.92779,1.92789,1.92799,1.92809,1.92819,1.92829,1.92839,1.92849,1.92859,1.92869,1.92879,1.92889,1.92899,1.92909,1.92919,1.92929,1.92939,1.92949,1.92959,1.92969,1.92979,
1.92989,1.92999,1.93008,1.93018,1.93028,1.93038,1.93048,1.93057,1.93067,1.93077,1.93087,1.93096,1.93106,1.93116,1.93125,1.93135,1.93145,1.93154,1.93164,1.93174,1.93183,1.93193,1.93202,1.93212,1.93222,1.93231,1.93241,1.9325,1.9326,1.93269,1.93279,1.93288,1.93298,1.93307,1.93316,1.93326,1.93335,1.93345,1.93354,1.93363,1.93373,1.93382,1.93391,1.93401,1.9341,1.93419,1.93429,1.93438,1.93447,1.93456,1.93466,1.93475,1.93484,1.93493,1.93502,1.93512,1.93521,1.9353,1.93539,1.93548,1.93557,1.93566,1.93575,1.93584,1.93593,1.93603,1.93612,1.93621,1.9363,1.93639,1.93648,1.93657,1.93666,1.93674,1.93683,1.93692,1.93701,1.9371,1.93719,1.93728,1.93737,1.93746,1.93754,1.93763,1.93772,1.93781,1.9379,1.93799,1.93807,1.93816,1.93825,1.93834,1.93842,1.93851,1.9386,1.93868,1.93877,1.93886,1.93894,1.93903,
1.93912,1.9392,1.93929,1.93937,1.93946,1.93955,1.93963,1.93972,1.9398,1.93989,1.93997,1.94006,1.94014,1.94023,1.94031,1.9404,1.94048,1.94057,1.94065,1.94074,1.94082,1.9409,1.94099,1.94107,1.94115,1.94124,1.94132,1.9414,1.94149,1.94157,1.94165,1.94174,1.94182,1.9419,1.94198,1.94207,1.94215,1.94223,1.94231,1.94239,1.94248,1.94256,1.94264,1.94272,1.9428,1.94288,1.94296,1.94305,1.94313,1.94321,1.94329,1.94337,1.94345,1.94353,1.94361,1.94369,1.94377,1.94385,1.94393,1.94401,1.94409,1.94417,1.94425,1.94433,1.94441,1.94449,1.94456,1.94464,1.94472,1.9448,1.94488,1.94496,1.94504,1.94511,1.94519,1.94527,1.94535,1.94543,1.9455,1.94558,1.94566,1.94574,1.94581,1.94589,1.94597,1.94605,1.94612,1.9462,1.94628,1.94635,1.94643,1.94651,1.94658,1.94666,1.94673,1.94681,1.94689,1.94696,1.94704,1.94711,
1.94719,1.94726,1.94734,1.94741,1.94749,1.94756,1.94764,1.94771,1.94779,1.94786,1.94794,1.94801,1.94809,1.94816,1.94823,1.94831,1.94838,1.94845,1.94853,1.9486,1.94868,1.94875,1.94882,1.94889,1.94897,1.94904,1.94911,1.94919,1.94926,1.94933,1.9494,1.94948,1.94955,1.94962,1.94969,1.94976,1.94984,1.94991,1.94998,1.95005,1.95012,1.95019,1.95027,1.95034,1.95041,1.95048,1.95055,1.95062,1.95069,1.95076,1.95083,1.9509,1.95097,1.95104,1.95111,1.95118,1.95125,1.95132,1.95139,1.95146,1.95153,1.9516,1.95167,1.95174,1.95181,1.95188,1.95195,1.95202,1.95208,1.95215,1.95222,1.95229,1.95236,1.95243,1.95249,1.95256,1.95263,1.9527,1.95277,1.95283,1.9529,1.95297,1.95304,1.9531,1.95317,1.95324,1.95331,1.95337,1.95344,1.95351,1.95357,1.95364,1.95371,1.95377,1.95384,1.95391,1.95397,1.95404,1.9541,1.95417,
1.95424,1.9543,1.95437,1.95443,1.9545,1.95456,1.95463,1.95469,1.95476,1.95482,1.95489,1.95495,1.95502,1.95508,1.95515,1.95521,1.95528,1.95534,1.95541,1.95547,1.95553,1.9556,1.95566,1.95573,1.95579,1.95585,1.95592,1.95598,1.95604,1.95611,1.95617,1.95623,1.9563,1.95636,1.95642,1.95648,1.95655,1.95661,1.95667,1.95673,1.9568,1.95686,1.95692,1.95698,1.95704,1.95711,1.95717,1.95723,1.95729,1.95735,1.95741,1.95748,1.95754,1.9576,1.95766,1.95772,1.95778,1.95784,1.9579,1.95796,1.95802,1.95808,1.95815,1.95821,1.95827,1.95833,1.95839,1.95845,1.95851,1.95857,1.95863,1.95869,1.95875,1.9588,1.95886,1.95892,1.95898,1.95904,1.9591,1.95916,1.95922,1.95928,1.95934,1.9594,1.95945,1.95951,1.95957,1.95963,1.95969,1.95975,1.9598,1.95986,1.95992,1.95998,1.96004,1.96009,1.96015,1.96021,1.96027,1.96032};
constexpr double stored_gamma_values_n5[] = {1.0,1.0,1.0,1.0,1.0,0.99999,0.99999,0.99999,0.99999,0.99998,0.99998,0.99997,0.99997,0.99996,0.99996,0.99995,0.99995,0.99994,0.99993,0.99993,0.99992,0.99991,0.9999,0.99989,0.99988,0.99987,0.99986,0.99985,0.99984,0.99983,0.99981,0.9998,0.99979,0.99978,0.99976,0.99975,0.99973,0.99972,0.9997,0.99969,0.99967,0.99965,0.99964,0.99962,0.9996,0.99958,0.99957,0.99955,0.99953,0.99951,0.99949,0.99947,0.99945,0.99943,0.9994,0.99938,0.99936,0.99934,0.99931,0.99929,0.99927,0.99924,0.99922,0.99919,0.99917,0.99914,0.99911,0.99909,0.99906,0.99903,0.99901,0.99898,0.99895,0.99892,0.99889,0.99886,0.99883,0.9988,0.99877,0.99874,0.99871,0.99867,0.99864,0.99861,0.99858,0.99854,0.99851,0.99847,0.99844,0.9984,0.99837,0.99833,0.9983,0.99826,0.99822,0.99819,0.99815,0.99811,0.99807,0.99803,
0.998,0.99796,0.99792,0.99788,0.99784,0.9978,0.99775,0.99771,0.99767,0.99763,0.99759,0.99754,0.9975,0.99746,0.99741,0.99737,0.99732,0.99728,0.99723,0.99718,0.99714,0.99709,0.99704,0.997,0.99695,0.9969,0.99685,0.9968,0.99676,0.99671,0.99666,0.99661,0.99656,0.9965,0.99645,0.9964,0.99635,0.9963,0.99624,0.99619,0.99614,0.99608,0.99603,0.99598,0.99592,0.99587,0.99581,0.99576,0.9957,0.99564,0.99559,0.99553,0.99547,0.99541,0.99536,0.9953,0.99524,0.99518,0.99512,0.99506,0.995,0.99494,0.99488,0.99482,0.99476,0.99469,0.99463,0.99457,0.99451,0.99444,0.99438,0.99431,0.99425,0.99419,0.99412,0.99406,0.99399,0.99392,0.99386,0.99379,0.99372,0.99366,0.99359,0.99352,0.99345,0.99339,0.99332,0.99325,0.99318,0.99311,0.99304,0.99297,0.9929,0.99283,0.99275,0.99268,0.99261,0.99254,0.99247,0.99239,
0.99232,0.99225,0.99217,0.9921,0.99202,0.99195,0.99187,0.9918,0.99172,0.99164,0.99157,0.99149,0.99141,0.99134,0.99126,0.99118,0.9911,0.99102,0.99094,0.99086,0.99078,0.9907,0.99062,0.99054,0.99046,0.99038,0.9903,0.99022,0.99014,0.99005,0.98997,0.98989,0.9898,0.98972,0.98964,0.98955,0.98947,0.98938,0.9893,0.98921,0.98913,0.98904,0.98895,0.98887,0.98878,0.98869,0.9886,0.98852,0.98843,0.98834,0.98825,0.98816,0.98807,0.98798,0.98789,0.9878,0.98771,0.98762,0.98753,0.98744,0.98735,0.98725,0.98716,0.98707,0.98698,0.98688,0.98679,0.9867,0.9866,0.98651,0.98641,0.98632,0.98622,0.98613,0.98603,0.98593,0.98584,0.98574,0.98564,0.98555,0.98545,0.98535,0.98525,0.98515,0.98506,0.98496,0.98486,0.98476,0.98466,0.98456,0.98446,0.98436,0.98426,0.98415,0.98405,0.98395,0.98385,0.98375,0.98364,0.98354,
0.98344,0.98333,0.98323,0.98313,0.98302,0.98292,0.98281,0.98271,0.9826,0.9825,0.98239,0.98228,0.98218,0.98207,0.98196,0.98186,0.98175,0.98164,0.98153,0.98142,0.98131,0.98121,0.9811,0.98099,0.98088,0.98077,0.98066,0.98055,0.98043,0.98032,0.98021,0.9801,0.97999,0.97988,0.97976,0.97965,0.97954,0.97942,0.97931,0.9792,0.97908,0.97897,0.97885,0.97874,0.97862,0.97851,0.97839,0.97828,0.97816,0.97805,0.97793,0.97781,0.97769,0.97758,0.97746,0.97734,0.97722,0.9771,0.97699,0.97687,0.97675,0.97663,0.97651,0.97639,0.97627,0.97615,0.97603,0.97591,0.97579,0.97566,0.97554,0.97542,0.9753,0.97518,0.97505,0.97493,0.97481,0.97468,0.97456,0.97443,0.97431,0.97419,0.97406,0.97394,0.97381,0.97369,0.97356,0.97343,0.97331,0.97318,0.97305,0.97293,0.9728,0.97267,0.97255,0.97242,0.97229,0.97216,0.97203,0.9719,
0.97177,0.97165,0.97152,0.97139,0.97126,0.97113,0.97099,0.97086,0.97073,0.9706,0.97047,0.97034,0.97021,0.97007,0.96994,0.96981,0.96968,0.96954,0.96941,0.96928,0.96914,0.96901,0.96887,0.96874,0.96861,0.96847,0.96833,0.9682,0.96806,0.96793,0.96779,0.96766,0.96752,0.96738,0.96724,0.96711,0.96697,0.96683,0.96669,0.96656,0.96642,0.96628,0.96614,0.966,0.96586,0.96572,0.96558,0.96544,0.9653,0.96516,0.96502,0.96488,0.96474,0.9646,0.96446,0.96432,0.96417,0.96403,0.96389,0.96375,0.9636,0.96346,0.96332,0.96317,0.96303,0.96289,0.96274,0.9626,0.96245,0.96231,0.96216,0.96202,0.96187,0.96173,0.96158,0.96143,0.96129,0.96114,0.961,0.96085,0.9607,0.96055,0.96041,0.96026,0.96011,0.95996,0.95981,0.95967,0.95952,0.95937,0.95922,0.95907,0.95892,0.95877,0.95862,0.95847,0.95832,0.95817,0.95802,0.95787,
0.95771,0.95756,0.95741,0.95726,0.95711,0.95695,0.9568,0.95665,0.9565,0.95634,0.95619,0.95604,0.95588,0.95573,0.95557,0.95542,0.95527,0.95511,0.95496,0.9548,0.95465,0.95449,0.95433,0.95418,0.95402,0.95387,0.95371,0.95355,0.9534,0.95324,0.95308,0.95292,0.95277,0.95261,0.95245,0.95229,0.95213,0.95197,0.95182,0.95166,0.9515,0.95134,0.95118,0.95102,0.95086,0.9507,0.95054,0.95038,0.95022,0.95006,0.94989,0.94973,0.94957,0.94941,0.94925,0.94909,0.94892,0.94876,0.9486,0.94844,0.94827,0.94811,0.94795,0.94778,0.94762,0.94745,0.94729,0.94713,0.94696,0.9468,0.94663,0.94647,0.9463,0.94614,0.94597,0.9458,0.94564,0.94547,0.94531,0.94514,0.94497,0.94481,0.94464,0.94447,0.9443,0.94414,0.94397,0.9438,0.94363,0.94347,0.9433,0.94313,0.94296,0.94279,0.94262,0.94245,0.94228,0.94211,0.94194,0.94177,
0.9416,0.94143,0.94126,0.94109,0.94092,0.94075,0.94058,0.94041,0.94023,0.94006,0.93989,0.93972,0.93955,0.93937,0.9392,0.93903,0.93886,0.93868,0.93851,0.93834,0.93816,0.93799,0.93781,0.93764,0.93747,0.93729,0.93712,0.93694,0.93677,0.93659,0.93642,0.93624,0.93607,0.93589,0.93571,0.93554,0.93536,0.93518,0.93501,0.93483,0.93465,0.93448,0.9343,0.93412,0.93394,0.93377,0.93359,0.93341,0.93323,0.93305,0.93288,0.9327,0.93252,0.93234,0.93216,0.93198,0.9318,0.93162,0.93144,0.93126,0.93108,0.9309,0.93072,0.93054,0.93036,0.93018,0.93,0.92982,0.92963,0.92945,0.92927,0.92909,0.92891,0.92873,0.92854,0.92836,0.92818,0.928,0.92781,0.92763,0.92745,0.92726,0.92708,0.9269,0.92671,0.92653,0.92634,0.92616,0.92598,0.92579,0.92561,0.92542,0.92524,0.92505,0.92487,0.92468,0.92449,0.92431,0.92412,0.92394,
0.92375,0.92356,0.92338,0.92319,0.923,0.92282,0.92263,0.92244,0.92226,0.92207,0.92188,0.92169,0.92151,0.92132,0.92113,0.92094,0.92075,0.92056,0.92038,0.92019,0.92,0.91981,0.91962,0.91943,0.91924,0.91905,0.91886,0.91867,0.91848,0.91829,0.9181,0.91791,0.91772,0.91753,0.91734,0.91714,0.91695,0.91676,0.91657,0.91638,0.91619,0.916,0.9158,0.91561,0.91542,0.91523,0.91503,0.91484,0.91465,0.91446,0.91426,0.91407,0.91388,0.91368,0.91349,0.91329,0.9131,0.91291,0.91271,0.91252,0.91232,0.91213,0.91193,0.91174,0.91154,0.91135,0.91115,0.91096,0.91076,0.91057,0.91037,0.91018,0.90998,0.90978,0.90959,0.90939,0.90919,0.909,0.9088,0.9086,0.90841,0.90821,0.90801,0.90782,0.90762,0.90742,0.90722,0.90702,0.90683,0.90663,0.90643,0.90623,0.90603,0.90584,0.90564,0.90544,0.90524,0.90504,0.90484,0.90464,
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modules/calib3d/src/usac/homography_solver.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#ifdef HAVE_EIGEN
#include <Eigen/Eigen>
#endif
namespace cv { namespace usac {
class HomographyMinimalSolver4ptsGEMImpl : public HomographyMinimalSolver4ptsGEM {
private:
const Mat * points_mat;
const float * const points;
public:
explicit HomographyMinimalSolver4ptsGEMImpl (const Mat &points_) :
points_mat(&points_), points ((float*) points_.data) {}
int estimate (const std::vector<int>& sample, std::vector<Mat> &models) const override {
// OpenCV RHO:
const int smpl0 = 4*sample[0], smpl1 = 4*sample[1], smpl2 = 4*sample[2], smpl3 = 4*sample[3];
const auto x0 = points[smpl0], y0 = points[smpl0+1], X0 = points[smpl0+2], Y0 = points[smpl0+3];
const auto x1 = points[smpl1], y1 = points[smpl1+1], X1 = points[smpl1+2], Y1 = points[smpl1+3];
const auto x2 = points[smpl2], y2 = points[smpl2+1], X2 = points[smpl2+2], Y2 = points[smpl2+3];
const auto x3 = points[smpl3], y3 = points[smpl3+1], X3 = points[smpl3+2], Y3 = points[smpl3+3];
const double x0X0 = x0*X0, x1X1 = x1*X1, x2X2 = x2*X2, x3X3 = x3*X3;
const double x0Y0 = x0*Y0, x1Y1 = x1*Y1, x2Y2 = x2*Y2, x3Y3 = x3*Y3;
const double y0X0 = y0*X0, y1X1 = y1*X1, y2X2 = y2*X2, y3X3 = y3*X3;
const double y0Y0 = y0*Y0, y1Y1 = y1*Y1, y2Y2 = y2*Y2, y3Y3 = y3*Y3;
double minor[2][4] = {{x0-x2, x1-x2, x2, x3-x2},
{y0-y2, y1-y2, y2, y3-y2}};
double major[3][8] = {{x2X2-x0X0, x2X2-x1X1, -x2X2, x2X2-x3X3, x2Y2-x0Y0, x2Y2-x1Y1, -x2Y2, x2Y2-x3Y3},
{y2X2-y0X0, y2X2-y1X1, -y2X2, y2X2-y3X3, y2Y2-y0Y0, y2Y2-y1Y1, -y2Y2, y2Y2-y3Y3},
{X0-X2 , X1-X2 , X2 , X3-X2 , Y0-Y2 , Y1-Y2 , Y2 , Y3-Y2 }};
/**
* int i;
* for(i=0;i<8;i++) major[2][i]=-major[2][i];
* Eliminate column 0 of rows 1 and 3
* R(1)=(x0-x2)*R(1)-(x1-x2)*R(0), y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
* R(3)=(x0-x2)*R(3)-(x3-x2)*R(0), y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
*/
double scalar1=minor[0][0], scalar2=minor[0][1];
minor[1][1]=minor[1][1]*scalar1-minor[1][0]*scalar2;
major[0][1]=major[0][1]*scalar1-major[0][0]*scalar2;
major[1][1]=major[1][1]*scalar1-major[1][0]*scalar2;
major[2][1]=major[2][1]*scalar1-major[2][0]*scalar2;
major[0][5]=major[0][5]*scalar1-major[0][4]*scalar2;
major[1][5]=major[1][5]*scalar1-major[1][4]*scalar2;
major[2][5]=major[2][5]*scalar1-major[2][4]*scalar2;
scalar2=minor[0][3];
minor[1][3]=minor[1][3]*scalar1-minor[1][0]*scalar2;
major[0][3]=major[0][3]*scalar1-major[0][0]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][0]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][0]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][4]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][4]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][4]*scalar2;
/**
* Eliminate column 1 of rows 0 and 3
* R(3)=y1'*R(3)-y3'*R(1)
* R(0)=y1'*R(0)-(y0-y2)*R(1)
*/
scalar1=minor[1][1];scalar2=minor[1][3];
major[0][3]=major[0][3]*scalar1-major[0][1]*scalar2;
major[1][3]=major[1][3]*scalar1-major[1][1]*scalar2;
major[2][3]=major[2][3]*scalar1-major[2][1]*scalar2;
major[0][7]=major[0][7]*scalar1-major[0][5]*scalar2;
major[1][7]=major[1][7]*scalar1-major[1][5]*scalar2;
major[2][7]=major[2][7]*scalar1-major[2][5]*scalar2;
scalar2=minor[1][0];
minor[0][0]=minor[0][0]*scalar1-minor[0][1]*scalar2;
major[0][0]=major[0][0]*scalar1-major[0][1]*scalar2;
major[1][0]=major[1][0]*scalar1-major[1][1]*scalar2;
major[2][0]=major[2][0]*scalar1-major[2][1]*scalar2;
major[0][4]=major[0][4]*scalar1-major[0][5]*scalar2;
major[1][4]=major[1][4]*scalar1-major[1][5]*scalar2;
major[2][4]=major[2][4]*scalar1-major[2][5]*scalar2;
/**
* Eliminate columns 0 and 1 of row 2
* R(0)/=x0'
* R(1)/=y1'
* R(2)-= (x2*R(0) + y2*R(1))
*/
scalar1=1.0f/minor[0][0];
major[0][0]*=scalar1;
major[1][0]*=scalar1;
major[2][0]*=scalar1;
major[0][4]*=scalar1;
major[1][4]*=scalar1;
major[2][4]*=scalar1;
scalar1=1.0f/minor[1][1];
major[0][1]*=scalar1;
major[1][1]*=scalar1;
major[2][1]*=scalar1;
major[0][5]*=scalar1;
major[1][5]*=scalar1;
major[2][5]*=scalar1;
scalar1=minor[0][2];scalar2=minor[1][2];
major[0][2]-=major[0][0]*scalar1+major[0][1]*scalar2;
major[1][2]-=major[1][0]*scalar1+major[1][1]*scalar2;
major[2][2]-=major[2][0]*scalar1+major[2][1]*scalar2;
major[0][6]-=major[0][4]*scalar1+major[0][5]*scalar2;
major[1][6]-=major[1][4]*scalar1+major[1][5]*scalar2;
major[2][6]-=major[2][4]*scalar1+major[2][5]*scalar2;
/* Only major matters now. R(3) and R(7) correspond to the hollowed-out rows. */
scalar1=major[0][7];
major[1][7]/=scalar1;
major[2][7]/=scalar1;
const double m17 = major[1][7], m27 = major[2][7];
scalar1=major[0][0];major[1][0]-=scalar1*m17;major[2][0]-=scalar1*m27;
scalar1=major[0][1];major[1][1]-=scalar1*m17;major[2][1]-=scalar1*m27;
scalar1=major[0][2];major[1][2]-=scalar1*m17;major[2][2]-=scalar1*m27;
scalar1=major[0][3];major[1][3]-=scalar1*m17;major[2][3]-=scalar1*m27;
scalar1=major[0][4];major[1][4]-=scalar1*m17;major[2][4]-=scalar1*m27;
scalar1=major[0][5];major[1][5]-=scalar1*m17;major[2][5]-=scalar1*m27;
scalar1=major[0][6];major[1][6]-=scalar1*m17;major[2][6]-=scalar1*m27;
/* One column left (Two in fact, but the last one is the homography) */
major[2][3]/=major[1][3];
const double m23 = major[2][3];
major[2][0]-=major[1][0]*m23;
major[2][1]-=major[1][1]*m23;
major[2][2]-=major[1][2]*m23;
major[2][4]-=major[1][4]*m23;
major[2][5]-=major[1][5]*m23;
major[2][6]-=major[1][6]*m23;
major[2][7]-=major[1][7]*m23;
// check if homography does not contain NaN values
for (int i = 0; i < 8; i++)
if (std::isnan(major[2][i])) return 0;
/* Homography is done. */
models = std::vector<Mat>(1, Mat_<double>(3,3));
auto * H_ = (double *) models[0].data;
H_[0]=major[2][0];
H_[1]=major[2][1];
H_[2]=major[2][2];
H_[3]=major[2][4];
H_[4]=major[2][5];
H_[5]=major[2][6];
H_[6]=major[2][7];
H_[7]=major[2][3];
H_[8]=1.0;
return 1;
}
int getMaxNumberOfSolutions () const override { return 1; }
int getSampleSize() const override { return 4; }
Ptr<MinimalSolver> clone () const override {
return makePtr<HomographyMinimalSolver4ptsGEMImpl>(*points_mat);
}
};
Ptr<HomographyMinimalSolver4ptsGEM> HomographyMinimalSolver4ptsGEM::create(const Mat &points_) {
return makePtr<HomographyMinimalSolver4ptsGEMImpl>(points_);
}
class HomographyNonMinimalSolverImpl : public HomographyNonMinimalSolver {
private:
const Mat * points_mat;
const Ptr<NormTransform> normTr;
public:
explicit HomographyNonMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), normTr (NormTransform::create(points_)) {}
/*
* Find Homography matrix using (weighted) non-minimal estimation.
* Use Principal Component Analysis. Use normalized points.
*/
int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat> &models,
const std::vector<double> &weights) const override {
if (sample_size < getMinimumRequiredSampleSize())
return 0;
Matx33d T1, T2;
Mat norm_points_;
normTr->getNormTransformation(norm_points_, sample, sample_size, T1, T2);
/*
* @norm_points is matrix 4 x inlier_size
* @weights is vector of inliers_size
* weights[i] is weight of i-th inlier
*/
const auto * const norm_points = (float *) norm_points_.data;
double a1[9] = {0, 0, -1, 0, 0, 0, 0, 0, 0},
a2[9] = {0, 0, 0, 0, 0, -1, 0, 0, 0},
AtA[81] = {0};
if (weights.empty()) {
for (int i = 0; i < sample_size; i++) {
const int smpl = 4*i;
const double x1 = norm_points[smpl ], y1 = norm_points[smpl+1],
x2 = norm_points[smpl+2], y2 = norm_points[smpl+3];
a1[0] = -x1;
a1[1] = -y1;
a1[6] = x2*x1;
a1[7] = x2*y1;
a1[8] = x2;
a2[3] = -x1;
a2[4] = -y1;
a2[6] = y2*x1;
a2[7] = y2*y1;
a2[8] = y2;
for (int j = 0; j < 9; j++)
for (int z = j; z < 9; z++)
AtA[j*9+z] += a1[j]*a1[z] + a2[j]*a2[z];
}
} else {
for (int i = 0; i < sample_size; i++) {
const int smpl = 4*i;
const double weight = weights[i];
const double x1 = norm_points[smpl ], y1 = norm_points[smpl+1],
x2 = norm_points[smpl+2], y2 = norm_points[smpl+3];
const double minus_weight_times_x1 = -weight * x1,
minus_weight_times_y1 = -weight * y1,
weight_times_x2 = weight * x2,
weight_times_y2 = weight * y2;
a1[0] = minus_weight_times_x1;
a1[1] = minus_weight_times_y1;
a1[2] = -weight;
a1[6] = weight_times_x2 * x1;
a1[7] = weight_times_x2 * y1;
a1[8] = weight_times_x2;
a2[3] = minus_weight_times_x1;
a2[4] = minus_weight_times_y1;
a2[5] = -weight;
a2[6] = weight_times_y2 * x1;
a2[7] = weight_times_y2 * y1;
a2[8] = weight_times_y2;
for (int j = 0; j < 9; j++)
for (int z = j; z < 9; z++)
AtA[j*9+z] += a1[j]*a1[z] + a2[j]*a2[z];
}
}
// copy symmetric part of covariance matrix
for (int j = 1; j < 9; j++)
for (int z = 0; z < j; z++)
AtA[j*9+z] = AtA[z*9+j];
#ifdef HAVE_EIGEN
Mat H = Mat_<double>(3,3);
Eigen::HouseholderQR<Eigen::Matrix<double, 9, 9>> qr((Eigen::Matrix<double, 9, 9> (AtA)));
const Eigen::Matrix<double, 9, 9> &Q = qr.householderQ();
// extract the last nullspace
Eigen::Map<Eigen::Matrix<double, 9, 1>>((double *)H.data) = Q.col(8);
#else
Matx<double, 9, 9> Vt;
Vec<double, 9> D;
if (! eigen(Matx<double, 9, 9>(AtA), D, Vt)) return 0;
Mat H = Mat(Vt.row(8).reshape<3,3>());
#endif
models = std::vector<Mat>{ T2.inv() * H * T1 };
return 1;
}
int getMinimumRequiredSampleSize() const override { return 4; }
int getMaxNumberOfSolutions () const override { return 1; }
Ptr<NonMinimalSolver> clone () const override {
return makePtr<HomographyNonMinimalSolverImpl>(*points_mat);
}
};
Ptr<HomographyNonMinimalSolver> HomographyNonMinimalSolver::create(const Mat &points_) {
return makePtr<HomographyNonMinimalSolverImpl>(points_);
}
class AffineMinimalSolverImpl : public AffineMinimalSolver {
private:
const Mat * points_mat;
const float * const points;
public:
explicit AffineMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), points((float *) points_.data) {}
/*
Affine transformation
x1 y1 1 0 0 0 a u1
0 0 0 x1 y1 1 b v1
x2 y2 1 0 0 0 c u2
0 0 0 x2 y2 1 * d = v2
x3 y3 1 0 0 0 e u3
0 0 0 x3 y3 1 f v3
*/
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
const int smpl1 = 4*sample[0], smpl2 = 4*sample[1], smpl3 = 4*sample[2];
const auto
x1 = points[smpl1], y1 = points[smpl1+1], u1 = points[smpl1+2], v1 = points[smpl1+3],
x2 = points[smpl2], y2 = points[smpl2+1], u2 = points[smpl2+2], v2 = points[smpl2+3],
x3 = points[smpl3], y3 = points[smpl3+1], u3 = points[smpl3+2], v3 = points[smpl3+3];
// covers degeneracy test when all 3 points are collinear.
// In this case denominator will be 0
double denominator = x1*y2 - x2*y1 - x1*y3 + x3*y1 + x2*y3 - x3*y2;
if (fabs(denominator) < FLT_EPSILON) // check if denominator is zero
return 0;
denominator = 1. / denominator;
double a = (u1*y2 - u2*y1 - u1*y3 + u3*y1 + u2*y3 - u3*y2) * denominator;
double b = -(u1*x2 - u2*x1 - u1*x3 + u3*x1 + u2*x3 - u3*x2) * denominator;
double c = u1 - a * x1 - b * y1; // ax1 + by1 + c = u1
double d = (v1*y2 - v2*y1 - v1*y3 + v3*y1 + v2*y3 - v3*y2) * denominator;
double e = -(v1*x2 - v2*x1 - v1*x3 + v3*x1 + v2*x3 - v3*x2) * denominator;
double f = v1 - d * x1 - e * y1; // dx1 + ey1 + f = v1
models[0] = Mat(Matx33d(a, b, c, d, e, f, 0, 0, 1));
return 1;
}
int getSampleSize() const override { return 3; }
int getMaxNumberOfSolutions () const override { return 1; }
Ptr<MinimalSolver> clone () const override {
return makePtr<AffineMinimalSolverImpl>(*points_mat);
}
};
Ptr<AffineMinimalSolver> AffineMinimalSolver::create(const Mat &points_) {
return makePtr<AffineMinimalSolverImpl>(points_);
}
class AffineNonMinimalSolverImpl : public AffineNonMinimalSolver {
private:
const Mat * points_mat;
const float * const points;
// const NormTransform<double> norm_transform;
public:
explicit AffineNonMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), points((float*) points_.data)
/*, norm_transform(points_)*/ {}
int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat> &models,
const std::vector<double> &weights) const override {
// surprisingly normalization of points does not improve the output model
// Mat norm_points_, T1, T2;
// norm_transform.getNormTransformation(norm_points_, sample, sample_size, T1, T2);
// const auto * const n_pts = (double *) norm_points_.data;
if (sample_size < getMinimumRequiredSampleSize())
return 0;
// do Least Squares
// Ax = b -> A^T Ax = A^T b
// x = (A^T A)^-1 A^T b
double AtA[36] = {0}, Ab[6] = {0};
double r1[6] = {0, 0, 1, 0, 0, 0}; // row 1 of A
double r2[6] = {0, 0, 0, 0, 0, 1}; // row 2 of A
if (weights.empty())
for (int p = 0; p < sample_size; p++) {
// if (weights != nullptr) weight = weights[sample[p]];
const int smpl = 4*sample[p];
const double x1=points[smpl], y1=points[smpl+1], x2=points[smpl+2], y2=points[smpl+3];
// const double x1=n_pts[smpl], y1=n_pts[smpl+1], x2=n_pts[smpl+2], y2=n_pts[smpl+3];
r1[0] = x1;
r1[1] = y1;
r2[3] = x1;
r2[4] = y1;
for (int j = 0; j < 6; j++) {
for (int z = j; z < 6; z++)
AtA[j * 6 + z] += r1[j] * r1[z] + r2[j] * r2[z];
Ab[j] += r1[j]*x2 + r2[j]*y2;
}
}
else
for (int p = 0; p < sample_size; p++) {
const int smpl = 4*sample[p];
const double weight = weights[p];
const double weight_times_x1 = weight * points[smpl ],
weight_times_y1 = weight * points[smpl+1],
weight_times_x2 = weight * points[smpl+2],
weight_times_y2 = weight * points[smpl+3];
r1[0] = weight_times_x1;
r1[1] = weight_times_y1;
r1[2] = weight;
r2[3] = weight_times_x1;
r2[4] = weight_times_y1;
r2[5] = weight;
for (int j = 0; j < 6; j++) {
for (int z = j; z < 6; z++)
AtA[j * 6 + z] += r1[j] * r1[z] + r2[j] * r2[z];
Ab[j] += r1[j]*weight_times_x2 + r2[j]*weight_times_y2;
}
}
// copy symmetric part
for (int j = 1; j < 6; j++)
for (int z = 0; z < j; z++)
AtA[j*6+z] = AtA[z*6+j];
Vec6d aff;
if (!solve(Matx66d(AtA), Vec6d(Ab), aff))
return 0;
models[0] = Mat(Matx33d(aff(0), aff(1), aff(2),
aff(3), aff(4), aff(5),
0, 0, 1));
// models[0] = T2.inv() * models[0] * T1;
return 1;
}
int getMinimumRequiredSampleSize() const override { return 3; }
int getMaxNumberOfSolutions () const override { return 1; }
Ptr<NonMinimalSolver> clone () const override {
return makePtr<AffineNonMinimalSolverImpl>(*points_mat);
}
};
Ptr<AffineNonMinimalSolver> AffineNonMinimalSolver::create(const Mat &points_) {
return makePtr<AffineNonMinimalSolverImpl>(points_);
}
}}

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modules/calib3d/src/usac/local_optimization.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#include "opencv2/imgproc/detail/gcgraph.hpp"
#include "gamma_values.hpp"
namespace cv { namespace usac {
class GraphCutImpl : public GraphCut {
protected:
const Ptr<NeighborhoodGraph> neighborhood_graph;
const Ptr<Estimator> estimator;
const Ptr<Quality> quality;
const Ptr<RandomGenerator> lo_sampler;
const Ptr<Error> error;
int gc_sample_size, lo_inner_iterations, points_size;
double spatial_coherence, sqr_trunc_thr, one_minus_lambda;
std::vector<int> labeling_inliers;
std::vector<double> energies, weights;
std::vector<bool> used_edges;
std::vector<Mat> gc_models;
public:
// In lo_sampler_ the sample size should be set and be equal gc_sample_size_
GraphCutImpl (const Ptr<Estimator> &estimator_, const Ptr<Error> &error_, const Ptr<Quality> &quality_,
const Ptr<NeighborhoodGraph> &neighborhood_graph_, const Ptr<RandomGenerator> &lo_sampler_,
double threshold_, double spatial_coherence_term, int gc_inner_iteration_number_) :
neighborhood_graph (neighborhood_graph_), estimator (estimator_), quality (quality_),
lo_sampler (lo_sampler_), error (error_) {
points_size = quality_->getPointsSize();
spatial_coherence = spatial_coherence_term;
sqr_trunc_thr = threshold_ * 2.25; // threshold is already squared
gc_sample_size = lo_sampler_->getSubsetSize();
lo_inner_iterations = gc_inner_iteration_number_;
one_minus_lambda = 1.0 - spatial_coherence;
energies = std::vector<double>(points_size);
labeling_inliers = std::vector<int>(points_size);
used_edges = std::vector<bool>(points_size*points_size);
gc_models = std::vector<Mat> (estimator->getMaxNumSolutionsNonMinimal());
}
bool refineModel (const Mat &best_model, const Score &best_model_score,
Mat &new_model, Score &new_model_score) override {
if (best_model_score.inlier_number < gc_sample_size)
return false;
// improve best model by non minimal estimation
new_model_score = Score(); // set score to inf (worst case)
best_model.copyTo(new_model);
bool is_best_model_updated = true;
while (is_best_model_updated) {
is_best_model_updated = false;
// Build graph problem. Apply graph cut to G
int labeling_inliers_size = labeling(new_model);
for (int iter = 0; iter < lo_inner_iterations; iter++) {
// sample to generate min (|I_7m|, |I|)
int num_of_estimated_models;
if (labeling_inliers_size > gc_sample_size) {
// generate random subset in range <0; |I|>
num_of_estimated_models = estimator->estimateModelNonMinimalSample
(lo_sampler->generateUniqueRandomSubset(labeling_inliers,
labeling_inliers_size), gc_sample_size, gc_models, weights);
} else {
if (iter > 0)
break; // break inliers are not updated
num_of_estimated_models = estimator->estimateModelNonMinimalSample
(labeling_inliers, labeling_inliers_size, gc_models, weights);
}
if (num_of_estimated_models == 0)
break;
bool zero_inliers = false;
for (int model_idx = 0; model_idx < num_of_estimated_models; model_idx++) {
Score gc_temp_score = quality->getScore(gc_models[model_idx]);
if (gc_temp_score.inlier_number == 0){
zero_inliers = true; break;
}
if (best_model_score.isBetter(gc_temp_score))
continue;
// store the best model from estimated models
if (gc_temp_score.isBetter(new_model_score)) {
is_best_model_updated = true;
new_model_score = gc_temp_score;
gc_models[model_idx].copyTo(new_model);
}
}
if (zero_inliers)
break;
} // end of inner GC local optimization
} // end of while loop
return true;
}
private:
// find inliers using graph cut algorithm.
int labeling (const Mat& model) {
const auto &errors = error->getErrors(model);
detail::GCGraph<double> graph;
for (int pt = 0; pt < points_size; pt++)
graph.addVtx();
// The distance and energy for each point
double tmp_squared_distance, energy;
// Estimate the vertex capacities
for (int pt = 0; pt < points_size; pt++) {
tmp_squared_distance = errors[pt];
if (std::isnan(tmp_squared_distance)) {
energies[pt] = std::numeric_limits<float>::max();
continue;
}
energy = tmp_squared_distance / sqr_trunc_thr; // Truncated quadratic cost
if (tmp_squared_distance <= sqr_trunc_thr)
graph.addTermWeights(pt, 0, one_minus_lambda * (1 - energy));
else
graph.addTermWeights(pt, one_minus_lambda * energy, 0);
if (energy > 1) energy = 1;
energies[pt] = energy;
}
std::fill(used_edges.begin(), used_edges.end(), false);
// Iterate through all points and set their edges
for (int point_idx = 0; point_idx < points_size; ++point_idx) {
energy = energies[point_idx];
// Iterate through all neighbors
for (int actual_neighbor_idx : neighborhood_graph->getNeighbors(point_idx)) {
if (actual_neighbor_idx == point_idx ||
used_edges[actual_neighbor_idx*points_size + point_idx] ||
used_edges[point_idx*points_size + actual_neighbor_idx])
continue;
used_edges[actual_neighbor_idx*points_size + point_idx] = true;
used_edges[point_idx*points_size + actual_neighbor_idx] = true;
double a = (0.5 * (energy + energies[actual_neighbor_idx])) * spatial_coherence,
b = spatial_coherence, c = spatial_coherence, d = 0;
graph.addTermWeights(point_idx, d, a);
b -= a;
if (b + c >= 0)
// Non-submodular expansion term detected; smooth costs must be a metric for expansion
continue;
if (b < 0) {
graph.addTermWeights(point_idx, 0, b);
graph.addTermWeights(actual_neighbor_idx, 0, -b);
graph.addEdges(point_idx, actual_neighbor_idx, 0, b + c);
} else if (c < 0) {
graph.addTermWeights(point_idx, 0, -c);
graph.addTermWeights(actual_neighbor_idx, 0, c);
graph.addEdges(point_idx, actual_neighbor_idx, b + c, 0);
} else
graph.addEdges(point_idx, actual_neighbor_idx, b, c);
}
}
graph.maxFlow();
int inlier_number = 0;
for (int pt = 0; pt < points_size; pt++)
if (! graph.inSourceSegment(pt)) // check for sink
labeling_inliers[inlier_number++] = pt;
return inlier_number;
}
Ptr<LocalOptimization> clone(int state) const override {
return makePtr<GraphCutImpl>(estimator->clone(), error->clone(), quality->clone(),
neighborhood_graph,lo_sampler->clone(state), sqrt(sqr_trunc_thr / 2),
spatial_coherence, lo_inner_iterations);
}
};
Ptr<GraphCut> GraphCut::create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
const Ptr<Quality> &quality_, const Ptr<NeighborhoodGraph> &neighborhood_graph_,
const Ptr<RandomGenerator> &lo_sampler_, double threshold_,
double spatial_coherence_term, int gc_inner_iteration_number) {
return makePtr<GraphCutImpl>(estimator_, error_, quality_, neighborhood_graph_, lo_sampler_,
threshold_, spatial_coherence_term, gc_inner_iteration_number);
}
/*
* http://cmp.felk.cvut.cz/~matas/papers/chum-dagm03.pdf
*/
class InnerIterativeLocalOptimizationImpl : public InnerIterativeLocalOptimization {
private:
const Ptr<Estimator> estimator;
const Ptr<Quality> quality;
const Ptr<RandomGenerator> lo_sampler;
Ptr<RandomGenerator> lo_iter_sampler;
std::vector<Mat> lo_models, lo_iter_models;
std::vector<int> inliers_of_best_model, virtual_inliers;
int lo_inner_max_iterations, lo_iter_max_iterations, lo_sample_size, lo_iter_sample_size;
bool is_iterative;
double threshold, new_threshold, threshold_step;
std::vector<double> weights;
public:
InnerIterativeLocalOptimizationImpl (const Ptr<Estimator> &estimator_, const Ptr<Quality> &quality_,
const Ptr<RandomGenerator> &lo_sampler_, int pts_size,
double threshold_, bool is_iterative_, int lo_iter_sample_size_,
int lo_inner_iterations_=10, int lo_iter_max_iterations_=5,
double threshold_multiplier_=4) : estimator (estimator_), quality (quality_),
lo_sampler (lo_sampler_) {
lo_inner_max_iterations = lo_inner_iterations_;
lo_iter_max_iterations = lo_iter_max_iterations_;
threshold = threshold_;
lo_sample_size = lo_sampler->getSubsetSize();
is_iterative = is_iterative_;
if (is_iterative) {
lo_iter_sample_size = lo_iter_sample_size_;
lo_iter_sampler = UniformRandomGenerator::create(0/*state*/, pts_size, lo_iter_sample_size_);
lo_iter_models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
virtual_inliers = std::vector<int>(pts_size);
new_threshold = threshold_multiplier_ * threshold;
// reduce multiplier threshold K·θ by this number in each iteration.
// In the last iteration there be original threshold θ.
threshold_step = (new_threshold - threshold) / lo_iter_max_iterations_;
}
lo_models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
// Allocate max memory to avoid reallocation
inliers_of_best_model = std::vector<int>(pts_size);
}
/*
* Implementation of Locally Optimized Ransac
* Inner + Iterative
*/
bool refineModel (const Mat &so_far_the_best_model, const Score &best_model_score,
Mat &new_model, Score &new_model_score) override {
if (best_model_score.inlier_number < lo_sample_size)
return false;
so_far_the_best_model.copyTo(new_model);
new_model_score = best_model_score;
// get inliers from so far the best model.
int num_inliers_of_best_model = quality->getInliers(so_far_the_best_model,
inliers_of_best_model);
// Inner Local Optimization Ransac.
for (int iters = 0; iters < lo_inner_max_iterations; iters++) {
int num_estimated_models;
// Generate sample of lo_sample_size from inliers from the best model.
if (num_inliers_of_best_model > lo_sample_size) {
// if there are many inliers take limited number at random.
num_estimated_models = estimator->estimateModelNonMinimalSample
(lo_sampler->generateUniqueRandomSubset(inliers_of_best_model,
num_inliers_of_best_model), lo_sample_size, lo_models, weights);
if (num_estimated_models == 0) continue;
} else {
// if model was not updated in first iteration, so break.
if (iters > 0) break;
// if inliers are less than limited number of sample then take all for estimation
// if it fails -> end Lo.
num_estimated_models = estimator->estimateModelNonMinimalSample
(inliers_of_best_model, num_inliers_of_best_model, lo_models, weights);
if (num_estimated_models == 0) return false;
}
//////// Choose the best lo_model from estimated lo_models.
for (int model_idx = 0; model_idx < num_estimated_models; model_idx++) {
Score temp_score = quality->getScore(lo_models[model_idx]);
if (temp_score.isBetter(new_model_score)) {
new_model_score = temp_score;
lo_models[model_idx].copyTo(new_model);
}
}
if (is_iterative) {
double lo_threshold = new_threshold;
// get max virtual inliers. Note that they are nor real inliers,
// because we got them with bigger threshold.
int virtual_inliers_size = quality->getInliers
(new_model, virtual_inliers, lo_threshold);
Mat lo_iter_model;
Score lo_iter_score = Score(); // set worst case
for (int iterations = 0; iterations < lo_iter_max_iterations; iterations++) {
lo_threshold -= threshold_step;
if (virtual_inliers_size > lo_iter_sample_size) {
// if there are more inliers than limit for sample size then generate at random
// sample from LO model.
num_estimated_models = estimator->estimateModelNonMinimalSample
(lo_iter_sampler->generateUniqueRandomSubset (virtual_inliers,
virtual_inliers_size), lo_iter_sample_size, lo_iter_models, weights);
} else {
// break if failed, very low probability that it will not fail in next iterations
// estimate model with all virtual inliers
num_estimated_models = estimator->estimateModelNonMinimalSample
(virtual_inliers, virtual_inliers_size, lo_iter_models, weights);
}
if (num_estimated_models == 0) break;
// Get score and update virtual inliers with current threshold
//////// Choose the best lo_iter_model from estimated lo_iter_models.
lo_iter_models[0].copyTo(lo_iter_model);
lo_iter_score = quality->getScore(lo_iter_model);
for (int model_idx = 1; model_idx < num_estimated_models; model_idx++) {
Score temp_score = quality->getScore(lo_iter_models[model_idx]);
if (temp_score.isBetter(lo_iter_score)) {
lo_iter_score = temp_score;
lo_iter_models[model_idx].copyTo(lo_iter_model);
}
}
virtual_inliers_size = quality->getInliers(lo_iter_model, virtual_inliers, lo_threshold);
}
if (fabs (lo_threshold - threshold) < FLT_EPSILON) {
// Success, threshold does not differ
// last score correspond to user-defined threshold. Inliers are real.
if (lo_iter_score.isBetter(new_model_score)) {
new_model_score = lo_iter_score;
lo_iter_model.copyTo(new_model);
}
}
}
if (num_inliers_of_best_model < new_model_score.inlier_number && iters != lo_inner_max_iterations-1)
num_inliers_of_best_model = quality->getInliers (new_model, inliers_of_best_model);
}
return true;
}
Ptr<LocalOptimization> clone(int state) const override {
return makePtr<InnerIterativeLocalOptimizationImpl>(estimator->clone(), quality->clone(),
lo_sampler->clone(state),(int)inliers_of_best_model.size(), threshold, is_iterative,
lo_iter_sample_size, lo_inner_max_iterations, lo_iter_max_iterations,
new_threshold / threshold);
}
};
Ptr<InnerIterativeLocalOptimization> InnerIterativeLocalOptimization::create
(const Ptr<Estimator> &estimator_, const Ptr<Quality> &quality_,
const Ptr<RandomGenerator> &lo_sampler_, int pts_size,
double threshold_, bool is_iterative_, int lo_iter_sample_size_,
int lo_inner_iterations_, int lo_iter_max_iterations_,
double threshold_multiplier_) {
return makePtr<InnerIterativeLocalOptimizationImpl>(estimator_, quality_, lo_sampler_,
pts_size, threshold_, is_iterative_, lo_iter_sample_size_,
lo_inner_iterations_, lo_iter_max_iterations_, threshold_multiplier_);
}
class SigmaConsensusImpl : public SigmaConsensus {
private:
const Ptr<Estimator> estimator;
const Ptr<Quality> quality;
const Ptr<Error> error;
const Ptr<ModelVerifier> verifier;
// The degrees of freedom of the data from which the model is estimated.
// E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
const int degrees_of_freedom;
// A 0.99 quantile of the Chi^2-distribution to convert sigma values to residuals
const double k;
// Calculating (DoF - 1) / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double dof_minus_one_per_two;
const double C;
// The size of a minimal sample used for the estimation
const int sample_size;
// Calculating 2^(DoF - 1) which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double two_ad_dof;
// Calculating C * 2^(DoF - 1) which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double C_times_two_ad_dof;
// Calculating the gamma value of (DoF - 1) / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double gamma_value, squared_sigma_max_2, one_over_sigma;
// Calculating the upper incomplete gamma value of (DoF - 1) / 2 with k^2 / 2.
const double gamma_k;
// Calculating the lower incomplete gamma value of (DoF - 1) / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double gamma_difference;
const int points_size, number_of_irwls_iters;
const double maximum_threshold, max_sigma;
std::vector<double> residuals, sigma_weights, stored_gamma_values;
std::vector<int> residuals_idxs;
// Models fit by weighted least-squares fitting
std::vector<Mat> sigma_models;
// Points used in the weighted least-squares fitting
std::vector<int> sigma_inliers;
// Weights used in the the weighted least-squares fitting
int max_lo_sample_size;
double scale_of_stored_gammas;
RNG rng;
public:
SigmaConsensusImpl (const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
const Ptr<Quality> &quality_, const Ptr<ModelVerifier> &verifier_,
int max_lo_sample_size_, int number_of_irwls_iters_, int DoF,
double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
double maximum_thr) : estimator (estimator_), quality(quality_),
error (error_), verifier(verifier_), degrees_of_freedom(DoF),
k (sigma_quantile), C(C_), sample_size(estimator_->getMinimalSampleSize()),
gamma_k (upper_incomplete_of_sigma_quantile), points_size (quality_->getPointsSize()),
number_of_irwls_iters (number_of_irwls_iters_),
maximum_threshold(maximum_thr), max_sigma (maximum_thr) {
dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
two_ad_dof = std::pow(2.0, dof_minus_one_per_two);
C_times_two_ad_dof = C * two_ad_dof;
gamma_value = tgamma(dof_minus_one_per_two);
gamma_difference = gamma_value - gamma_k;
// Calculate 2 * \sigma_{max}^2 a priori
squared_sigma_max_2 = max_sigma * max_sigma * 2.0;
// Divide C * 2^(DoF - 1) by \sigma_{max} a priori
one_over_sigma = C_times_two_ad_dof / max_sigma;
residuals = std::vector<double>(points_size);
residuals_idxs = std::vector<int>(points_size);
sigma_inliers = std::vector<int>(points_size);
max_lo_sample_size = max_lo_sample_size_;
sigma_weights = std::vector<double>(points_size);
sigma_models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
if (DoF == 4) {
scale_of_stored_gammas = scale_of_stored_gammas_n4;
stored_gamma_values = std::vector<double>(stored_gamma_values_n4,
stored_gamma_values_n4+stored_gamma_number+1);
} else if (DoF == 5) {
scale_of_stored_gammas = scale_of_stored_gammas_n5;
stored_gamma_values = std::vector<double>(stored_gamma_values_n5,
stored_gamma_values_n5+stored_gamma_number+1);
} else
CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
}
// https://github.com/danini/magsac
bool refineModel (const Mat &in_model, const Score &in_model_score,
Mat &new_model, Score &new_model_score) override {
int residual_cnt = 0;
if (verifier->isModelGood(in_model)) {
if (verifier->hasErrors()) {
const std::vector<float> &errors = verifier->getErrors();
for (int point_idx = 0; point_idx < points_size; ++point_idx) {
// Calculate the residual of the current point
const auto residual = sqrtf(errors[point_idx]);
if (max_sigma > residual) {
// Store the residual of the current point and its index
residuals[residual_cnt] = residual;
residuals_idxs[residual_cnt++] = point_idx;
}
// Interrupt if there is no chance of being better
if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
return false;
}
} else {
error->setModelParameters(in_model);
for (int point_idx = 0; point_idx < points_size; ++point_idx) {
const double residual = sqrtf(error->getError(point_idx));
if (max_sigma > residual) {
// Store the residual of the current point and its index
residuals[residual_cnt] = residual;
residuals_idxs[residual_cnt++] = point_idx;
}
if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
return false;
}
}
} else return false;
// Initialize the polished model with the initial one
Mat polished_model;
in_model.copyTo(polished_model);
// A flag to determine if the initial model has been updated
bool updated = false;
// Do the iteratively re-weighted least squares fitting
for (int iterations = 0; iterations < number_of_irwls_iters; ++iterations) {
int sigma_inliers_cnt = 0;
// If the current iteration is not the first, the set of possibly inliers
// (i.e., points closer than the maximum threshold) have to be recalculated.
if (iterations > 0) {
error->setModelParameters(polished_model);
// Remove everything from the residual vector
residual_cnt = 0;
// Collect the points which are closer than the maximum threshold
for (int point_idx = 0; point_idx < points_size; ++point_idx) {
// Calculate the residual of the current point
const double residual = error->getError(point_idx);
if (residual < max_sigma) {
// Store the residual of the current point and its index
residuals[residual_cnt] = residual;
residuals_idxs[residual_cnt++] = point_idx;
}
}
sigma_inliers_cnt = 0;
}
// Calculate the weight of each point
for (int i = 0; i < residual_cnt; i++) {
const double residual = residuals[i];
const int idx = residuals_idxs[i];
// If the residual is ~0, the point fits perfectly and it is handled differently
if (residual > std::numeric_limits<double>::epsilon()) {
// Calculate the squared residual
const double squared_residual = residual * residual;
// Get the position of the gamma value in the lookup table
int x = (int)round(scale_of_stored_gammas * squared_residual
/ squared_sigma_max_2);
// If the sought gamma value is not stored in the lookup, return the closest element
if (x >= stored_gamma_number || x < 0 /*overflow*/) // actual number of gamma values is 1 more, so >=
x = stored_gamma_number;
sigma_inliers[sigma_inliers_cnt] = idx; // store index of point for LSQ
sigma_weights[sigma_inliers_cnt++] = one_over_sigma * (stored_gamma_values[x] - gamma_k);
}
}
if (sigma_inliers_cnt > max_lo_sample_size)
for (int i = sigma_inliers_cnt-1; i > 0; i--) {
const int idx = rng.uniform(0, i+1);
std::swap(sigma_inliers[i], sigma_inliers[idx]);
std::swap(sigma_weights[i], sigma_weights[idx]);
}
int num_est_models = estimator->estimateModelNonMinimalSample
(sigma_inliers, std::min(max_lo_sample_size, sigma_inliers_cnt),
sigma_models, sigma_weights);
// If there are fewer than the minimum point close to the model, terminate.
// Estimate the model parameters using weighted least-squares fitting
if (num_est_models == 0) {
// If the estimation failed and the iteration was never successfull,
// terminate with failure.
if (iterations == 0)
return false;
// Otherwise, if the iteration was successfull at least one,
// simply break it.
break;
}
// Update the model parameters
polished_model = sigma_models[0];
if (num_est_models > 1) {
// find best over other models
Score sigma_best_score = quality->getScore(polished_model);
for (int m = 1; m < num_est_models; m++) {
Score sc = quality->getScore(sigma_models[m]);
if (sc.isBetter(sigma_best_score)) {
polished_model = sigma_models[m];
sigma_best_score = sc;
}
}
}
// The model has been updated
updated = true;
}
if (updated) {
new_model_score = quality->getScore(polished_model);
new_model = polished_model;
return true;
}
return false;
}
Ptr<LocalOptimization> clone(int state) const override {
return makePtr<SigmaConsensusImpl>(estimator->clone(), error->clone(), quality->clone(),
verifier->clone(state), max_lo_sample_size, number_of_irwls_iters,
degrees_of_freedom, k, gamma_k, C, maximum_threshold);
}
};
Ptr<SigmaConsensus>
SigmaConsensus::create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
const Ptr<Quality> &quality, const Ptr<ModelVerifier> &verifier_,
int max_lo_sample_size, int number_of_irwls_iters_, int DoF,
double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
double maximum_thr) {
return makePtr<SigmaConsensusImpl>(estimator_, error_, quality, verifier_, max_lo_sample_size,
number_of_irwls_iters_, DoF, sigma_quantile, upper_incomplete_of_sigma_quantile,
C_, maximum_thr);
}
/////////////////////////////////////////// FINAL MODEL POLISHER ////////////////////////
class LeastSquaresPolishingImpl : public LeastSquaresPolishing {
private:
const Ptr<Estimator> estimator;
const Ptr<Quality> quality;
Score score;
int lsq_iterations;
std::vector<int> inliers;
std::vector<Mat> models;
std::vector<double> weights;
public:
LeastSquaresPolishingImpl(const Ptr<Estimator> &estimator_, const Ptr<Quality> &quality_,
int lsq_iterations_) :
estimator(estimator_), quality(quality_) {
lsq_iterations = lsq_iterations_;
// allocate memory for inliers array and models
inliers = std::vector<int>(quality_->getPointsSize());
models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
}
bool polishSoFarTheBestModel(const Mat &model, const Score &best_model_score,
Mat &new_model, Score &out_score) override {
// get inliers from input model
int inlier_number = quality->getInliers(model, inliers);
if (inlier_number < estimator->getMinimalSampleSize())
return false;
out_score = Score(); // set the worst case
// several all-inlier least-squares refines model better than only one but for
// big amount of points may be too time-consuming.
for (int lsq_iter = 0; lsq_iter < lsq_iterations; lsq_iter++) {
bool model_updated = false;
// estimate non minimal models with all inliers
const int num_models = estimator->estimateModelNonMinimalSample(inliers,
inlier_number, models, weights);
for (int model_idx = 0; model_idx < num_models; model_idx++) {
score = quality->getScore(models[model_idx]);
if (best_model_score.isBetter(score))
continue;
if (score.isBetter(out_score)) {
models[model_idx].copyTo(new_model);
out_score = score;
model_updated = true;
}
}
if (!model_updated)
// if model was not updated at the first iteration then return false
// otherwise if all-inliers LSQ has not updated model then no sense
// to do it again -> return true (model was updated before).
return lsq_iter > 0;
// if number of inliers doesn't increase more than 5% then break
if (fabs(static_cast<double>(out_score.inlier_number) - static_cast<double>
(best_model_score.inlier_number)) / best_model_score.inlier_number < 0.05)
return true;
if (lsq_iter != lsq_iterations - 1)
// if not the last LSQ normalization then get inliers for next normalization
inlier_number = quality->getInliers(new_model, inliers);
}
return true;
}
};
Ptr<LeastSquaresPolishing> LeastSquaresPolishing::create (const Ptr<Estimator> &estimator_,
const Ptr<Quality> &quality_, int lsq_iterations_) {
return makePtr<LeastSquaresPolishingImpl>(estimator_, quality_, lsq_iterations_);
}
}}

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modules/calib3d/src/usac/pnp_solver.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#include "../polynom_solver.h"
#if defined(HAVE_EIGEN)
#include <Eigen/Eigen>
#include <Eigen/QR>
#elif defined(HAVE_LAPACK)
#include "opencv_lapack.h"
#endif
namespace cv { namespace usac {
class PnPMinimalSolver6PtsImpl : public PnPMinimalSolver6Pts {
private:
const Mat * points_mat;
const float * const points;
public:
// linear 6 points required (11 equations)
int getSampleSize() const override { return 6; }
int getMaxNumberOfSolutions () const override { return 1; }
explicit PnPMinimalSolver6PtsImpl (const Mat &points_) :
points_mat(&points_), points ((float*)points_.data) {}
/*
DLT:
d x = P X, x = (u, v, 1), X = (X, Y, Z, 1), P = K[R t]
is 3x4 projection matrix with rows p1, p2, p3. d is depth
u = p1^T X / p3^T X
v = p2^T X / p3^T X
(p1^T - u p3^T) X = 0
(p2^T - v p3^T) X = 0
(p11 - u p31) X + (p12 - u p32) Y + (p13 - u p33) Z + (p14 - u p34) = 0
(p12 - v p31) X + (p22 - v p32) Y + (p23 - v p33) Z + (p24 - v p34) = 0
[X, Y, Z, 1, 0, 0, 0, 0, -u X, -u Y, -u Z, -u] [p11] [0]
[0, 0, 0, 0, X, Y, Z, 1, -v X, -v Y, -v Z, -v] [p12] [0]
. = [0]
.
. [p34] [0]
minimum 11 equations, each point gives 2 equation, so at least 6 points are required.
@points is array Nx5
u1 v1 X1 Y1 Z1
...
uN vN XN YN ZN
@P is output projection matrix
A1 =
[X1, Y1, Z1, 1, 0, 0, 0, 0, -u1 X1, -u1 Y1, -u1 Z1, -u1] [p11] [0]
[X2, Y2, Z2, 1, 0, 0, 0, 0, -u2 X2, -u2 Y2, -u2 Z2, -u2] [p12] [0]
[X3, Y3, Z3, 1, 0, 0, 0, 0, -u3 X3, -u3 Y3, -u3 Z3, -u3] [p13] [0]
[X4, Y4, Z4, 1, 0, 0, 0, 0, -u4 X4, -u4 Y4, -u4 Z4, -u4] [p14] [0]
[X5, Y5, Z5, 1, 0, 0, 0, 0, -u5 X5, -u5 Y5, -u5 Z5, -u5] [p21] [0]
[p22]
A2 = (without first 4 columns)
[0, 0, 0, 0, X1, Y1, Z1, 1, -v1 X1, -v1 Y1, -v1 Z1, -v1] [p23] = [0]
[0, 0, 0, 0, X2, Y2, Z2, 1, -v2 X2, -v2 Y2, -v2 Z2, -v2] [p24] [0]
[0, 0, 0, 0, X3, Y3, Z3, 1, -v3 X3, -v3 Y3, -v3 Z3, -v3] [p31] [0]
[0, 0, 0, 0, X4, Y4, Z4, 1, -v4 X4, -v4 Y4, -v4 Z4, -v4] [p32] [0]
[0, 0, 0, 0, X5, Y5, Z5, 1, -v5 X5, -v5 Y5, -v5 Z5, -v5] [p33] [0]
[0, 0, 0, 0, X6, Y6, Z6, 1, -v6 X6, -v6 Y6, -v6 Z6, -v6] [p34=1] [0]
P = null A; dim null A = n - rank(A) = 12 - 11 = 1
*/
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
std::vector<double> A1 (5*12, 0), A2(7*8, 0);
int cnt1 = 0, cnt2 = 0;
for (int i = 0; i < 6; i++) {
const int smpl = 5 * sample[i];
const double u = points[smpl ], v = points[smpl + 1];
const double X = points[smpl + 2], Y = points[smpl + 3], Z = points[smpl + 4];
if (i != 5) {
A1[cnt1++] = X;
A1[cnt1++] = Y;
A1[cnt1++] = Z;
A1[cnt1++] = 1;
cnt1 += 4; // skip zeros
A1[cnt1++] = -u * X;
A1[cnt1++] = -u * Y;
A1[cnt1++] = -u * Z;
A1[cnt1++] = -u;
}
A2[cnt2++] = X;
A2[cnt2++] = Y;
A2[cnt2++] = Z;
A2[cnt2++] = 1;
A2[cnt2++] = -v * X;
A2[cnt2++] = -v * Y;
A2[cnt2++] = -v * Z;
A2[cnt2++] = -v;
}
Math::eliminateUpperTriangular(A1, 5, 12);
int offset = 4*12;
// add last eliminated row of A1
for (int i = 0; i < 8; i++)
A2[cnt2++] = A1[offset + i + 4/* skip 4 first cols*/];
Math::eliminateUpperTriangular(A2, 7, 8);
// fixed scale to 1. In general the projection matrix is up-to-scale.
// P = alpha * P^, alpha = 1 / P^_[3,4]
Mat P = Mat_<double>(3,4);
auto * p = (double *) P.data;
p[11] = 1;
// start from the last row
for (int i = 6; i >= 0; i--) {
double acc = 0;
for (int j = i+1; j < 8; j++)
acc -= A2[i*8+j]*p[j+4];
p[i+4] = acc / A2[i*8+i];
// due to numerical errors return 0 solutions
if (std::isnan(p[i+4]))
return 0;
}
for (int i = 3; i >= 0; i--) {
double acc = 0;
for (int j = i+1; j < 12; j++)
acc -= A1[i*12+j]*p[j];
p[i] = acc / A1[i*12+i];
if (std::isnan(p[i]))
return 0;
}
models = std::vector<Mat>{P};
return 1;
}
Ptr<MinimalSolver> clone () const override {
return makePtr<PnPMinimalSolver6PtsImpl>(*points_mat);
}
};
Ptr<PnPMinimalSolver6Pts> PnPMinimalSolver6Pts::create(const Mat &points_) {
return makePtr<PnPMinimalSolver6PtsImpl>(points_);
}
class PnPNonMinimalSolverImpl : public PnPNonMinimalSolver {
private:
const Mat * points_mat;
const float * const points;
public:
explicit PnPNonMinimalSolverImpl (const Mat &points_) :
points_mat(&points_), points ((float*)points_.data){}
int estimate (const std::vector<int> &sample, int sample_size,
std::vector<Mat> &models, const std::vector<double> &weights) const override {
if (sample_size < 6)
return 0;
double AtA [144] = {0}; // 12x12
double a1[12] = {0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0},
a2[12] = {0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0};
if (weights.empty())
for (int i = 0; i < sample_size; i++) {
const int smpl = 5 * sample[i];
const double u = points[smpl], v = points[smpl + 1];
const double X = points[smpl + 2], Y = points[smpl + 3], Z = points[smpl + 4];
a1[0 ] = -X;
a1[1 ] = -Y;
a1[2 ] = -Z;
a1[8 ] = u * X;
a1[9 ] = u * Y;
a1[10] = u * Z;
a1[11] = u;
a2[4 ] = -X;
a2[5 ] = -Y;
a2[6 ] = -Z;
a2[8 ] = v * X;
a2[9 ] = v * Y;
a2[10] = v * Z;
a2[11] = v;
// fill covarinace matrix
for (int j = 0; j < 12; j++)
for (int z = j; z < 12; z++)
AtA[j * 12 + z] += a1[j] * a1[z] + a2[j] * a2[z];
}
else
for (int i = 0; i < sample_size; i++) {
const int smpl = 5 * sample[i];
const double weight = weights[i], u = points[smpl], v = points[smpl + 1];
const double weight_X = weight * points[smpl + 2],
weight_Y = weight * points[smpl + 3],
weight_Z = weight * points[smpl + 4];
a1[0 ] = -weight_X;
a1[1 ] = -weight_Y;
a1[2 ] = -weight_Z;
a1[3 ] = -weight;
a1[8 ] = u * weight_X;
a1[9 ] = u * weight_Y;
a1[10] = u * weight_Z;
a1[11] = u * weight;
a2[4 ] = -weight_X;
a2[5 ] = -weight_Y;
a2[6 ] = -weight_Z;
a2[7 ] = -weight;
a2[8 ] = v * weight_X;
a2[9 ] = v * weight_Y;
a2[10] = v * weight_Z;
a2[11] = v * weight;
// fill covarinace matrix
for (int j = 0; j < 12; j++)
for (int z = j; z < 12; z++)
AtA[j * 12 + z] += a1[j] * a1[z] + a2[j] * a2[z];
}
// copy symmetric part of covariance matrix
for (int j = 1; j < 12; j++)
for (int z = 0; z < j; z++)
AtA[j*12+z] = AtA[z*12+j];
#ifdef HAVE_EIGEN
models = std::vector<Mat>{ Mat_<double>(3,4) };
Eigen::HouseholderQR<Eigen::Matrix<double, 12, 12>> qr((Eigen::Matrix<double, 12, 12>(AtA)));
const Eigen::Matrix<double, 12, 12> &Q = qr.householderQ();
// extract the last nullspace
Eigen::Map<Eigen::Matrix<double, 12, 1>>((double *)models[0].data) = Q.col(11);
#else
Matx<double, 12, 12> Vt;
Vec<double, 12> D;
if (! eigen(Matx<double, 12, 12>(AtA), D, Vt)) return 0;
models = std::vector<Mat>{ Mat(Vt.row(11).reshape<3,4>()) };
#endif
return 1;
}
int getMinimumRequiredSampleSize() const override { return 6; }
int getMaxNumberOfSolutions () const override { return 1; }
Ptr<NonMinimalSolver> clone () const override {
return makePtr<PnPNonMinimalSolverImpl>(*points_mat);
}
};
Ptr<PnPNonMinimalSolver> PnPNonMinimalSolver::create(const Mat &points) {
return makePtr<PnPNonMinimalSolverImpl>(points);
}
class P3PSolverImpl : public P3PSolver {
private:
/*
* calibrated normalized points
* K^-1 [u v 1]^T / ||K^-1 [u v 1]^T||
*/
const Mat * points_mat, * calib_norm_points_mat, * K_mat, &K;
const float * const calib_norm_points, * const points;
const double VAL_THR = 1e-4;
public:
/*
* @points_ is matrix N x 5
* u v x y z. (u,v) is image point, (x y z) is world point
*/
P3PSolverImpl (const Mat &points_, const Mat &calib_norm_points_, const Mat &K_) :
points_mat(&points_), calib_norm_points_mat(&calib_norm_points_), K_mat (&K_),
K(K_), calib_norm_points((float*)calib_norm_points_.data), points((float*)points_.data) {}
int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
/*
* The description of this solution can be found here:
* http://cmp.felk.cvut.cz/~pajdla/gvg/GVG-2016-Lecture.pdf
* pages: 51-59
*/
const int idx1 = 5*sample[0], idx2 = 5*sample[1], idx3 = 5*sample[2];
const Vec3d X1 (points[idx1+2], points[idx1+3], points[idx1+4]);
const Vec3d X2 (points[idx2+2], points[idx2+3], points[idx2+4]);
const Vec3d X3 (points[idx3+2], points[idx3+3], points[idx3+4]);
// find distance between world points d_ij = ||Xi - Xj||
const double d12 = norm(X1 - X2);
const double d23 = norm(X2 - X3);
const double d31 = norm(X3 - X1);
if (d12 < VAL_THR || d23 < VAL_THR || d31 < VAL_THR)
return 0;
const int c_idx1 = 3*sample[0], c_idx2 = 3*sample[1], c_idx3 = 3*sample[2];
const Vec3d cx1 (calib_norm_points[c_idx1], calib_norm_points[c_idx1+1], calib_norm_points[c_idx1+2]);
const Vec3d cx2 (calib_norm_points[c_idx2], calib_norm_points[c_idx2+1], calib_norm_points[c_idx2+2]);
const Vec3d cx3 (calib_norm_points[c_idx3], calib_norm_points[c_idx3+1], calib_norm_points[c_idx3+2]);
// find cosine angles, cos(x1,x2) = K^-1 x1.dot(K^-1 x2) / (||K^-1 x1|| * ||K^-1 x2||)
// calib_norm_points are already K^-1 x / ||K^-1 x||, so we perform only dot product
const double c12 = cx1(0)*cx2(0) + cx1(1)*cx2(1) + cx1(2)*cx2(2);
const double c23 = cx2(0)*cx3(0) + cx2(1)*cx3(1) + cx2(2)*cx3(2);
const double c31 = cx3(0)*cx1(0) + cx3(1)*cx1(1) + cx3(2)*cx1(2);
Matx33d Z, Zw;
auto * z = Z.val, * zw = Zw.val;
// find coefficients of polynomial a4 x^4 + ... + a0 = 0
const double c12_p2 = c12*c12, c23_p2 = c23*c23, c31_p2 = c31*c31;
const double d12_p2 = d12*d12, d12_p4 = d12_p2*d12_p2;
const double d23_p2 = d23*d23, d23_p4 = d23_p2*d23_p2, d23_p6 = d23_p2*d23_p4, d23_p8 = d23_p4*d23_p4;
const double d31_p2 = d31*d31, d31_p4 = d31_p2*d31_p2;
const double a4 = -4*d23_p4*d12_p2*d31_p2*c23_p2+d23_p8-2*d23_p6*d12_p2-2*d23_p6*d31_p2+d23_p4*d12_p4+2*d23_p4*d12_p2*d31_p2+d23_p4*d31_p4;
const double a3 = 8*d23_p4*d12_p2*d31_p2*c12*c23_p2+4*d23_p6*d12_p2*c31*c23-4*d23_p4*d12_p4*c31*c23+4*d23_p4*d12_p2*d31_p2*c31*c23-4*d23_p8*c12+4*d23_p6*d12_p2*c12+8*d23_p6*d31_p2*c12-4*d23_p4*d12_p2*d31_p2*c12-4*d23_p4*d31_p4*c12;
const double a2 = -8*d23_p6*d12_p2*c31*c12*c23-8*d23_p4*d12_p2*d31_p2*c31*c12*c23+4*d23_p8*c12_p2-4*d23_p6*d12_p2*c31_p2-8*d23_p6*d31_p2*c12_p2+4*d23_p4*d12_p4*c31_p2+4*d23_p4*d12_p4*c23_p2-4*d23_p4*d12_p2*d31_p2*c23_p2+4*d23_p4*d31_p4*c12_p2+2*d23_p8-4*d23_p6*d31_p2-2*d23_p4*d12_p4+2*d23_p4*d31_p4;
const double a1 = 8*d23_p6*d12_p2*c31_p2*c12+4*d23_p6*d12_p2*c31*c23-4*d23_p4*d12_p4*c31*c23+4*d23_p4*d12_p2*d31_p2*c31*c23-4*d23_p8*c12-4*d23_p6*d12_p2*c12+8*d23_p6*d31_p2*c12+4*d23_p4*d12_p2*d31_p2*c12-4*d23_p4*d31_p4*c12;
const double a0 = -4*d23_p6*d12_p2*c31_p2+d23_p8-2*d23_p4*d12_p2*d31_p2+2*d23_p6*d12_p2+d23_p4*d31_p4+d23_p4*d12_p4-2*d23_p6*d31_p2;
double roots[4] = {0};
int num_roots = solve_deg4(a4, a3, a2, a1, a0, roots[0], roots[1], roots[2], roots[3]);
models = std::vector<Mat>(); models.reserve(num_roots);
for (double root : roots) {
if (root <= 0) continue;
const double n12 = root, n12_p2 = n12 * n12;
const double n13 = (d12_p2*(d23_p2-d31_p2*n12_p2)+(d23_p2-d31_p2)*(d23_p2*(1+n12_p2-2*n12*c12)-d12_p2*n12_p2))
/ (2*d12_p2*(d23_p2*c31 - d31_p2*c23*n12) + 2*(d31_p2-d23_p2)*d12_p2*c23*n12);
const double n1 = d12 / sqrt(1 + n12_p2 - 2*n12*c12); // 1+n12^2-2n12c12 is always > 0
const double n2 = n1 * n12;
const double n3 = n1 * n13;
if (n1 <= 0 || n2 <= 0 || n3 <= 0)
continue;
// compute and check errors
if (fabs((sqrt(n1*n1 + n2*n2 - 2*n1*n2*c12) - d12) / d12) > VAL_THR ||
fabs((sqrt(n2*n2 + n3*n3 - 2*n2*n3*c23) - d23) / d23) > VAL_THR ||
fabs((sqrt(n3*n3 + n1*n1 - 2*n3*n1*c31) - d31) / d31) > VAL_THR)
continue;
const Vec3d nX1 = n1 * cx1;
Vec3d Z2 = n2 * cx2 - nX1; Z2 /= norm(Z2);
Vec3d Z3 = n3 * cx3 - nX1; Z3 /= norm(Z3);
Vec3d Z1 = Z2.cross(Z3); Z1 /= norm(Z1);
const Vec3d Z3crZ1 = Z3.cross(Z1);
z[0] = Z1(0); z[3] = Z1(1); z[6] = Z1(2);
z[1] = Z2(0); z[4] = Z2(1); z[7] = Z2(2);
z[2] = Z3crZ1(0); z[5] = Z3crZ1(1); z[8] = Z3crZ1(2);
Vec3d Zw2 = (X2 - X1) / d12;
Vec3d Zw3 = (X3 - X1) / d31;
Vec3d Zw1 = Zw2.cross(Zw3); Zw1 /= norm(Zw1);
const Vec3d Z3crZ1w = Zw3.cross(Zw1);
zw[0] = Zw1(0); zw[3] = Zw1(1); zw[6] = Zw1(2);
zw[1] = Zw2(0); zw[4] = Zw2(1); zw[7] = Zw2(2);
zw[2] = Z3crZ1w(0); zw[5] = Z3crZ1w(1); zw[8] = Z3crZ1w(2);
const Matx33d R = Math::rotVec2RotMat(Math::rotMat2RotVec(Z * Zw.inv()));
Mat P, KR = K * R;
hconcat(KR, -KR * (X1 - R.t() * nX1), P);
models.emplace_back(P);
}
return static_cast<int>(models.size());
}
int getSampleSize() const override { return 3; }
int getMaxNumberOfSolutions () const override { return 4; }
Ptr<MinimalSolver> clone () const override {
return makePtr<P3PSolverImpl>(*points_mat, *calib_norm_points_mat, *K_mat);
}
};
Ptr<P3PSolver> P3PSolver::create(const Mat &points_, const Mat &calib_norm_pts, const Mat &K) {
return makePtr<P3PSolverImpl>(points_, calib_norm_pts, K);
}
}}

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modules/calib3d/src/usac/quality.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#include "gamma_values.hpp"
namespace cv { namespace usac {
int Quality::getInliers(const Ptr<Error> &error, const Mat &model, std::vector<int> &inliers, double threshold) {
const auto &errors = error->getErrors(model);
int num_inliers = 0;
for (int point = 0; point < (int)inliers.size(); point++)
if (errors[point] < threshold)
inliers[num_inliers++] = point;
return num_inliers;
}
int Quality::getInliers(const Ptr<Error> &error, const Mat &model, std::vector<bool> &inliers_mask, double threshold) {
std::fill(inliers_mask.begin(), inliers_mask.end(), false);
const auto &errors = error->getErrors(model);
int num_inliers = 0;
for (int point = 0; point < (int)inliers_mask.size(); point++)
if (errors[point] < threshold) {
inliers_mask[point] = true;
num_inliers++;
}
return num_inliers;
}
class RansacQualityImpl : public RansacQuality {
private:
const Ptr<Error> error;
const int points_size;
const double threshold;
double best_score;
public:
RansacQualityImpl (int points_size_, double threshold_, const Ptr<Error> &error_)
: error (error_), points_size(points_size_), threshold(threshold_) {
best_score = std::numeric_limits<double>::max();
}
Score getScore (const Mat &model) const override {
error->setModelParameters(model);
int inlier_number = 0;
for (int point = 0; point < points_size; point++) {
if (error->getError(point) < threshold)
inlier_number++;
if (inlier_number + (points_size - point) < -best_score)
break;
}
// score is negative inlier number! If less then better
return Score(inlier_number, -static_cast<double>(inlier_number));
}
void setBestScore(double best_score_) override {
if (best_score > best_score_) best_score = best_score_;
}
int getInliers (const Mat &model, std::vector<int> &inliers) const override
{ return Quality::getInliers(error, model, inliers, threshold); }
int getInliers (const Mat &model, std::vector<int> &inliers, double thr) const override
{ return Quality::getInliers(error, model, inliers, thr); }
int getInliers (const Mat &model, std::vector<bool> &inliers_mask) const override
{ return Quality::getInliers(error, model, inliers_mask, threshold); }
int getPointsSize () const override { return points_size; }
Ptr<Quality> clone () const override {
return makePtr<RansacQualityImpl>(points_size, threshold, error->clone());
}
};
Ptr<RansacQuality> RansacQuality::create(int points_size_, double threshold_,
const Ptr<Error> &error_) {
return makePtr<RansacQualityImpl>(points_size_, threshold_, error_);
}
class MsacQualityImpl : public MsacQuality {
protected:
const Ptr<Error> error;
const int points_size;
const double threshold;
double best_score;
public:
MsacQualityImpl (int points_size_, double threshold_, const Ptr<Error> &error_)
: error (error_), points_size (points_size_), threshold (threshold_) {
best_score = std::numeric_limits<double>::max();
}
inline Score getScore (const Mat &model) const override {
error->setModelParameters(model);
double err, sum_errors = 0;
int inlier_number = 0;
for (int point = 0; point < points_size; point++) {
err = error->getError(point);
if (err < threshold) {
sum_errors += err;
inlier_number++;
} else
sum_errors += threshold;
if (sum_errors > best_score)
break;
}
return Score(inlier_number, sum_errors);
}
void setBestScore(double best_score_) override {
if (best_score > best_score_) best_score = best_score_;
}
int getInliers (const Mat &model, std::vector<int> &inliers) const override
{ return Quality::getInliers(error, model, inliers, threshold); }
int getInliers (const Mat &model, std::vector<int> &inliers, double thr) const override
{ return Quality::getInliers(error, model, inliers, thr); }
int getInliers (const Mat &model, std::vector<bool> &inliers_mask) const override
{ return Quality::getInliers(error, model, inliers_mask, threshold); }
int getPointsSize () const override { return points_size; }
Ptr<Quality> clone () const override {
return makePtr<MsacQualityImpl>(points_size, threshold, error->clone());
}
};
Ptr<MsacQuality> MsacQuality::create(int points_size_, double threshold_,
const Ptr<Error> &error_) {
return makePtr<MsacQualityImpl>(points_size_, threshold_, error_);
}
class MagsacQualityImpl : public MagsacQuality {
private:
const Ptr<Error> error;
const int points_size;
// for example, maximum standard deviation of noise.
const double maximum_threshold, tentative_inlier_threshold;
// The degrees of freedom of the data from which the model is estimated.
// E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
const int degrees_of_freedom;
// A 0.99 quantile of the Chi^2-distribution to convert sigma values to residuals
const double k;
// A multiplier to convert residual values to sigmas
float threshold_to_sigma_multiplier;
// Calculating k^2 / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double squared_k_per_2;
// Calculating (DoF - 1) / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double dof_minus_one_per_two;
// Calculating (DoF + 1) / 2 which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double dof_plus_one_per_two;
const double C;
// Calculating 2^(DoF - 1) which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double two_ad_dof_minus_one;
// Calculating 2^(DoF + 1) which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double two_ad_dof_plus_one;
// Calculate the gamma value of k
const double gamma_value_of_k;
// Calculate the lower incomplete gamma value of k
const double lower_gamma_value_of_k;
double previous_best_loss;
// Convert the maximum threshold to a sigma value
float maximum_sigma;
// Calculate the squared maximum sigma
float maximum_sigma_2;
// Calculate \sigma_{max}^2 / 2
float maximum_sigma_2_per_2;
// Calculate 2 * \sigma_{max}^2
float maximum_sigma_2_times_2;
// Calculate the loss implied by an outlier
double outlier_loss;
// Calculating 2^(DoF + 1) / \sigma_{max} which will be used for the estimation and,
// due to being constant, it is better to calculate it a priori.
double two_ad_dof_plus_one_per_maximum_sigma;
double scale_of_stored_incomplete_gammas;
std::vector<double> stored_complete_gamma_values, stored_lower_incomplete_gamma_values;
public:
MagsacQualityImpl (double maximum_thr, int points_size_, const Ptr<Error> &error_,
double tentative_inlier_threshold_, int DoF, double sigma_quantile,
double upper_incomplete_of_sigma_quantile,
double lower_incomplete_of_sigma_quantile, double C_)
: error (error_), points_size(points_size_), maximum_threshold(maximum_thr),
tentative_inlier_threshold(tentative_inlier_threshold_), degrees_of_freedom(DoF),
k(sigma_quantile), C(C_), gamma_value_of_k (upper_incomplete_of_sigma_quantile),
lower_gamma_value_of_k (lower_incomplete_of_sigma_quantile) {
previous_best_loss = std::numeric_limits<double>::max();
threshold_to_sigma_multiplier = 1.f / (float)k;
squared_k_per_2 = k * k / 2.0;
dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
dof_plus_one_per_two = (degrees_of_freedom + 1.0) / 2.0;
two_ad_dof_minus_one = std::pow(2.0, dof_minus_one_per_two);
two_ad_dof_plus_one = std::pow(2.0, dof_plus_one_per_two);
maximum_sigma = threshold_to_sigma_multiplier * (float)maximum_threshold;
maximum_sigma_2 = maximum_sigma * maximum_sigma;
maximum_sigma_2_per_2 = maximum_sigma_2 / 2.f;
maximum_sigma_2_times_2 = maximum_sigma_2 * 2.f;
// penalization for outlier
outlier_loss = 10 * maximum_sigma * two_ad_dof_minus_one * lower_gamma_value_of_k;
two_ad_dof_plus_one_per_maximum_sigma = two_ad_dof_plus_one / maximum_sigma;
if (DoF == 4) {
scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n4;
stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n4,
stored_complete_gamma_values_n4+stored_incomplete_gamma_number+1);
stored_lower_incomplete_gamma_values = std::vector<double>
(stored_lower_incomplete_gamma_values_n4,
stored_lower_incomplete_gamma_values_n4+stored_incomplete_gamma_number+1);
} else if (DoF == 5) {
scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n5;
stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n5,
stored_complete_gamma_values_n5+stored_incomplete_gamma_number+1);
stored_lower_incomplete_gamma_values = std::vector<double>
(stored_lower_incomplete_gamma_values_n5,
stored_lower_incomplete_gamma_values_n5+stored_incomplete_gamma_number+1);
} else
CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
}
// https://github.com/danini/magsac
Score getScore (const Mat &model) const override {
error->setModelParameters(model);
double total_loss = 0.0;
int num_tentative_inliers = 0;
for (int point_idx = 0; point_idx < points_size; point_idx++) {
const float squared_residual = error->getError(point_idx);
if (squared_residual < tentative_inlier_threshold)
num_tentative_inliers++;
if (squared_residual < maximum_threshold) { // consider point as inlier
// Get the position of the gamma value in the lookup table
int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
/ maximum_sigma_2_times_2);
// If the sought gamma value is not stored in the lookup, return the closest element
if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
x = stored_incomplete_gamma_number;
// Calculate the loss implied by the current point
total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
(stored_complete_gamma_values[x] - gamma_value_of_k));
} else total_loss += outlier_loss; // outlier
if (total_loss > previous_best_loss)
break; // break if total loss is alreay higher than the best one
}
return Score(num_tentative_inliers, total_loss);
}
Score getScore (const std::vector<float> &errors) const override {
double total_loss = 0.0;
int num_tentative_inliers = 0;
for (int point_idx = 0; point_idx < points_size; point_idx++) {
const float squared_residual = errors[point_idx];
if (squared_residual < tentative_inlier_threshold)
num_tentative_inliers++;
if (squared_residual < maximum_threshold) {
int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
/ maximum_sigma_2_times_2);
if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
x = stored_incomplete_gamma_number;
total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
(stored_complete_gamma_values[x] - gamma_value_of_k));
} else total_loss += outlier_loss;
if (total_loss > previous_best_loss)
break;
}
return Score(num_tentative_inliers, total_loss);
}
void setBestScore (double best_loss) override {
if (previous_best_loss > best_loss) previous_best_loss = best_loss;
}
int getInliers (const Mat &model, std::vector<int> &inliers) const override
{ return Quality::getInliers(error, model, inliers, tentative_inlier_threshold); }
int getInliers (const Mat &model, std::vector<int> &inliers, double thr) const override
{ return Quality::getInliers(error, model, inliers, thr); }
int getInliers (const Mat &model, std::vector<bool> &inliers_mask) const override
{ return Quality::getInliers(error, model, inliers_mask, tentative_inlier_threshold); }
int getPointsSize () const override { return points_size; }
Ptr<Quality> clone () const override {
return makePtr<MagsacQualityImpl>(maximum_sigma, points_size, error->clone(),
tentative_inlier_threshold, degrees_of_freedom, k, gamma_value_of_k,
lower_gamma_value_of_k, C);
}
};
Ptr<MagsacQuality> MagsacQuality::create(double maximum_thr, int points_size_, const Ptr<Error> &error_,
double tentative_inlier_threshold_, int DoF, double sigma_quantile,
double upper_incomplete_of_sigma_quantile,
double lower_incomplete_of_sigma_quantile, double C_) {
return makePtr<MagsacQualityImpl>(maximum_thr, points_size_, error_,
tentative_inlier_threshold_, DoF, sigma_quantile, upper_incomplete_of_sigma_quantile,
lower_incomplete_of_sigma_quantile, C_);
}
class LMedsQualityImpl : public LMedsQuality {
private:
const Ptr<Error> error;
const int points_size;
const double threshold;
public:
LMedsQualityImpl (int points_size_, double threshold_, const Ptr<Error> &error_) :
error (error_), points_size (points_size_), threshold (threshold_) {}
// Finds median of errors.
Score getScore (const Mat &model) const override {
std::vector<float> errors = error->getErrors(model);
int inlier_number = 0;
for (int point = 0; point < points_size; point++)
if (errors[point] < threshold)
inlier_number++;
// score is median of errors
return Score(inlier_number, Utils::findMedian (errors));
}
void setBestScore (double /*best_score*/) override {}
int getPointsSize () const override { return points_size; }
int getInliers (const Mat &model, std::vector<int> &inliers) const override
{ return Quality::getInliers(error, model, inliers, threshold); }
int getInliers (const Mat &model, std::vector<int> &inliers, double thr) const override
{ return Quality::getInliers(error, model, inliers, thr); }
int getInliers (const Mat &model, std::vector<bool> &inliers_mask) const override
{ return Quality::getInliers(error, model, inliers_mask, threshold); }
Ptr<Quality> clone () const override {
return makePtr<LMedsQualityImpl>(points_size, threshold, error->clone());
}
};
Ptr<LMedsQuality> LMedsQuality::create(int points_size_, double threshold_, const Ptr<Error> &error_) {
return makePtr<LMedsQualityImpl>(points_size_, threshold_, error_);
}
class ModelVerifierImpl : public ModelVerifier {
private:
std::vector<float> errors;
public:
inline bool isModelGood(const Mat &/*model*/) override { return true; }
inline bool getScore(Score &/*score*/) const override { return false; }
void update (int /*highest_inlier_number*/) override {}
const std::vector<float> &getErrors() const override { return errors; }
bool hasErrors () const override { return false; }
Ptr<ModelVerifier> clone (int /*state*/) const override { return makePtr<ModelVerifierImpl>();}
};
Ptr<ModelVerifier> ModelVerifier::create() {
return makePtr<ModelVerifierImpl>();
}
///////////////////////////////////// SPRT VERIFIER //////////////////////////////////////////
class SPRTImpl : public SPRT {
private:
RNG rng;
const Ptr<Error> err;
const int points_size;
int highest_inlier_number, current_sprt_idx; // i
// time t_M needed to instantiate a model hypothesis given a sample
// Let m_S be the number of models that are verified per sample
const double inlier_threshold, t_M, m_S;
double lowest_sum_errors, current_epsilon, current_delta, current_A,
delta_to_epsilon, complement_delta_to_complement_epsilon;
std::vector<SPRT_history> sprt_histories;
std::vector<int> points_random_pool;
std::vector<float> errors;
Score score;
const ScoreMethod score_type;
bool last_model_is_good, can_compute_score, has_errors;
public:
SPRTImpl (int state, const Ptr<Error> &err_, int points_size_,
double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model,
double time_sample, double avg_num_models, ScoreMethod score_type_) : rng(state), err(err_),
points_size(points_size_), inlier_threshold (inlier_threshold_),
t_M (time_sample), m_S (avg_num_models), score_type (score_type_) {
// Generate array of random points for randomized evaluation
points_random_pool = std::vector<int> (points_size_);
// fill values from 0 to points_size-1
for (int i = 0; i < points_size; i++)
points_random_pool[i] = i;
randShuffle(points_random_pool, 1, &rng);
// reserve (approximately) some space for sprt vector.
sprt_histories.reserve(20);
createTest(prob_pt_of_good_model, prob_pt_of_bad_model);
highest_inlier_number = 0;
lowest_sum_errors = std::numeric_limits<double>::max();
last_model_is_good = false;
can_compute_score = score_type_ == ScoreMethod::SCORE_METHOD_MSAC
|| score_type_ == ScoreMethod::SCORE_METHOD_RANSAC
|| score_type_ == ScoreMethod::SCORE_METHOD_LMEDS;
// for MSAC and RANSAC errors not needed
if (score_type_ != ScoreMethod::SCORE_METHOD_MSAC && score_type_ != ScoreMethod::SCORE_METHOD_RANSAC)
errors = std::vector<float>(points_size_);
// however return errors only if we can't compute score
has_errors = !can_compute_score;
}
/*
* p(x(r)|Hb) p(x(j)|Hb)
* lambda(j) = Product (----------) = lambda(j-1) * ----------
* p(x(r)|Hg) p(x(j)|Hg)
* Set j = 1
* 1. Check whether j-th data point is consistent with the
* model
* 2. Compute the likelihood ratio λj eq. (1)
* 3. If λj > A, decide the model is ’bad’ (model ”re-jected”),
* else increment j or continue testing
* 4. If j = N the number of correspondences decide model ”accepted”
*
* Verifies model and returns model score.
* Returns true if model is good, false - otherwise.
* @model: model to verify
* @current_hypothesis: current RANSAC iteration
* Return: true if model is good, false - otherwise.
*/
inline bool isModelGood (const Mat &model) override {
// update error object with current model
err->setModelParameters(model);
double lambda = 1, sum_errors = 0;
last_model_is_good = true;
int random_pool_idx = rng.uniform(0, points_size), tested_point, tested_inliers = 0;
for (tested_point = 0; tested_point < points_size; tested_point++) {
if (random_pool_idx >= points_size)
random_pool_idx = 0;
const double error = err->getError (points_random_pool[random_pool_idx++]);
if (error < inlier_threshold) {
tested_inliers++;
lambda *= delta_to_epsilon;
} else {
lambda *= complement_delta_to_complement_epsilon;
// since delta is always higher than epsilon, then lambda can increase only
// when point is not consistent with model
if (lambda > current_A)
break;
}
if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
sum_errors += error < inlier_threshold ? error : inlier_threshold;
if (sum_errors > lowest_sum_errors)
break;
} else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC) {
if (tested_inliers + points_size - tested_point < highest_inlier_number)
break;
} else errors[points_random_pool[random_pool_idx-1]] = (float)error;
}
last_model_is_good = tested_point == points_size;
// increase number of samples processed by current test
sprt_histories[current_sprt_idx].tested_samples++;
if (last_model_is_good) {
score.inlier_number = tested_inliers;
if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
score.score = sum_errors;
lowest_sum_errors = sum_errors;
} else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC)
score.score = -static_cast<double>(tested_inliers);
else if (score_type == ScoreMethod::SCORE_METHOD_LMEDS)
score.score = Utils::findMedian(errors);
const double new_epsilon = static_cast<double>(tested_inliers) / points_size;
if (new_epsilon > current_epsilon) {
highest_inlier_number = tested_inliers; // update max inlier number
/*
* Model accepted and the largest support so far:
* design (i+1)-th test (εi + 1= εˆ, δi+1 = δ, i := i + 1).
* Store the current model parameters θ
*/
createTest(new_epsilon, current_delta);
}
} else {
/*
* Since almost all tested models are ‘bad’, the probability
* δ can be estimated as the average fraction of consistent data points
* in rejected models.
*/
// add 1 to tested_point, because loop over tested_point starts from 0
const double delta_estimated = static_cast<double> (tested_inliers) / (tested_point+1);
if (delta_estimated > 0 && fabs(current_delta - delta_estimated)
/ current_delta > 0.05)
/*
* Model rejected: re-estimate δ. If the estimate δ_ differs
* from δi by more than 5% design (i+1)-th test (εi+1 = εi,
* δi+1 = δˆ, i := i + 1)
*/
createTest(current_epsilon, delta_estimated);
}
return last_model_is_good;
}
inline bool getScore (Score &score_) const override {
if (!last_model_is_good || !can_compute_score)
return false;
score_ = score;
return true;
}
bool hasErrors () const override { return has_errors; }
const std::vector<float> &getErrors () const override { return errors; }
const std::vector<SPRT_history> &getSPRTvector () const override { return sprt_histories; }
void update (int highest_inlier_number_) override {
const double new_epsilon = static_cast<double>(highest_inlier_number_) / points_size;
if (new_epsilon > current_epsilon) {
highest_inlier_number = highest_inlier_number_;
if (sprt_histories[current_sprt_idx].tested_samples == 0)
sprt_histories[current_sprt_idx].tested_samples = 1;
// save sprt test and create new one
createTest(new_epsilon, current_delta);
}
}
Ptr<ModelVerifier> clone (int state) const override {
return makePtr<SPRTImpl>(state, err->clone(), points_size, inlier_threshold,
sprt_histories[current_sprt_idx].epsilon,
sprt_histories[current_sprt_idx].delta, t_M, m_S, score_type);
}
private:
// Saves sprt test to sprt history and update current epsilon, delta and threshold.
void createTest (double epsilon, double delta) {
// if epsilon is closed to 1 then set them to 0.99 to avoid numerical problems
if (epsilon > 0.999999) epsilon = 0.999;
// delta can't be higher than epsilon, because ratio delta / epsilon will be greater than 1
if (epsilon < delta) delta = epsilon-0.0001;
// avoid delta going too high as it is very unlikely
// e.g., 30% of points are consistent with bad model is not very real
if (delta > 0.3) delta = 0.3;
SPRT_history new_sprt_history;
new_sprt_history.epsilon = epsilon;
new_sprt_history.delta = delta;
new_sprt_history.A = estimateThresholdA (epsilon, delta);
sprt_histories.emplace_back(new_sprt_history);
current_A = new_sprt_history.A;
current_delta = delta;
current_epsilon = epsilon;
delta_to_epsilon = delta / epsilon;
complement_delta_to_complement_epsilon = (1 - delta) / (1 - epsilon);
current_sprt_idx = static_cast<int>(sprt_histories.size()) - 1;
}
/*
* A(0) = K1/K2 + 1
* A(n+1) = K1/K2 + 1 + log (A(n))
* K1 = t_M / P_g
* K2 = m_S/(P_g*C)
* t_M is time needed to instantiate a model hypotheses given a sample
* P_g = epsilon ^ m, m is the number of data point in the Ransac sample.
* m_S is the number of models that are verified per sample.
* p (0|Hb) p (1|Hb)
* C = p(0|Hb) log (---------) + p(1|Hb) log (---------)
* p (0|Hg) p (1|Hg)
*/
double estimateThresholdA (double epsilon, double delta) {
const double C = (1 - delta) * log ((1 - delta) / (1 - epsilon)) +
delta * (log(delta / epsilon));
// K = K1/K2 + 1 = (t_M / P_g) / (m_S / (C * P_g)) + 1 = (t_M * C)/m_S + 1
const double K = t_M * C / m_S + 1;
double An, An_1 = K;
// compute A using a recursive relation
// A* = lim(n->inf)(An), the series typically converges within 4 iterations
for (int i = 0; i < 10; i++) {
An = K + log(An_1);
if (fabs(An - An_1) < FLT_EPSILON)
break;
An_1 = An;
}
return An;
}
};
Ptr<SPRT> SPRT::create (int state, const Ptr<Error> &err_, int points_size_,
double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model,
double time_sample, double avg_num_models, ScoreMethod score_type_) {
return makePtr<SPRTImpl>(state, err_, points_size_, inlier_threshold_,
prob_pt_of_good_model, prob_pt_of_bad_model, time_sample, avg_num_models, score_type_);
}
}}

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modules/calib3d/src/usac/ransac_solvers.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#include <atomic>
namespace cv { namespace usac {
int mergePoints (InputArray pts1_, InputArray pts2_, Mat &pts, bool ispnp);
void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, double thr,
int max_iters, double conf, bool mask_needed);
class RansacOutputImpl : public RansacOutput {
private:
Mat model;
// vector of number_inliers size
std::vector<int> inliers;
// vector of points size, true if inlier, false-outlier
std::vector<bool> inliers_mask;
// vector of points size, value of i-th index corresponds to error of i-th point if i is inlier.
std::vector<double> errors;
// the best found score of RANSAC
double score;
int seconds, milliseconds, microseconds;
int time_mcs, number_inliers, number_estimated_models, number_good_models;
int number_iterations; // number of iterations of main RANSAC
public:
RansacOutputImpl (const Mat &model_, const std::vector<bool> &inliers_mask_,
int time_mcs_, double score_, int number_inliers_, int number_iterations_,
int number_estimated_models_, int number_good_models_) {
model_.copyTo(model);
inliers_mask = inliers_mask_;
time_mcs = time_mcs_;
score = score_;
number_inliers = number_inliers_;
number_iterations = number_iterations_;
number_estimated_models = number_estimated_models_;
number_good_models = number_good_models_;
microseconds = time_mcs % 1000;
milliseconds = ((time_mcs - microseconds)/1000) % 1000;
seconds = ((time_mcs - 1000*milliseconds - microseconds)/(1000*1000)) % 60;
}
/*
* Return inliers' indices.
* size of vector = number of inliers
*/
const std::vector<int> &getInliers() override {
if (inliers.empty()) {
inliers.reserve(inliers_mask.size());
int pt_cnt = 0;
for (bool is_inlier : inliers_mask) {
if (is_inlier)
inliers.emplace_back(pt_cnt);
pt_cnt++;
}
}
return inliers;
}
// Return inliers mask. Vector of points size. 1-inlier, 0-outlier.
const std::vector<bool> &getInliersMask() const override { return inliers_mask; }
int getTimeMicroSeconds() const override {return time_mcs; }
int getTimeMicroSeconds1() const override {return microseconds; }
int getTimeMilliSeconds2() const override {return milliseconds; }
int getTimeSeconds3() const override {return seconds; }
int getNumberOfInliers() const override { return number_inliers; }
int getNumberOfMainIterations() const override { return number_iterations; }
int getNumberOfGoodModels () const override { return number_good_models; }
int getNumberOfEstimatedModels () const override { return number_estimated_models; }
const Mat &getModel() const override { return model; }
};
Ptr<RansacOutput> RansacOutput::create(const Mat &model_, const std::vector<bool> &inliers_mask_,
int time_mcs_, double score_, int number_inliers_, int number_iterations_,
int number_estimated_models_, int number_good_models_) {
return makePtr<RansacOutputImpl>(model_, inliers_mask_, time_mcs_, score_, number_inliers_,
number_iterations_, number_estimated_models_, number_good_models_);
}
class Ransac {
protected:
const Ptr<const Model> params;
const Ptr<const Estimator> _estimator;
const Ptr<Quality> _quality;
const Ptr<Sampler> _sampler;
const Ptr<TerminationCriteria> _termination_criteria;
const Ptr<ModelVerifier> _model_verifier;
const Ptr<Degeneracy> _degeneracy;
const Ptr<LocalOptimization> _local_optimization;
const Ptr<FinalModelPolisher> model_polisher;
const int points_size, state;
const bool parallel;
public:
Ransac (const Ptr<const Model> &params_, int points_size_, const Ptr<const Estimator> &estimator_, const Ptr<Quality> &quality_,
const Ptr<Sampler> &sampler_, const Ptr<TerminationCriteria> &termination_criteria_,
const Ptr<ModelVerifier> &model_verifier_, const Ptr<Degeneracy> &degeneracy_,
const Ptr<LocalOptimization> &local_optimization_, const Ptr<FinalModelPolisher> &model_polisher_,
bool parallel_=false, int state_ = 0) :
params (params_), _estimator (estimator_), _quality (quality_), _sampler (sampler_),
_termination_criteria (termination_criteria_), _model_verifier (model_verifier_),
_degeneracy (degeneracy_), _local_optimization (local_optimization_),
model_polisher (model_polisher_), points_size (points_size_), state(state_),
parallel(parallel_) {}
bool run(Ptr<RansacOutput> &ransac_output) {
if (points_size < params->getSampleSize())
return false;
const auto begin_time = std::chrono::steady_clock::now();
// check if LO
const bool LO = params->getLO() != LocalOptimMethod::LOCAL_OPTIM_NULL;
const bool is_magsac = params->getLO() == LocalOptimMethod::LOCAL_OPTIM_SIGMA;
const int repeat_magsac = 10;
Score best_score;
Mat best_model;
int final_iters;
if (! parallel) {
Mat non_degenerate_model, lo_model;
Score current_score, lo_score, non_denegenerate_model_score;
// reallocate memory for models
std::vector<Mat> models(_estimator->getMaxNumSolutions());
// allocate memory for sample
std::vector<int> sample(_estimator->getMinimalSampleSize());
int iters = 0, max_iters = params->getMaxIters();
for (; iters < max_iters; iters++) {
_sampler->generateSample(sample);
const int number_of_models = _estimator->estimateModels(sample, models);
for (int i = 0; i < number_of_models; i++) {
if (is_magsac && iters % repeat_magsac == 0) {
if (!_local_optimization->refineModel
(models[i], best_score, models[i], current_score))
continue;
} else if (_model_verifier->isModelGood(models[i])) {
if (!_model_verifier->getScore(current_score)) {
if (_model_verifier->hasErrors())
current_score = _quality->getScore(_model_verifier->getErrors());
else current_score = _quality->getScore(models[i]);
}
} else continue;
if (current_score.isBetter(best_score)) {
if (_degeneracy->recoverIfDegenerate(sample, models[i],
non_degenerate_model, non_denegenerate_model_score)) {
// check if best non degenerate model is better than so far the best model
if (non_denegenerate_model_score.isBetter(best_score)) {
best_score = non_denegenerate_model_score;
non_degenerate_model.copyTo(best_model);
} else
// non degenerate models are worse then so far the best model.
continue;
} else {
// copy current score to best score
best_score = current_score;
// remember best model
models[i].copyTo(best_model);
}
// update quality to save evaluation time of a model
// with no chance of being better than so-far-the-best
_quality->setBestScore(best_score.score);
// update upper bound of iterations
max_iters = _termination_criteria->update
(best_model, best_score.inlier_number);
if (iters > max_iters)
break;
if (LO) {//} && iters >= max_iters_before_LO) {
// do magsac if it wasn't already run
if (is_magsac && iters % repeat_magsac == 0) continue; // magsac has already run
// update model by Local optimization
if (_local_optimization->refineModel
(best_model, best_score, lo_model, lo_score))
if (lo_score.isBetter(best_score)) {
best_score = lo_score;
lo_model.copyTo(best_model);
// update quality and verifier and termination again
_quality->setBestScore(best_score.score);
_model_verifier->update(best_score.inlier_number);
max_iters = _termination_criteria->update
(best_model, best_score.inlier_number);
if (iters > max_iters)
break;
}
}
} // end of if so far the best score
} // end loop of number of models
} // end main while loop
final_iters = iters;
} else {
const int MAX_THREADS = getNumThreads();
const bool is_prosac = params->getSampler() == SamplingMethod::SAMPLING_PROSAC;
std::atomic_bool success(false);
std::atomic_int num_hypothesis_tested(0);
std::atomic_int thread_cnt(0);
std::vector<Score> best_scores(MAX_THREADS);
std::vector<Mat> best_models(MAX_THREADS);
Mutex mutex; // only for prosac
///////////////////////////////////////////////////////////////////////////////////////////////////////
parallel_for_(Range(0, MAX_THREADS), [&](const Range & /*range*/) {
if (!success) { // cover all if not success to avoid thread creating new variables
const int thread_rng_id = thread_cnt++;
int thread_state = state + 10*thread_rng_id;
Ptr<Estimator> estimator = _estimator->clone();
Ptr<Degeneracy> degeneracy = _degeneracy->clone(thread_state++);
Ptr<Quality> quality = _quality->clone();
Ptr<ModelVerifier> model_verifier = _model_verifier->clone(thread_state++); // update verifier
Ptr<LocalOptimization> local_optimization = _local_optimization->clone(thread_state++);
Ptr<TerminationCriteria> termination_criteria = _termination_criteria->clone();
Ptr<Sampler> sampler;
if (!is_prosac)
sampler = _sampler->clone(thread_state);
Mat best_model_thread, non_degenerate_model, lo_model;
Score best_score_thread, current_score, non_denegenerate_model_score, lo_score,
best_score_all_threads;
std::vector<int> sample(estimator->getMinimalSampleSize());
std::vector<Mat> models(estimator->getMaxNumSolutions());
int iters, max_iters = params->getMaxIters();
auto update_best = [&] (const Score &new_score, const Mat &new_model) {
// copy new score to best score
best_score_thread = new_score;
best_scores[thread_rng_id] = best_score_thread;
// remember best model
new_model.copyTo(best_model_thread);
best_model_thread.copyTo(best_models[thread_rng_id]);
best_score_all_threads = best_score_thread;
};
for (iters = 0; iters < max_iters && !success; iters++) {
success = num_hypothesis_tested++ > max_iters;
if (iters % 10) {
// Synchronize threads. just to speed verification of model.
int best_thread_idx = thread_rng_id;
bool updated = false;
for (int t = 0; t < MAX_THREADS; t++) {
if (best_scores[t].isBetter(best_score_all_threads)) {
best_score_all_threads = best_scores[t];
updated = true;
best_thread_idx = t;
}
}
if (updated && best_thread_idx != thread_rng_id) {
quality->setBestScore(best_score_all_threads.score);
model_verifier->update(best_score_all_threads.inlier_number);
}
}
if (is_prosac) {
// use global sampler
mutex.lock();
_sampler->generateSample(sample);
mutex.unlock();
} else sampler->generateSample(sample); // use local sampler
const int number_of_models = estimator->estimateModels(sample, models);
for (int i = 0; i < number_of_models; i++) {
if (is_magsac && iters % repeat_magsac == 0) {
if (!local_optimization->refineModel
(models[i], best_score_thread, models[i], current_score))
continue;
} else if (model_verifier->isModelGood(models[i])) {
if (!model_verifier->getScore(current_score)) {
if (model_verifier->hasErrors())
current_score = quality->getScore(model_verifier->getErrors());
else current_score = quality->getScore(models[i]);
}
} else continue;
if (current_score.isBetter(best_score_all_threads)) {
if (degeneracy->recoverIfDegenerate(sample, models[i],
non_degenerate_model, non_denegenerate_model_score)) {
// check if best non degenerate model is better than so far the best model
if (non_denegenerate_model_score.isBetter(best_score_thread))
update_best(non_denegenerate_model_score, non_degenerate_model);
else
// non degenerate models are worse then so far the best model.
continue;
} else
update_best(current_score, models[i]);
// update upper bound of iterations
max_iters = termination_criteria->update
(best_model_thread, best_score_thread.inlier_number);
if (num_hypothesis_tested > max_iters) {
success = true; break;
}
if (LO) {
// do magsac if it wasn't already run
if (is_magsac && iters % repeat_magsac == 0) continue;
// update model by Local optimizaion
if (local_optimization->refineModel
(best_model_thread, best_score_thread, lo_model, lo_score))
if (lo_score.isBetter(best_score_thread)) {
update_best(lo_score, lo_model);
// update termination again
max_iters = termination_criteria->update
(best_model_thread, best_score_thread.inlier_number);
if (num_hypothesis_tested > max_iters) {
success = true;
break;
}
}
}
} // end of if so far the best score
} // end loop of number of models
} // end of loop over iters
}}); // end parallel
///////////////////////////////////////////////////////////////////////////////////////////////////////
// find best model from all threads' models
best_score = best_scores[0];
int best_thread_idx = 0;
for (int i = 1; i < MAX_THREADS; i++) {
if (best_scores[i].isBetter(best_score)) {
best_score = best_scores[i];
best_thread_idx = i;
}
}
best_model = best_models[best_thread_idx];
final_iters = num_hypothesis_tested;
}
if (best_model.empty())
return false;
// polish final model
if (params->getFinalPolisher() != PolishingMethod::NonePolisher) {
Mat polished_model;
Score polisher_score;
if (model_polisher->polishSoFarTheBestModel(best_model, best_score,
polished_model, polisher_score))
if (polisher_score.isBetter(best_score)) {
best_score = polisher_score;
polished_model.copyTo(best_model);
}
}
// ================= here is ending ransac main implementation ===========================
std::vector<bool> inliers_mask;
if (params->isMaskRequired()) {
inliers_mask = std::vector<bool>(points_size);
// get final inliers from the best model
_quality->getInliers(best_model, inliers_mask);
}
// Store results
ransac_output = RansacOutput::create(best_model, inliers_mask,
static_cast<int>(std::chrono::duration_cast<std::chrono::microseconds>
(std::chrono::steady_clock::now() - begin_time).count()), best_score.score,
best_score.inlier_number, final_iters, -1, -1);
return true;
}
};
/*
* pts1, pts2 are matrices either N x a, N x b or a x N or b x N, where N > a and N > b
* pts1 are image points, if pnp pts2 are object points otherwise - image points as well.
* output is matrix of size N x (a + b)
* return points_size = N
*/
int mergePoints (InputArray pts1_, InputArray pts2_, Mat &pts, bool ispnp) {
Mat pts1 = pts1_.getMat(), pts2 = pts2_.getMat();
auto convertPoints = [] (Mat &points, int pt_dim) {
points.convertTo(points, CV_32F); // convert points to have float precision
if (points.channels() > 1)
points = points.reshape(1, (int)points.total()); // convert point to have 1 channel
if (points.rows < points.cols)
transpose(points, points); // transpose so points will be in rows
CV_CheckGE(points.cols, pt_dim, "Invalid dimension of point");
if (points.cols != pt_dim) // in case when image points are 3D convert them to 2D
points = points.colRange(0, pt_dim);
};
convertPoints(pts1, 2); // pts1 are always image points
convertPoints(pts2, ispnp ? 3 : 2); // for PnP points are 3D
// points are of size [Nx2 Nx2] = Nx4 for H, F, E
// points are of size [Nx2 Nx3] = Nx5 for PnP
hconcat(pts1, pts2, pts);
return pts.rows;
}
void saveMask (OutputArray mask, const std::vector<bool> &inliers_mask) {
if (mask.needed()) {
const int points_size = (int) inliers_mask.size();
mask.create(1, points_size, CV_8U);
auto * maskptr = mask.getMat().ptr<uchar>();
for (int i = 0; i < points_size; i++)
maskptr[i] = (uchar) inliers_mask[i];
}
}
void setParameters (Ptr<Model> &params, EstimationMethod estimator, const UsacParams &usac_params,
bool mask_needed) {
params = Model::create(usac_params.threshold, estimator, usac_params.sampler,
usac_params.confidence, usac_params.maxIterations, usac_params.score);
params->setLocalOptimization(usac_params.loMethod);
params->setLOSampleSize(usac_params.loSampleSize);
params->setLOIterations(usac_params.loIterations);
params->setParallel(usac_params.isParallel);
params->setNeighborsType(usac_params.neighborsSearch);
params->setRandomGeneratorState(usac_params.randomGeneratorState);
params->maskRequired(mask_needed);
}
void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, double thr,
int max_iters, double conf, bool mask_needed) {
switch (flag) {
case USAC_DEFAULT:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
ScoreMethod::SCORE_METHOD_MSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO);
break;
case USAC_MAGSAC:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
ScoreMethod::SCORE_METHOD_MAGSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_SIGMA);
params->setLOSampleSize(100);
break;
case USAC_PARALLEL:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
ScoreMethod::SCORE_METHOD_MSAC);
params->setParallel(true);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_LO);
break;
case USAC_ACCURATE:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
ScoreMethod::SCORE_METHOD_MSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_GC);
break;
case USAC_FAST:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
ScoreMethod::SCORE_METHOD_RANSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO);
params->setLOIterations(7);
params->setLOIterativeIters(4);
break;
case USAC_PROSAC:
params = Model::create(thr, estimator, SamplingMethod::SAMPLING_PROSAC, conf, max_iters,
ScoreMethod::SCORE_METHOD_MSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_LO);
break;
case USAC_FM_8PTS:
params = Model::create(thr, EstimationMethod::Fundamental8,SamplingMethod::SAMPLING_UNIFORM,
conf, max_iters,ScoreMethod::SCORE_METHOD_MSAC);
params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_LO);
break;
default: CV_Error(cv::Error::StsBadFlag, "Incorrect flag for USAC!");
}
params->maskRequired(mask_needed);
}
Mat findHomography (InputArray srcPoints, InputArray dstPoints, int method, double thr,
OutputArray mask, const int max_iters, const double confidence) {
Ptr<Model> params;
setParameters(method, params, EstimationMethod::Homography, thr, max_iters, confidence, mask.needed());
Ptr<RansacOutput> ransac_output;
if (run(params, srcPoints, dstPoints, params->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel() / ransac_output->getModel().at<double>(2,2);
} else return Mat();
}
Mat findFundamentalMat( InputArray points1, InputArray points2, int method, double thr,
double confidence, int max_iters, OutputArray mask ) {
Ptr<Model> params;
setParameters(method, params, EstimationMethod::Fundamental, thr, max_iters, confidence, mask.needed());
Ptr<RansacOutput> ransac_output;
if (run(params, points1, points2, params->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel();
} else return Mat();
}
Mat findEssentialMat (InputArray points1, InputArray points2, InputArray cameraMatrix1,
int method, double prob, double thr, OutputArray mask) {
Ptr<Model> params;
setParameters(method, params, EstimationMethod::Essential, thr, 1000, prob, mask.needed());
Ptr<RansacOutput> ransac_output;
if (run(params, points1, points2, params->getRandomGeneratorState(),
ransac_output, cameraMatrix1, cameraMatrix1, noArray(), noArray())) {
saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel();
} else return Mat();
}
bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
InputArray cameraMatrix, InputArray distCoeffs, OutputArray rvec, OutputArray tvec,
bool /*useExtrinsicGuess*/, int max_iters, float thr, double conf,
OutputArray mask, int method) {
Ptr<Model> params;
setParameters(method, params, cameraMatrix.empty() ? EstimationMethod ::P6P : EstimationMethod ::P3P,
thr, max_iters, conf, mask.needed());
Ptr<RansacOutput> ransac_output;
if (run(params, imagePoints, objectPoints, params->getRandomGeneratorState(),
ransac_output, cameraMatrix, noArray(), distCoeffs, noArray())) {
saveMask(mask, ransac_output->getInliersMask());
const Mat &model = ransac_output->getModel();
model.col(0).copyTo(rvec);
model.col(1).copyTo(tvec);
return true;
} else return false;
}
Mat estimateAffine2D(InputArray from, InputArray to, OutputArray mask, int method,
double thr, int max_iters, double conf, int /*refineIters*/) {
Ptr<Model> params;
setParameters(method, params, EstimationMethod ::Affine, thr, max_iters, conf, mask.needed());
Ptr<RansacOutput> ransac_output;
if (run(params, from, to, params->getRandomGeneratorState(),
ransac_output, noArray(), noArray(), noArray(), noArray())) {
saveMask(mask, ransac_output->getInliersMask());
return ransac_output->getModel().rowRange(0,2);
} else return Mat();
}
class ModelImpl : public Model {
private:
// main parameters:
double threshold, confidence;
int sample_size, max_iterations;
EstimationMethod estimator;
SamplingMethod sampler;
ScoreMethod score;
// for neighborhood graph
int k_nearest_neighbors = 8;//, flann_search_params = 5, num_kd_trees = 1; // for FLANN
int cell_size = 25; // pixels, for grid neighbors searching
int radius = 20; // pixels, for radius-search neighborhood graph
NeighborSearchMethod neighborsType = NeighborSearchMethod::NEIGH_GRID;
// Local Optimization parameters
LocalOptimMethod lo = LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO;
int lo_sample_size=14, lo_inner_iterations=15, lo_iterative_iterations=5,
lo_thr_multiplier=3, lo_iter_sample_size = 30;
// Graph cut parameters
const double spatial_coherence_term = 0.975;
// apply polisher for final RANSAC model
PolishingMethod polisher = PolishingMethod ::LSQPolisher;
// preemptive verification test
VerificationMethod verifier = VerificationMethod ::SprtVerifier;
const int max_hypothesis_test_before_verification = 10;
// sprt parameters
// lower bound estimate is 1.1% of inliers
double sprt_eps = 0.011, sprt_delta = 0.01, avg_num_models, time_for_model_est;
// estimator error
ErrorMetric est_error;
// progressive napsac
double relax_coef = 0.1;
// for building neighborhood graphs
const std::vector<int> grid_cell_number = {16, 8, 4, 2};
//for final least squares polisher
int final_lsq_iters = 2;
bool need_mask = true, is_parallel = false;
int random_generator_state = 0;
// magsac parameters:
int DoF = 4;
double sigma_quantile = 3.64, upper_incomplete_of_sigma_quantile = 0.00365,
lower_incomplete_of_sigma_quantile = 1.30122, C = 0.25, maximum_thr = 10.;
public:
ModelImpl (double threshold_, EstimationMethod estimator_, SamplingMethod sampler_, double confidence_=0.95,
int max_iterations_=5000, ScoreMethod score_ =ScoreMethod::SCORE_METHOD_MSAC) {
estimator = estimator_;
sampler = sampler_;
confidence = confidence_;
max_iterations = max_iterations_;
score = score_;
switch (estimator_) {
// time for model estimation is basically a ratio of time need to estimate a model to
// time needed to verify if a point is consistent with this model
case (EstimationMethod::Affine):
avg_num_models = 1; time_for_model_est = 50;
sample_size = 3; est_error = ErrorMetric ::FORW_REPR_ERR; break;
case (EstimationMethod::Homography):
avg_num_models = 1; time_for_model_est = 90;
sample_size = 4; est_error = ErrorMetric ::FORW_REPR_ERR; break;
case (EstimationMethod::Fundamental):
avg_num_models = 2.38; time_for_model_est = 150; maximum_thr = 3;
sample_size = 7; est_error = ErrorMetric ::SAMPSON_ERR; break;
case (EstimationMethod::Fundamental8):
avg_num_models = 1; time_for_model_est = 100; maximum_thr = 3;
sample_size = 8; est_error = ErrorMetric ::SAMPSON_ERR; break;
case (EstimationMethod::Essential):
avg_num_models = 3.93; time_for_model_est = 2000; maximum_thr = 3;
sample_size = 5; est_error = ErrorMetric ::SGD_ERR; break;
case (EstimationMethod::P3P):
avg_num_models = 1.38; time_for_model_est = 800;
sample_size = 3; est_error = ErrorMetric ::RERPOJ; break;
case (EstimationMethod::P6P):
avg_num_models = 1; time_for_model_est = 300;
sample_size = 6; est_error = ErrorMetric ::RERPOJ; break;
default: CV_Assert(0 && "Estimator has not implemented yet!");
}
if (estimator_ == EstimationMethod::P3P || estimator_ == EstimationMethod::P6P) {
neighborsType = NeighborSearchMethod::NEIGH_FLANN_KNN;
k_nearest_neighbors = 2;
DoF = 5;
sigma_quantile = 3.88;
upper_incomplete_of_sigma_quantile = 0.00458;
lower_incomplete_of_sigma_quantile = 1.96032;
C = 0.13298;
}
threshold = threshold_;
}
void setVerifier (VerificationMethod verifier_) override { verifier = verifier_; }
void setPolisher (PolishingMethod polisher_) override { polisher = polisher_; }
void setParallel (bool is_parallel_) override { is_parallel = is_parallel_; }
void setError (ErrorMetric error_) override { est_error = error_; }
void setLocalOptimization (LocalOptimMethod lo_) override { lo = lo_; }
void setKNearestNeighhbors (int knn_) override { k_nearest_neighbors = knn_; }
void setNeighborsType (NeighborSearchMethod neighbors) override { neighborsType = neighbors; }
void setCellSize (int cell_size_) override { cell_size = cell_size_; }
void setLOIterations (int iters) override { lo_inner_iterations = iters; }
void setLOIterativeIters (int iters) override {lo_iterative_iterations = iters; }
void setLOSampleSize (int lo_sample_size_) override { lo_sample_size = lo_sample_size_; }
void maskRequired (bool need_mask_) override { need_mask = need_mask_; }
void setRandomGeneratorState (int state) override { random_generator_state = state; }
bool isMaskRequired () const override { return need_mask; }
NeighborSearchMethod getNeighborsSearch () const override { return neighborsType; }
int getKNN () const override { return k_nearest_neighbors; }
ErrorMetric getError () const override { return est_error; }
EstimationMethod getEstimator () const override { return estimator; }
int getSampleSize () const override { return sample_size; }
int getFinalLSQIterations () const override { return final_lsq_iters; }
int getDegreesOfFreedom () const override { return DoF; }
double getSigmaQuantile () const override { return sigma_quantile; }
double getUpperIncompleteOfSigmaQuantile () const override {
return upper_incomplete_of_sigma_quantile;
}
double getLowerIncompleteOfSigmaQuantile () const override {
return lower_incomplete_of_sigma_quantile;
}
double getC () const override { return C; }
double getMaximumThreshold () const override { return maximum_thr; }
double getGraphCutSpatialCoherenceTerm () const override { return spatial_coherence_term; }
int getLOSampleSize () const override { return lo_sample_size; }
int getMaxNumHypothesisToTestBeforeRejection() const override {
return max_hypothesis_test_before_verification;
}
PolishingMethod getFinalPolisher () const override { return polisher; }
int getLOThresholdMultiplier() const override { return lo_thr_multiplier; }
int getLOIterativeSampleSize() const override { return lo_iter_sample_size; }
int getLOIterativeMaxIters() const override { return lo_iterative_iterations; }
int getLOInnerMaxIters() const override { return lo_inner_iterations; }
LocalOptimMethod getLO () const override { return lo; }
ScoreMethod getScore () const override { return score; }
int getMaxIters () const override { return max_iterations; }
double getConfidence () const override { return confidence; }
double getThreshold () const override { return threshold; }
VerificationMethod getVerifier () const override { return verifier; }
SamplingMethod getSampler () const override { return sampler; }
int getRandomGeneratorState () const override { return random_generator_state; }
double getSPRTdelta () const override { return sprt_delta; }
double getSPRTepsilon () const override { return sprt_eps; }
double getSPRTavgNumModels () const override { return avg_num_models; }
int getCellSize () const override { return cell_size; }
int getGraphRadius() const override { return radius; }
double getTimeForModelEstimation () const override { return time_for_model_est; }
double getRelaxCoef () const override { return relax_coef; }
const std::vector<int> &getGridCellNumber () const override { return grid_cell_number; }
bool isParallel () const override { return is_parallel; }
bool isFundamental () const override {
return estimator == EstimationMethod ::Fundamental ||
estimator == EstimationMethod ::Fundamental8;
}
bool isHomography () const override { return estimator == EstimationMethod ::Homography; }
bool isEssential () const override { return estimator == EstimationMethod ::Essential; }
bool isPnP() const override {
return estimator == EstimationMethod ::P3P || estimator == EstimationMethod ::P6P;
}
};
Ptr<Model> Model::create(double threshold_, EstimationMethod estimator_, SamplingMethod sampler_,
double confidence_, int max_iterations_, ScoreMethod score_) {
return makePtr<ModelImpl>(threshold_, estimator_, sampler_, confidence_,
max_iterations_, score_);
}
bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2, int state,
Ptr<RansacOutput> &ransac_output, InputArray K1_, InputArray K2_,
InputArray dist_coeff1, InputArray dist_coeff2) {
Ptr<Error> error;
Ptr<Estimator> estimator;
Ptr<NeighborhoodGraph> graph;
Ptr<Degeneracy> degeneracy;
Ptr<Quality> quality;
Ptr<ModelVerifier> verifier;
Ptr<Sampler> sampler;
Ptr<RandomGenerator> lo_sampler;
Ptr<TerminationCriteria> termination;
Ptr<LocalOptimization> lo;
Ptr<FinalModelPolisher> polisher;
Ptr<MinimalSolver> min_solver;
Ptr<NonMinimalSolver> non_min_solver;
Mat points, K1, K2, calib_points, undist_points1, undist_points2;
int points_size;
double threshold = params->getThreshold(), max_thr = params->getMaximumThreshold();
const int min_sample_size = params->getSampleSize();
if (params->isPnP()) {
if (! K1_.empty()) {
K1 = K1_.getMat(); K1.convertTo(K1, CV_64F);
if (! dist_coeff1.empty()) {
// undistortPoints also calibrate points using K
undistortPoints(points1, undist_points1, K1_, dist_coeff1);
points_size = mergePoints(undist_points1, points2, points, true);
Utils::normalizeAndDecalibPointsPnP (K1, points, calib_points);
} else {
points_size = mergePoints(points1, points2, points, true);
Utils::calibrateAndNormalizePointsPnP(K1, points, calib_points);
}
} else
points_size = mergePoints(points1, points2, points, true);
} else {
if (params->isEssential()) {
CV_CheckEQ(!K1_.empty() && !K2_.empty(), true, "Intrinsic matrix must not be empty!");
K1 = K1_.getMat(); K1.convertTo(K1, CV_64F);
K2 = K2_.getMat(); K2.convertTo(K2, CV_64F);
if (! dist_coeff1.empty() || ! dist_coeff2.empty()) {
// undistortPoints also calibrate points using K
cv::undistortPoints(points1, undist_points1, K1_, dist_coeff1);
cv::undistortPoints(points2, undist_points2, K2_, dist_coeff2);
points_size = mergePoints(undist_points1, undist_points2, calib_points, false);
} else {
points_size = mergePoints(points1, points2, points, false);
Utils::calibratePoints(K1, K2, points, calib_points);
}
threshold = Utils::getCalibratedThreshold(threshold, K1, K2);
max_thr = Utils::getCalibratedThreshold(max_thr, K1, K2);
} else
points_size = mergePoints(points1, points2, points, false);
}
// Since error function output squared error distance, so make
// threshold squared as well
threshold *= threshold;
if (params->getSampler() == SamplingMethod::SAMPLING_NAPSAC || params->getLO() == LocalOptimMethod::LOCAL_OPTIM_GC) {
if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_GRID) {
graph = GridNeighborhoodGraph::create(points, points_size,
params->getCellSize(), params->getCellSize(),
params->getCellSize(), params->getCellSize());
} else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_KNN) {
graph = FlannNeighborhoodGraph::create(points, points_size,params->getKNN(), false, 5, 1);
} else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_RADIUS) {
graph = RadiusSearchNeighborhoodGraph::create(points, points_size,
params->getGraphRadius(), 5, 1);
} else CV_Error(cv::Error::StsNotImplemented, "Graph type is not implemented!");
}
std::vector<Ptr<NeighborhoodGraph>> layers;
if (params->getSampler() == SamplingMethod::SAMPLING_PROGRESSIVE_NAPSAC) {
CV_CheckEQ(params->isPnP(), false, "ProgressiveNAPSAC for PnP is not implemented!");
const auto &cell_number_per_layer = params->getGridCellNumber();
layers.reserve(cell_number_per_layer.size());
const auto * const pts = (float *) points.data;
float img1_width = 0, img1_height = 0, img2_width = 0, img2_height = 0;
for (int i = 0; i < 4 * points_size; i += 4) {
if (pts[i ] > img1_width ) img1_width = pts[i ];
if (pts[i + 1] > img1_height) img1_height = pts[i + 1];
if (pts[i + 2] > img2_width ) img2_width = pts[i + 2];
if (pts[i + 3] > img2_height) img2_height = pts[i + 3];
}
// Create grid graphs (overlapping layes of given cell numbers)
for (int layer_idx = 0; layer_idx < (int)cell_number_per_layer.size(); layer_idx++) {
const int cell_number = cell_number_per_layer[layer_idx];
if (layer_idx > 0)
if (cell_number_per_layer[layer_idx-1] <= cell_number)
CV_Error(cv::Error::StsError, "Progressive NAPSAC sampler: "
"Cell number in layers must be in decreasing order!");
layers.emplace_back(GridNeighborhoodGraph::create(points, points_size,
(int)(img1_width / (float)cell_number), (int)(img1_height / (float)cell_number),
(int)(img2_width / (float)cell_number), (int)(img2_height / (float)cell_number)));
}
}
// update points by calibrated for Essential matrix after graph is calculated
if (params->isEssential()) {
points = calib_points;
// if maximum calibrated threshold significanlty differs threshold then set upper bound
if (max_thr > 10*threshold)
max_thr = 10*threshold;
}
switch (params->getError()) {
case ErrorMetric::SYMM_REPR_ERR:
error = ReprojectionErrorSymmetric::create(points); break;
case ErrorMetric::FORW_REPR_ERR:
if (params->getEstimator() == EstimationMethod::Affine)
error = ReprojectionErrorAffine::create(points);
else error = ReprojectionErrorForward::create(points);
break;
case ErrorMetric::SAMPSON_ERR:
error = SampsonError::create(points); break;
case ErrorMetric::SGD_ERR:
error = SymmetricGeometricDistance::create(points); break;
case ErrorMetric::RERPOJ:
error = ReprojectionErrorPmatrix::create(points); break;
default: CV_Error(cv::Error::StsNotImplemented , "Error metric is not implemented!");
}
switch (params->getScore()) {
case ScoreMethod::SCORE_METHOD_RANSAC :
quality = RansacQuality::create(points_size, threshold, error); break;
case ScoreMethod::SCORE_METHOD_MSAC :
quality = MsacQuality::create(points_size, threshold, error); break;
case ScoreMethod::SCORE_METHOD_MAGSAC :
quality = MagsacQuality::create(max_thr, points_size, error,
threshold, params->getDegreesOfFreedom(), params->getSigmaQuantile(),
params->getUpperIncompleteOfSigmaQuantile(),
params->getLowerIncompleteOfSigmaQuantile(), params->getC()); break;
case ScoreMethod::SCORE_METHOD_LMEDS :
quality = LMedsQuality::create(points_size, threshold, error); break;
default: CV_Error(cv::Error::StsNotImplemented, "Score is not imeplemeted!");
}
if (params->isHomography()) {
degeneracy = HomographyDegeneracy::create(points);
min_solver = HomographyMinimalSolver4ptsGEM::create(points);
non_min_solver = HomographyNonMinimalSolver::create(points);
estimator = HomographyEstimator::create(min_solver, non_min_solver, degeneracy);
} else if (params->isFundamental()) {
degeneracy = FundamentalDegeneracy::create(state++, quality, points, min_sample_size, 5. /*sqr homogr thr*/);
if(min_sample_size == 7) min_solver = FundamentalMinimalSolver7pts::create(points);
else min_solver = FundamentalMinimalSolver8pts::create(points);
non_min_solver = FundamentalNonMinimalSolver::create(points);
estimator = FundamentalEstimator::create(min_solver, non_min_solver, degeneracy);
} else if (params->isEssential()) {
degeneracy = EssentialDegeneracy::create(points, min_sample_size);
min_solver = EssentialMinimalSolverStewenius5pts::create(points);
non_min_solver = EssentialNonMinimalSolver::create(points);
estimator = EssentialEstimator::create(min_solver, non_min_solver, degeneracy);
} else if (params->isPnP()) {
degeneracy = makePtr<Degeneracy>();
if (min_sample_size == 3) {
non_min_solver = DLSPnP::create(points, calib_points, K1);
min_solver = P3PSolver::create(points, calib_points, K1);
} else {
min_solver = PnPMinimalSolver6Pts::create(points);
non_min_solver = PnPNonMinimalSolver::create(points);
}
estimator = PnPEstimator::create(min_solver, non_min_solver);
} else if (params->getEstimator() == EstimationMethod::Affine) {
degeneracy = makePtr<Degeneracy>();
min_solver = AffineMinimalSolver::create(points);
non_min_solver = AffineNonMinimalSolver::create(points);
estimator = AffineEstimator::create(min_solver, non_min_solver);
} else CV_Error(cv::Error::StsNotImplemented, "Estimator not implemented!");
switch (params->getSampler()) {
case SamplingMethod::SAMPLING_UNIFORM:
sampler = UniformSampler::create(state++, min_sample_size, points_size); break;
case SamplingMethod::SAMPLING_PROSAC:
sampler = ProsacSampler::create(state++, points_size, min_sample_size, 200000); break;
case SamplingMethod::SAMPLING_PROGRESSIVE_NAPSAC:
sampler = ProgressiveNapsac::create(state++, points_size, min_sample_size, layers, 20); break;
case SamplingMethod::SAMPLING_NAPSAC:
sampler = NapsacSampler::create(state++, points_size, min_sample_size, graph); break;
default: CV_Error(cv::Error::StsNotImplemented, "Sampler is not implemented!");
}
switch (params->getVerifier()) {
case VerificationMethod::NullVerifier: verifier = ModelVerifier::create(); break;
case VerificationMethod::SprtVerifier:
verifier = SPRT::create(state++, error, points_size, params->getScore() == ScoreMethod ::SCORE_METHOD_MAGSAC ? max_thr : threshold,
params->getSPRTepsilon(), params->getSPRTdelta(), params->getTimeForModelEstimation(),
params->getSPRTavgNumModels(), params->getScore()); break;
default: CV_Error(cv::Error::StsNotImplemented, "Verifier is not imeplemented!");
}
if (params->getSampler() == SamplingMethod::SAMPLING_PROSAC) {
termination = ProsacTerminationCriteria::create(sampler.dynamicCast<ProsacSampler>(), error,
points_size, min_sample_size, params->getConfidence(),
params->getMaxIters(), 100, 0.05, 0.05, threshold);
} else if (params->getSampler() == SamplingMethod::SAMPLING_PROGRESSIVE_NAPSAC) {
if (params->getVerifier() == VerificationMethod::SprtVerifier)
termination = SPRTPNapsacTermination::create(((SPRT *)verifier.get())->getSPRTvector(),
params->getConfidence(), points_size, min_sample_size,
params->getMaxIters(), params->getRelaxCoef());
else
termination = StandardTerminationCriteria::create (params->getConfidence(),
points_size, min_sample_size, params->getMaxIters());
} else if (params->getVerifier() == VerificationMethod::SprtVerifier) {
termination = SPRTTermination::create(((SPRT *) verifier.get())->getSPRTvector(),
params->getConfidence(), points_size, min_sample_size, params->getMaxIters());
} else
termination = StandardTerminationCriteria::create
(params->getConfidence(), points_size, min_sample_size, params->getMaxIters());
if (params->getLO() != LocalOptimMethod::LOCAL_OPTIM_NULL) {
lo_sampler = UniformRandomGenerator::create(state++, points_size, params->getLOSampleSize());
switch (params->getLO()) {
case LocalOptimMethod::LOCAL_OPTIM_INNER_LO:
lo = InnerIterativeLocalOptimization::create(estimator, quality, lo_sampler,
points_size, threshold, false, params->getLOIterativeSampleSize(),
params->getLOInnerMaxIters(), params->getLOIterativeMaxIters(),
params->getLOThresholdMultiplier()); break;
case LocalOptimMethod::LOCAL_OPTIM_INNER_AND_ITER_LO:
lo = InnerIterativeLocalOptimization::create(estimator, quality, lo_sampler,
points_size, threshold, true, params->getLOIterativeSampleSize(),
params->getLOInnerMaxIters(), params->getLOIterativeMaxIters(),
params->getLOThresholdMultiplier()); break;
case LocalOptimMethod::LOCAL_OPTIM_GC:
lo = GraphCut::create(estimator, error, quality, graph, lo_sampler, threshold,
params->getGraphCutSpatialCoherenceTerm(), params->getLOInnerMaxIters()); break;
case LocalOptimMethod::LOCAL_OPTIM_SIGMA:
lo = SigmaConsensus::create(estimator, error, quality, verifier, params->getLOSampleSize(), 1,
params->getDegreesOfFreedom(), params->getSigmaQuantile(),
params->getUpperIncompleteOfSigmaQuantile(), params->getC(), max_thr); break;
default: CV_Error(cv::Error::StsNotImplemented , "Local Optimization is not implemented!");
}
}
if (params->getFinalPolisher() == PolishingMethod::LSQPolisher)
polisher = LeastSquaresPolishing::create(estimator, quality, params->getFinalLSQIterations());
Ransac ransac (params, points_size, estimator, quality, sampler,
termination, verifier, degeneracy, lo, polisher, params->isParallel(), state);
if (ransac.run(ransac_output)) {
if (params->isPnP()) {
// convert R to rodrigues and back and recalculate inliers which due to numerical
// issues can differ
Mat out, R, newR, newP, t, rvec;
if (K1.empty()) {
usac::Utils::decomposeProjection (ransac_output->getModel(), K1, R, t);
Rodrigues(R, rvec);
hconcat(rvec, t, out);
hconcat(out, K1, out);
} else {
const Mat Rt = K1.inv() * ransac_output->getModel();
t = Rt.col(3);
Rodrigues(Rt.colRange(0,3), rvec);
hconcat(rvec, t, out);
}
Rodrigues(rvec, newR);
hconcat(K1 * newR, K1 * t, newP);
std::vector<bool> inliers_mask(points_size);
quality->getInliers(newP, inliers_mask);
ransac_output = RansacOutput::create(out, inliers_mask, 0,0,0,0,0,0);
}
return true;
}
return false;
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
namespace cv { namespace usac {
/*
* Uniform Sampler:
* Choose uniformly m (sample size) points from N (points size).
* Uses Fisher-Yates shuffle.
*/
class UniformSamplerImpl : public UniformSampler {
private:
std::vector<int> points_random_pool;
int sample_size, random_pool_size, points_size = 0;
RNG rng;
public:
UniformSamplerImpl (int state, int sample_size_, int points_size_) : rng(state) {
sample_size = sample_size_;
setPointsSize (points_size_);
}
void setNewPointsSize (int points_size_) override {
setPointsSize(points_size_);
}
void generateSample (std::vector<int> &sample) override {
random_pool_size = points_size; // random points of entire range
for (int i = 0; i < sample_size; i++) {
// get random point index
const int array_random_index = rng.uniform(0, random_pool_size);
// get point by random index
// store sample
sample[i] = points_random_pool[array_random_index];
// swap random point with the end of random pool
std::swap(points_random_pool[array_random_index],
points_random_pool[--random_pool_size]);
}
}
Ptr<Sampler> clone (int state) const override {
return makePtr<UniformSamplerImpl>(state, sample_size, points_size);
}
private:
void setPointsSize (int points_size_) {
CV_Assert (sample_size <= points_size_);
if (points_size_ > points_size)
points_random_pool = std::vector<int>(points_size_);
if (points_size != points_size_) {
points_size = points_size_;
for (int i = 0; i < points_size; i++)
points_random_pool[i] = i;
}
}
};
Ptr<UniformSampler> UniformSampler::create(int state, int sample_size_, int points_size_) {
return makePtr<UniformSamplerImpl>(state, sample_size_, points_size_);
}
/////////////////////////////////// PROSAC (SIMPLE) SAMPLER ///////////////////////////////////////
/*
* PROSAC (simple) sampler does not use array of precalculated T_n (n is subset size) samples, but computes T_n for
* specific n directy in generateSample() function.
* Also, the stopping length (or maximum subset size n*) by default is set to points_size (N) and does not updating
* during computation.
*/
class ProsacSimpleSamplerImpl : public ProsacSimpleSampler {
protected:
int points_size, subset_size, t_n_prime, kth_sample_number,
max_prosac_samples_count, largest_sample_size, sample_size;
double t_n;
Ptr<UniformRandomGenerator> random_gen;
public:
ProsacSimpleSamplerImpl (int state, int points_size_, int sample_size_,
int max_prosac_samples_count_) : random_gen(UniformRandomGenerator::create(state)) {
CV_Assert(sample_size_ <= points_size_);
sample_size = sample_size_;
points_size = points_size_;
max_prosac_samples_count = max_prosac_samples_count_;
initialize ();
}
void generateSample (std::vector<int> &sample) override {
if (kth_sample_number > max_prosac_samples_count) {
// do uniform sampling, if prosac has not found solution
random_gen->generateUniqueRandomSet(sample, sample_size, points_size);
return;
}
kth_sample_number++; // t := t + 1
// Choice of the hypothesis generation set
if (kth_sample_number >= t_n_prime && subset_size < largest_sample_size) {
// do not use array of growth sample, calculate it directly
double t_n_plus1 = (subset_size + 1) * t_n / (subset_size + 1 - sample_size);
t_n_prime += static_cast<int>(ceil(t_n_plus1 - t_n));
t_n = t_n_plus1;
subset_size++;
}
// Semi-random sample Mt of size m
if (t_n_prime < kth_sample_number) {
random_gen->generateUniqueRandomSet(sample, sample_size, subset_size);
} else {
random_gen->generateUniqueRandomSet(sample, sample_size-1, subset_size-1);
sample[sample_size-1] = subset_size-1; // Make the last point from the nth position.
}
}
// Set the sample such that you are sampling the kth prosac sample (Eq. 6).
void setSampleNumber (int k) {
kth_sample_number = k;
// If the method should act exactly like RANSAC
if (kth_sample_number > max_prosac_samples_count)
return;
else { // Increment the size of the sampling pool while required
t_n = max_prosac_samples_count;
t_n_prime = 1; // reset growth function
subset_size = sample_size; // reset subset size as from the beginning
for (int i = 0; i < sample_size; i++)
t_n *= static_cast<double>(subset_size - i) / (points_size - i);
while (kth_sample_number > t_n_prime) { // t_n_prime == growth_function
double t_n_plus1 = static_cast<double>(subset_size + 1) * t_n / (subset_size + 1 - sample_size);
t_n_prime += static_cast<int>(ceil(t_n_plus1 - t_n));
t_n = t_n_plus1;
subset_size++;
}
if (subset_size > points_size)
subset_size = points_size;
}
}
void setNewPointsSize (int points_size_) override {
CV_Assert(sample_size <= points_size_);
points_size = points_size_;
initialize ();
}
Ptr<Sampler> clone (int state) const override {
return makePtr<ProsacSimpleSamplerImpl>(state, points_size, sample_size,
max_prosac_samples_count);
}
private:
void initialize () {
largest_sample_size = points_size; // termination length, n*
subset_size = sample_size; // n
t_n = max_prosac_samples_count;
t_n_prime = 1;
// From Equations leading up to Eq 3 in Chum et al.
// t_n samples containing only data points from U_n and
// t_n+1 samples containing only data points from U_n+1
for (int i = 0; i < sample_size; i++)
t_n *= static_cast<double>(subset_size - i) / (points_size - i);
kth_sample_number = 0;
}
};
Ptr<ProsacSimpleSampler> ProsacSimpleSampler::create(int state, int points_size_, int sample_size_,
int max_prosac_samples_count_) {
return makePtr<ProsacSimpleSamplerImpl>(state, points_size_, sample_size_,
max_prosac_samples_count_);
}
////////////////////////////////////// PROSAC SAMPLER ////////////////////////////////////////////
class ProsacSamplerImpl : public ProsacSampler {
protected:
std::vector<int> growth_function;
// subset_size = size of sampling range (subset of good sorted points)
// termination_length = n*, maximum sampling range (largest subset size)
int points_size, sample_size, subset_size, termination_length;
// it is T_N
// Imagine standard RANSAC drawing T_N samples of size m out of N data points
// In our experiments, the parameter was set to T_N = 200000
int growth_max_samples;
// how many time PROSAC generateSample() was called
int kth_sample_number;
Ptr<UniformRandomGenerator> random_gen;
public:
void setTerminationLength (int termination_length_) override {
termination_length = termination_length_;
}
// return constant reference to prosac termination criteria
int getKthSample () const override {
return kth_sample_number;
}
// return constant points of growth function to prosac termination criteria
const std::vector<int> & getGrowthFunction () const override {
return growth_function;
}
ProsacSamplerImpl (int state, int points_size_, int sample_size_,
int growth_max_samples_) : random_gen(UniformRandomGenerator::create(state)) {
CV_Assert(sample_size_ <= points_size_);
sample_size = sample_size_;
points_size = points_size_;
growth_max_samples = growth_max_samples_;
growth_function = std::vector<int>(points_size);
kth_sample_number = 0;
// The data points in U_N are sorted in descending order w.r.t. the quality function q.
// Let {Mi}i = 1...T_N denote the sequence of samples Mi c U_N that are uniformly drawn by Ransac.
// Let T_n be an average number of samples from {Mi}i=1...T_N that contain data points from U_n only.
// compute initial value for T_n
// n - i
// T_n = T_N * Product i = 0...m-1 -------, n >= sample size, N = points size
// N - i
double T_n = growth_max_samples;
for (int i = 0; i < sample_size; i++)
T_n *= static_cast<double> (sample_size-i) / (points_size-i);
int T_n_prime = 1;
// fill growth function with T'_n until sample_size
for (int n = 0; n < sample_size; n++)
growth_function[n] = T_n_prime;
// compute values using recurrent relation
// n + 1
// T(n+1) = --------- T(n), m is sample size.
// n + 1 - m
// growth function is defined as
// g(t) = min {n, T'_(n) >= t}
// T'_(n+1) = T'_(n) + (T_(n+1) - T_(n))
// T'_m = 1
for (int n = sample_size; n < points_size; n++) {
double Tn_plus1 = static_cast<double>(n + 1) * T_n / (n + 1 - sample_size);
growth_function[n] = T_n_prime + (int) ceil(Tn_plus1 - T_n); // T'_{n+1}
// update
T_n = Tn_plus1;
T_n_prime = growth_function[n]; // T'_{n+1}
}
// other initializations
termination_length = points_size; // n* = N, largest set sampled in PROSAC (termination length)
subset_size = sample_size; // n, size of the current sampling pool
kth_sample_number = 0; // t (iteration)
}
void generateSample (std::vector<int> &sample) override {
// std::cout << "PROSAC sampler, termination length " << termination_length << "\n";
if (kth_sample_number > growth_max_samples) {
// if PROSAC has not converged to solution then do uniform sampling.
random_gen->generateUniqueRandomSet(sample, sample_size, points_size);
return;
}
kth_sample_number++; // t := t + 1
// Choice of the hypothesis generation set
// if (t = T'_n) & (n < n*) then n = n + 1 (eqn. 4)
if (kth_sample_number == growth_function[subset_size-1] && subset_size < termination_length)
subset_size++;
// Semi-random sample M_t of size m
// if T'n < t then
if (growth_function[subset_size-1] < kth_sample_number) {
// The sample contains m-1 points selected from U_(n-1) at random and u_n
random_gen->generateUniqueRandomSet(sample, sample_size-1, subset_size-1);
sample[sample_size-1] = subset_size-1;
} else {
// Select m points from U_n at random.
random_gen->generateUniqueRandomSet(sample, sample_size, subset_size);
}
}
// Set the sample such that you are sampling the kth prosac sample (Eq. 6).
void setSampleNumber (int k) {
kth_sample_number = k;
// If the method should act exactly like RANSAC
if (kth_sample_number > growth_max_samples)
return;
else { // Increment the size of the sampling pool while required
subset_size = sample_size; // reset subset size as from the beginning
while (kth_sample_number > growth_function[subset_size-1]) {
subset_size++;
if (subset_size >= points_size){
subset_size = points_size;
break;
}
}
if (termination_length < subset_size)
termination_length = subset_size;
}
}
void setNewPointsSize (int /*points_size_*/) override {
CV_Error(cv::Error::StsError, "Changing points size in PROSAC requires to change also "
"termination criteria! Use PROSAC simpler version");
}
Ptr<Sampler> clone (int state) const override {
return makePtr<ProsacSamplerImpl>(state, points_size, sample_size,
growth_max_samples);
}
};
Ptr<ProsacSampler> ProsacSampler::create(int state, int points_size_, int sample_size_,
int growth_max_samples_) {
return makePtr<ProsacSamplerImpl>(state, points_size_, sample_size_, growth_max_samples_);
}
////////////////////////////////////// P-NAPSAC SAMPLER ////////////////////////////////////////////
class ProgressiveNapsacImpl : public ProgressiveNapsac {
private:
int max_progressive_napsac_iterations, points_size;
// how many times generateSample() was called.
int kth_sample_number, grid_layers_number, sample_size, sampler_length;
const Ptr<UniformRandomGenerator> random_generator;
ProsacSamplerImpl one_point_prosac, prosac_sampler;
// The overlapping neighborhood layers
const std::vector<Ptr<NeighborhoodGraph>> * layers;
std::vector<int> growth_function;
std::vector<int> hits_per_point; // number of iterations, t
std::vector<int> subset_size_per_point; // k
std::vector<int> current_layer_per_point; // layer of grid neighborhood graph
public:
// points must be sorted
ProgressiveNapsacImpl (int state,int points_size_, int sample_size_,
const std::vector<Ptr<NeighborhoodGraph>> &layers_, int sampler_length_) :
// initialize one-point prosac sampler and global prosac sampler
random_generator (UniformRandomGenerator::create(state)),
one_point_prosac (random_generator->getRandomNumber(INT_MAX), points_size_,
1 /* sample_size*/,points_size_),
prosac_sampler (random_generator->getRandomNumber(INT_MAX), points_size_,
sample_size_, 200000), layers(&layers_) {
CV_Assert(sample_size_ <= points_size_);
sample_size = sample_size_;
points_size = points_size_;
sampler_length = sampler_length_;
grid_layers_number = static_cast<int>(layers_.size());
// Create growth function for P-NAPSAC
growth_function = std::vector<int>(points_size);
// 20 is sampler_length = The length of fully blending to global sampling
max_progressive_napsac_iterations = sampler_length * points_size;
const int local_sample_size = sample_size - 1; // not including initial point
double T_n = max_progressive_napsac_iterations;
for (int i = 0; i < local_sample_size; i++)
T_n *= static_cast<double> (local_sample_size - i) / (points_size - i);
// calculate growth function by recurrent relation (see PROSAC)
int T_n_prime = 1;
for (int n = 0; n < points_size; n++) {
if (n + 1 <= local_sample_size) {
growth_function[n] = T_n_prime;
continue;
}
double Tn_plus1 = (n+1) * T_n / (n + 1 - local_sample_size);
growth_function[n] = T_n_prime + static_cast<int>(ceil(Tn_plus1 - T_n));
T_n = Tn_plus1;
T_n_prime = growth_function[n];
}
subset_size_per_point = std::vector<int>(points_size, sample_size); // subset size
hits_per_point = std::vector<int>(points_size, 0); // 0 hits
current_layer_per_point = std::vector<int>(points_size, 0); // 0-th layer
kth_sample_number = 0; // iteration
}
void generateSample (std::vector<int> &sample) override {
// Do completely global sampling (PROSAC is used now), instead of Progressive NAPSAC,
// if the maximum iterations has been done without finding the sought model.
if (kth_sample_number > max_progressive_napsac_iterations) {
prosac_sampler.generateSample(sample);
return;
}
kth_sample_number++;
// get PROSAC one-point sample (initial point)
one_point_prosac.generateSample(sample);
const int initial_point = sample[0];
// get hits number and subset size (i.e., the size of the neighborhood sphere)
// of initial point (note, get by reference)
int &iters_of_init_pt = ++hits_per_point[initial_point]; // t := t + 1, increase iteration
int &subset_size_of_init_pt = subset_size_per_point[initial_point];
while (iters_of_init_pt > growth_function[subset_size_of_init_pt - 1] && subset_size_of_init_pt < points_size)
subset_size_of_init_pt++;
// Get layer of initial point (note, get by reference)
int &current_layer = current_layer_per_point[initial_point];
bool is_last_layer = false;
do {// Try to find the grid which contains enough points
// In the case when the grid with a single cell is used,
// apply PROSAC.
if (current_layer >= grid_layers_number) {
is_last_layer = true;
break;
}
// If there are not enough points in the cell, start using a
// less fine grid.
if ((int)layers->at(current_layer)->getNeighbors(initial_point).size() < subset_size_of_init_pt) {
++current_layer; // Jump to the next layer with bigger cells.
continue;
}
// If the procedure got to this point, there is no reason to choose a different layer of grids
// since the current one has enough points.
break;
} while (true);
// If not the last layer has been chosen, sample from the neighbors of the initially selected point.
if (!is_last_layer) {
// The indices of the points which are in the same cell as the
// initially selected one.
const std::vector<int> &neighbors = layers->at(current_layer)->getNeighbors(initial_point);
// Put the selected point to the end of the sample array to avoid
// being overwritten when sampling the remaining points.
sample[sample_size - 1] = initial_point;
// The next point should be the farthest one from the initial point. Note that the points in the grid cell are
// not ordered w.r.t. to their distances from the initial point. However, they are ordered as in PROSAC.
sample[sample_size - 2] = neighbors[subset_size_of_init_pt - 1];
// Select n - 2 points randomly
random_generator->generateUniqueRandomSet(sample, sample_size - 2, subset_size_of_init_pt - 1);
for (int i = 0; i < sample_size - 2; i++) {
sample[i] = neighbors[sample[i]]; // Replace the neighbor index by the index of the point
++hits_per_point[sample[i]]; // Increase the hit number of each selected point
}
++hits_per_point[sample[sample_size - 2]]; // Increase the hit number of each selected point
}
// If the last layer (i.e., the layer with a single cell) has been chosen, do global sampling
// by PROSAC sampler.
else {
// last layer, all points are neighbors
// If local sampling
prosac_sampler.setSampleNumber(kth_sample_number);
prosac_sampler.generateSample (sample);
sample[sample_size - 1] = initial_point;
}
}
void setNewPointsSize (int /*points_size_*/) override {
CV_Error(cv::Error::StsError, "Changing points size requires changing neighborhood graph! "
"You must reinitialize P-NAPSAC!");
}
Ptr<Sampler> clone (int state) const override {
return makePtr<ProgressiveNapsacImpl>(state, points_size, sample_size, *layers,
sampler_length);
}
};
Ptr<ProgressiveNapsac> ProgressiveNapsac::create(int state, int points_size_, int sample_size_,
const std::vector<Ptr<NeighborhoodGraph>> &layers, int sampler_length_) {
return makePtr<ProgressiveNapsacImpl>(state, points_size_, sample_size_,
layers, sampler_length_);
}
////////////////////// N adjacent points sample consensus (NAPSAC) SAMPLER ////////////////////////
class NapsacSamplerImpl : public NapsacSampler {
private:
const Ptr<NeighborhoodGraph> neighborhood_graph;
const Ptr<UniformRandomGenerator> random_generator;
bool do_uniform = false;
std::vector<int> points_large_neighborhood;
int points_large_neighborhood_size, points_size, sample_size;
public:
NapsacSamplerImpl (int state, int points_size_, int sample_size_,
const Ptr<NeighborhoodGraph> &neighborhood_graph_) :
neighborhood_graph (neighborhood_graph_),
random_generator(UniformRandomGenerator::create(state, points_size_, sample_size_)) {
CV_Assert(points_size_ >= sample_size_);
points_size = points_size_;
sample_size = sample_size_;
points_large_neighborhood = std::vector<int>(points_size);
points_large_neighborhood_size = 0;
// find indicies of points that have sufficient neighborhood (at least sample_size-1)
for (int pt_idx = 0; pt_idx < points_size; pt_idx++)
if ((int)neighborhood_graph->getNeighbors(pt_idx).size() >= sample_size-1)
points_large_neighborhood[points_large_neighborhood_size++] = pt_idx;
// if no points with sufficient neighborhood then do only uniform sampling
if (points_large_neighborhood_size == 0)
do_uniform = true;
// set random generator to generate random points of sample_size-1
random_generator->setSubsetSize(sample_size-1);
}
void generateSample (std::vector<int> &sample) override {
if (do_uniform)
// uniform sampling
random_generator->generateUniqueRandomSet(sample, points_size);
else {
// Take uniformly one initial point from points with sufficient neighborhood
int initial_point = points_large_neighborhood
[random_generator->getRandomNumber(points_large_neighborhood_size)];
const std::vector<int> &neighbors = neighborhood_graph->getNeighbors(initial_point);
// select random neighbors of initial point
random_generator->generateUniqueRandomSet(sample, (int)neighbors.size());
for (int i = 0; i < sample_size-1; i++)
sample[i] = neighbors[sample[i]];
// sample includes initial point too.
sample[sample_size-1] = initial_point;
}
}
void setNewPointsSize (int /*points_size_*/) override {
CV_Error(cv::Error::StsError, "Changing points size requires changing neighborhood graph!"
" You must reinitialize NAPSAC!");
}
Ptr<Sampler> clone (int state) const override {
return makePtr<NapsacSamplerImpl>(state, points_size, sample_size, neighborhood_graph);
}
};
Ptr<NapsacSampler> NapsacSampler::create(int state, int points_size_, int sample_size_,
const Ptr<NeighborhoodGraph> &neighborhood_graph_) {
return makePtr<NapsacSamplerImpl>(state, points_size_, sample_size_, neighborhood_graph_);
}
}}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
namespace cv { namespace usac {
////////////////////////////////// STANDARD TERMINATION ///////////////////////////////////////////
class StandardTerminationCriteriaImpl : public StandardTerminationCriteria {
private:
const double log_confidence;
const int points_size, sample_size, MAX_ITERATIONS;
public:
StandardTerminationCriteriaImpl (double confidence, int points_size_,
int sample_size_, int max_iterations_) :
log_confidence(log(1 - confidence)), points_size (points_size_),
sample_size (sample_size_), MAX_ITERATIONS(max_iterations_) {}
/*
* Get upper bound iterations for any sample number
* n is points size, w is inlier ratio, p is desired probability, k is expceted number of iterations.
* 1 - p = (1 - w^n)^k,
* k = log_(1-w^n) (1-p)
* k = ln (1-p) / ln (1-w^n)
*
* w^n is probability that all N points are inliers.
* (1 - w^n) is probability that at least one point of N is outlier.
* 1 - p = (1-w^n)^k is probability that in K steps of getting at least one outlier is 1% (5%).
*/
int update (const Mat &/*model*/, int inlier_number) override {
const double predicted_iters = log_confidence / log(1 - std::pow
(static_cast<double>(inlier_number) / points_size, sample_size));
// if inlier_prob == 1 then log(0) = -inf, predicted_iters == -0
// if inlier_prob == 0 then log(1) = 0 , predicted_iters == (+-) inf
if (! std::isinf(predicted_iters) && predicted_iters < MAX_ITERATIONS)
return static_cast<int>(predicted_iters);
return MAX_ITERATIONS;
}
Ptr<TerminationCriteria> clone () const override {
return makePtr<StandardTerminationCriteriaImpl>(1-exp(log_confidence), points_size,
sample_size, MAX_ITERATIONS);
}
};
Ptr<StandardTerminationCriteria> StandardTerminationCriteria::create(double confidence,
int points_size_, int sample_size_, int max_iterations_) {
return makePtr<StandardTerminationCriteriaImpl>(confidence, points_size_,
sample_size_, max_iterations_);
}
/////////////////////////////////////// SPRT TERMINATION //////////////////////////////////////////
class SPRTTerminationImpl : public SPRTTermination {
private:
const std::vector<SPRT_history> &sprt_histories;
const double log_eta_0;
const int points_size, sample_size, MAX_ITERATIONS;
public:
SPRTTerminationImpl (const std::vector<SPRT_history> &sprt_histories_, double confidence,
int points_size_, int sample_size_, int max_iterations_)
: sprt_histories (sprt_histories_), log_eta_0(log(1-confidence)),
points_size (points_size_), sample_size (sample_size_),MAX_ITERATIONS(max_iterations_){}
/*
* Termination criterion:
* l is number of tests
* n(l) = Product from i = 0 to l ( 1 - P_g (1 - A(i)^(-h(i)))^k(i) )
* log n(l) = sum from i = 0 to l k(i) * ( 1 - P_g (1 - A(i)^(-h(i))) )
*
* log (n0) - log (n(l-1))
* k(l) = ----------------------- (9)
* log (1 - P_g*A(l)^-1)
*
* A is decision threshold
* P_g is probability of good model.
* k(i) is number of samples verified by i-th sprt.
* n0 is typically set to 0.05
* this equation does not have to be evaluated before nR < n0
* nR = (1 - P_g)^k
*/
int update (const Mat &/*model*/, int inlier_size) override {
if (sprt_histories.empty())
return std::min(MAX_ITERATIONS, getStandardUpperBound(inlier_size));
const double epsilon = static_cast<double>(inlier_size) / points_size; // inlier probability
const double P_g = pow (epsilon, sample_size); // probability of good sample
double log_eta_lmin1 = 0;
int total_number_of_tested_samples = 0;
const int sprts_size_min1 = static_cast<int>(sprt_histories.size())-1;
if (sprts_size_min1 < 0) return getStandardUpperBound(inlier_size);
// compute log n(l-1), l is number of tests
for (int test = 0; test < sprts_size_min1; test++) {
log_eta_lmin1 += log (1 - P_g * (1 - pow (sprt_histories[test].A,
-computeExponentH(sprt_histories[test].epsilon, epsilon,sprt_histories[test].delta))))
* sprt_histories[test].tested_samples;
total_number_of_tested_samples += sprt_histories[test].tested_samples;
}
// Implementation note: since η > ηR the equation (9) does not have to be evaluated
// before ηR < η0 is satisfied.
if (std::pow(1 - P_g, total_number_of_tested_samples) < log_eta_0)
return std::min(MAX_ITERATIONS, getStandardUpperBound(inlier_size));
// use decision threshold A for last test (l-th)
const double predicted_iters_sprt = (log_eta_0 - log_eta_lmin1) /
log (1 - P_g * (1 - 1 / sprt_histories[sprts_size_min1].A)); // last A
if (std::isnan(predicted_iters_sprt) || std::isinf(predicted_iters_sprt))
return getStandardUpperBound(inlier_size);
if (predicted_iters_sprt < 0) return 0;
// compare with standard upper bound
if (predicted_iters_sprt < MAX_ITERATIONS)
return std::min(static_cast<int>(predicted_iters_sprt),
getStandardUpperBound(inlier_size));
return getStandardUpperBound(inlier_size);
}
Ptr<TerminationCriteria> clone () const override {
return makePtr<SPRTTerminationImpl>(sprt_histories, 1-exp(log_eta_0), points_size,
sample_size, MAX_ITERATIONS);
}
private:
inline int getStandardUpperBound(int inlier_size) const {
const double predicted_iters = log_eta_0 / log(1 - std::pow
(static_cast<double>(inlier_size) / points_size, sample_size));
return (! std::isinf(predicted_iters) && predicted_iters < MAX_ITERATIONS) ?
static_cast<int>(predicted_iters) : MAX_ITERATIONS;
}
/*
* h(i) must hold
*
* δ(i) 1 - δ(i)
* ε (-----)^h(i) + (1 - ε) (--------)^h(i) = 1
* ε(i) 1 - ε(i)
*
* ε * a^h + (1 - ε) * b^h = 1
* Has numerical solution.
*/
static double computeExponentH (double epsilon, double epsilon_new, double delta) {
const double a = log (delta / epsilon); // log likelihood ratio
const double b = log ((1 - delta) / (1 - epsilon));
const double x0 = log (1 / (1 - epsilon_new)) / b;
const double v0 = epsilon_new * exp (x0 * a);
const double x1 = log ((1 - 2*v0) / (1 - epsilon_new)) / b;
const double v1 = epsilon_new * exp (x1 * a) + (1 - epsilon_new) * exp(x1 * b);
const double h = x0 - (x0 - x1) / (1 + v0 - v1) * v0;
if (std::isnan(h))
// The equation always has solution for h = 0
// ε * a^0 + (1 - ε) * b^0 = 1
// ε + 1 - ε = 1 -> 1 = 1
return 0;
return h;
}
};
Ptr<SPRTTermination> SPRTTermination::create(const std::vector<SPRT_history> &sprt_histories_,
double confidence, int points_size_, int sample_size_, int max_iterations_) {
return makePtr<SPRTTerminationImpl>(sprt_histories_, confidence, points_size_, sample_size_,
max_iterations_);
}
///////////////////////////// PROGRESSIVE-NAPSAC-SPRT TERMINATION /////////////////////////////////
class SPRTPNapsacTerminationImpl : public SPRTPNapsacTermination {
private:
SPRTTerminationImpl sprt_termination;
const std::vector<SPRT_history> &sprt_histories;
const double relax_coef, log_confidence;
const int points_size, sample_size, MAX_ITERS;
public:
SPRTPNapsacTerminationImpl (const std::vector<SPRT_history> &sprt_histories_,
double confidence, int points_size_, int sample_size_,
int max_iterations_, double relax_coef_)
: sprt_termination (sprt_histories_, confidence, points_size_, sample_size_,
max_iterations_), sprt_histories (sprt_histories_),
relax_coef (relax_coef_), log_confidence(log(1-confidence)),
points_size (points_size_), sample_size (sample_size_),
MAX_ITERS (max_iterations_) {}
int update (const Mat &model, int inlier_number) override {
int predicted_iterations = sprt_termination.update(model, inlier_number);
const double inlier_prob = static_cast<double>(inlier_number) / points_size + relax_coef;
if (inlier_prob >= 1)
return 0;
const double predicted_iters = log_confidence / log(1 - std::pow(inlier_prob, sample_size));
if (! std::isinf(predicted_iters) && predicted_iters < predicted_iterations)
return static_cast<int>(predicted_iters);
return predicted_iterations;
}
Ptr<TerminationCriteria> clone () const override {
return makePtr<SPRTPNapsacTerminationImpl>(sprt_histories, 1-exp(log_confidence),
points_size, sample_size, MAX_ITERS, relax_coef);
}
};
Ptr<SPRTPNapsacTermination> SPRTPNapsacTermination::create(const std::vector<SPRT_history>&
sprt_histories_, double confidence, int points_size_, int sample_size_,
int max_iterations_, double relax_coef_) {
return makePtr<SPRTPNapsacTerminationImpl>(sprt_histories_, confidence, points_size_,
sample_size_, max_iterations_, relax_coef_);
}
////////////////////////////////////// PROSAC TERMINATION /////////////////////////////////////////
class ProsacTerminationCriteriaImpl : public ProsacTerminationCriteria {
private:
const double log_confidence, beta, non_randomness_phi, inlier_threshold;
const int MAX_ITERATIONS, points_size, min_termination_length, sample_size;
const Ptr<ProsacSampler> sampler;
std::vector<int> non_random_inliers;
const Ptr<Error> error;
public:
ProsacTerminationCriteriaImpl (const Ptr<Error> &error_, int points_size_,int sample_size_,
double confidence, int max_iterations, int min_termination_length_, double beta_,
double non_randomness_phi_, double inlier_threshold_) : log_confidence
(log(1-confidence)), beta(beta_), non_randomness_phi(non_randomness_phi_),
inlier_threshold(inlier_threshold_), MAX_ITERATIONS(max_iterations),
points_size (points_size_), min_termination_length (min_termination_length_),
sample_size(sample_size_), error (error_) { init(); }
ProsacTerminationCriteriaImpl (const Ptr<ProsacSampler> &sampler_,const Ptr<Error> &error_,
int points_size_, int sample_size_, double confidence, int max_iterations,
int min_termination_length_, double beta_, double non_randomness_phi_,
double inlier_threshold_) : log_confidence(log(1-confidence)), beta(beta_),
non_randomness_phi(non_randomness_phi_), inlier_threshold(inlier_threshold_),
MAX_ITERATIONS(max_iterations), points_size (points_size_),
min_termination_length (min_termination_length_), sample_size(sample_size_),
sampler(sampler_), error (error_) { init(); }
void init () {
// m is sample_size
// N is points_size
// non-randomness constraint
// The non-randomness requirement prevents PROSAC
// from selecting a solution supported by outliers that are
// by chance consistent with it. The constraint is typically
// checked ex-post in standard approaches [1]. The distribution
// of the cardinalities of sets of random ‘inliers’ is binomial
// i-th entry - inlier counts for termination up to i-th point (term length = i+1)
// ------------------------------------------------------------------------
// initialize the data structures that determine stopping
// see probabilities description below.
non_random_inliers = std::vector<int>(points_size, 0);
std::vector<double> pn_i_arr(points_size);
const double beta2compl_beta = beta / (1-beta);
const int step_n = 50, max_n = std::min(points_size, 1200);
for (int n = sample_size; n <= points_size; n+=step_n) {
if (n > max_n) {
// skip expensive calculation
break;
}
// P^R_n(i) = β^(i−m) (1−β)^(n−i+m) (n−m i−m). (7) i = m,...,N
// initial value for i = m = sample_size
// P^R_n(i=m) = β^(0) (1−β)^(n) (n-m 0) = (1-β)^(n)
// P^R_n(i=m+1) = β^(1) (1−β)^(n−1) (n−m 1) = P^R_n(i=m) * β / (1-β) * (n-m) / 1
// P^R_n(i=m+2) = β^(2) (1−β)^(n−2) (n−m 2) = P^R_n(i=m) * β^2 / (1-β)^2 * (n-m-1)(n-m) / 2
// So, for each i=m+1.., P^R_n(i+1) must be calculated as P^R_n(i) * β / (1-β) * (n-i+1) / (i-m)
pn_i_arr[sample_size-1] = std::pow(1-beta, n);
double pn_i = pn_i_arr[sample_size-1]; // prob of random inlier set of size i for subset size n
for (int i = sample_size+1; i <= n; i++) {
// use recurrent relation to fulfill remaining values
pn_i *= beta2compl_beta * static_cast<double>(n-i+1) / (i-sample_size);
// update
pn_i_arr[i-1] = pn_i;
}
// find minimum number of inliers satisfying the non-randomness constraint
// Imin n = min{j : n∑i=j P^R_n(i) < Ψ }. (8)
double acc = 0;
int i_min = sample_size; // there is always sample_size inliers
for (int i = n; i >= sample_size; i--) {
acc += pn_i_arr[i-1];
if (acc < non_randomness_phi) i_min = i;
else break;
}
non_random_inliers[n-1] = i_min;
}
// approximate values of binomial distribution
for (int n = sample_size; n <= points_size; n+=step_n) {
if (n-1+step_n >= max_n) {
// copy rest of the values
std::fill(&non_random_inliers[0]+n-1, &non_random_inliers[0]+points_size, non_random_inliers[n-1]);
break;
}
const int non_rand_n = non_random_inliers[n-1];
const double step = (double)(non_random_inliers[n-1+step_n] - non_rand_n) / (double)step_n;
for (int i = 0; i < step_n-1; i++)
non_random_inliers[n+i] = (int)(non_rand_n + (i+1)*step);
}
}
/*
* The PROSAC algorithm terminates if the number of inliers I_n*
* within the set U_n* satisfies the following conditions:
*
* • non-randomness – the probability that I_n* out of n* (termination_length)
* data points are by chance inliers to an arbitrary incorrect model
* is smaller than Ψ (typically set to 5%)
*
* • maximality – the probability that a solution with more than
* In* inliers in U_n* exists and was not found after k
* samples is smaller than η0 (typically set to 5%).
*/
int update (const Mat &model, int inliers_size) override {
int predicted_iterations = MAX_ITERATIONS;
/*
* The termination length n* is chosen to minimize k_n*(η0) subject to I_n* ≥ I_min n*;
* k_n*(η0) >= log(η0) / log(1 - (I_n* / n*)^m)
* g(k) <= n, I_n is number of inliers under termination length n.
*/
const auto &errors = error->getErrors(model);
// find number of inliers under g(k)
int num_inliers_under_termination_len = 0;
for (int pt = 0; pt < min_termination_length; pt++)
if (errors[pt] < inlier_threshold)
num_inliers_under_termination_len++;
for (int termination_len = min_termination_length; termination_len < points_size;termination_len++){
if (errors[termination_len /* = point*/] < inlier_threshold) {
num_inliers_under_termination_len++;
// non-random constraint must satisfy I_n* ≥ I_min n*.
if (num_inliers_under_termination_len < non_random_inliers[termination_len])
continue;
// add 1 to termination length since num_inliers_under_termination_len is updated
const double new_max_samples = log_confidence / log(1 -
std::pow(static_cast<double>(num_inliers_under_termination_len)
/ (termination_len+1), sample_size));
if (! std::isinf(new_max_samples) && predicted_iterations > new_max_samples) {
predicted_iterations = static_cast<int>(new_max_samples);
if (predicted_iterations == 0) break;
if (sampler != nullptr)
sampler->setTerminationLength(termination_len);
}
}
}
// compare also when termination length = points_size,
// so inliers under termination length is total number of inliers:
const double predicted_iters = log_confidence / log(1 - std::pow
(static_cast<double>(inliers_size) / points_size, sample_size));
if (! std::isinf(predicted_iters) && predicted_iters < predicted_iterations)
return static_cast<int>(predicted_iters);
return predicted_iterations;
}
Ptr<TerminationCriteria> clone () const override {
return makePtr<ProsacTerminationCriteriaImpl>(error->clone(),
points_size, sample_size, 1-exp(log_confidence), MAX_ITERATIONS,
min_termination_length, beta, non_randomness_phi, inlier_threshold);
}
};
Ptr<ProsacTerminationCriteria>
ProsacTerminationCriteria::create(const Ptr<ProsacSampler> &sampler, const Ptr<Error> &error,
int points_size_, int sample_size_, double confidence, int max_iterations,
int min_termination_length_, double beta, double non_randomness_phi, double inlier_thresh) {
return makePtr<ProsacTerminationCriteriaImpl> (sampler, error, points_size_, sample_size_,
confidence, max_iterations, min_termination_length_,
beta, non_randomness_phi, inlier_thresh);
}
}}

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modules/calib3d/src/usac/utils.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "../precomp.hpp"
#include "../usac.hpp"
#include "opencv2/flann/miniflann.hpp"
#include <map>
namespace cv { namespace usac {
double Utils::getCalibratedThreshold (double threshold, const Mat &K1, const Mat &K2) {
return threshold / ((K1.at<double>(0, 0) + K1.at<double>(1, 1) +
K2.at<double>(0, 0) + K2.at<double>(1, 1)) / 4.0);
}
/*
* K1, K2 are 3x3 intrinsics matrices
* points is matrix of size |N| x 4
* Assume K = [k11 k12 k13
* 0 k22 k23
* 0 0 1]
*/
void Utils::calibratePoints (const Mat &K1, const Mat &K2, const Mat &points, Mat &calib_points) {
const auto * const points_ = (float *) points.data;
const auto * const k1 = (double *) K1.data;
const auto inv1_k11 = float(1 / k1[0]); // 1 / k11
const auto inv1_k12 = float(-k1[1] / (k1[0]*k1[4])); // -k12 / (k11*k22)
// (-k13*k22 + k12*k23) / (k11*k22)
const auto inv1_k13 = float((-k1[2]*k1[4] + k1[1]*k1[5]) / (k1[0]*k1[4]));
const auto inv1_k22 = float(1 / k1[4]); // 1 / k22
const auto inv1_k23 = float(-k1[5] / k1[4]); // -k23 / k22
const auto * const k2 = (double *) K2.data;
const auto inv2_k11 = float(1 / k2[0]);
const auto inv2_k12 = float(-k2[1] / (k2[0]*k2[4]));
const auto inv2_k13 = float((-k2[2]*k2[4] + k2[1]*k2[5]) / (k2[0]*k2[4]));
const auto inv2_k22 = float(1 / k2[4]);
const auto inv2_k23 = float(-k2[5] / k2[4]);
calib_points = Mat ( points.rows, 4, points.type());
auto * calib_points_ = (float *) calib_points.data;
for (int i = 0; i < points.rows; i++) {
const int idx = 4*i;
(*calib_points_++) = inv1_k11 * points_[idx ] + inv1_k12 * points_[idx+1] + inv1_k13;
(*calib_points_++) = inv1_k22 * points_[idx+1] + inv1_k23;
(*calib_points_++) = inv2_k11 * points_[idx+2] + inv2_k12 * points_[idx+3] + inv2_k13;
(*calib_points_++) = inv2_k22 * points_[idx+3] + inv2_k23;
}
}
/*
* K is 3x3 intrinsic matrix
* points is matrix of size |N| x 5, first two columns are image points [u_i, v_i]
* calib_norm_pts are K^-1 [u v 1]^T / ||K^-1 [u v 1]^T||
*/
void Utils::calibrateAndNormalizePointsPnP (const Mat &K, const Mat &pts, Mat &calib_norm_pts) {
const auto * const points = (float *) pts.data;
const auto * const k = (double *) K.data;
const auto inv_k11 = float(1 / k[0]);
const auto inv_k12 = float(-k[1] / (k[0]*k[4]));
const auto inv_k13 = float((-k[2]*k[4] + k[1]*k[5]) / (k[0]*k[4]));
const auto inv_k22 = float(1 / k[4]);
const auto inv_k23 = float(-k[5] / k[4]);
calib_norm_pts = Mat (pts.rows, 3, pts.type());
auto * calib_norm_pts_ = (float *) calib_norm_pts.data;
for (int i = 0; i < pts.rows; i++) {
const int idx = 5 * i;
const float k_inv_u = inv_k11 * points[idx] + inv_k12 * points[idx+1] + inv_k13;
const float k_inv_v = inv_k22 * points[idx+1] + inv_k23;
const float norm = 1.f / sqrtf(k_inv_u*k_inv_u + k_inv_v*k_inv_v + 1);
(*calib_norm_pts_++) = k_inv_u * norm;
(*calib_norm_pts_++) = k_inv_v * norm;
(*calib_norm_pts_++) = norm;
}
}
void Utils::normalizeAndDecalibPointsPnP (const Mat &K_, Mat &pts, Mat &calib_norm_pts) {
const auto * const K = (double *) K_.data;
const auto k11 = (float)K[0], k12 = (float)K[1], k13 = (float)K[2],
k22 = (float)K[4], k23 = (float)K[5];
calib_norm_pts = Mat (pts.rows, 3, pts.type());
auto * points = (float *) pts.data;
auto * calib_norm_pts_ = (float *) calib_norm_pts.data;
for (int i = 0; i < pts.rows; i++) {
const int idx = 5 * i;
const float k_inv_u = points[idx ];
const float k_inv_v = points[idx+1];
const float norm = 1.f / sqrtf(k_inv_u*k_inv_u + k_inv_v*k_inv_v + 1);
(*calib_norm_pts_++) = k_inv_u * norm;
(*calib_norm_pts_++) = k_inv_v * norm;
(*calib_norm_pts_++) = norm;
points[idx ] = k11 * k_inv_u + k12 * k_inv_v + k13;
points[idx+1] = k22 * k_inv_v + k23;
}
}
/*
* decompose Projection Matrix to calibration, rotation and translation
* Assume K = [fx 0 tx
* 0 fy ty
* 0 0 1]
*/
void Utils::decomposeProjection (const Mat &P, Mat &K_, Mat &R, Mat &t, bool same_focal) {
const Mat M = P.colRange(0,3);
double scale = norm(M.row(2)); scale *= scale;
Matx33d K = Matx33d::eye();
K(1,2) = M.row(1).dot(M.row(2)) / scale;
K(0,2) = M.row(0).dot(M.row(2)) / scale;
K(1,1) = sqrt(M.row(1).dot(M.row(1)) / scale - K(1,2)*K(1,2));
K(0,0) = sqrt(M.row(0).dot(M.row(0)) / scale - K(0,2)*K(0,2));
if (same_focal)
K(0,0) = K(1,1) = (K(0,0) + K(1,1)) / 2;
R = K.inv() * M / sqrt(scale);
if (determinant(M) < 0) R *= -1;
t = R * M.inv() * P.col(3);
K_ = Mat(K);
}
Matx33d Math::getSkewSymmetric(const Vec3d &v) {
return Matx33d(0, -v[2], v[1],
v[2], 0, -v[0],
-v[1], v[0], 0);
}
Matx33d Math::rotVec2RotMat (const Vec3d &v) {
const double phi = sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
const double x = v[0] / phi, y = v[1] / phi, z = v[2] / phi;
const double a = sin(phi), b = cos(phi);
// R = I + sin(phi) * skew(v) + (1 - cos(phi) * skew(v)^2
return Matx33d((b - 1)*y*y + (b - 1)*z*z + 1, -a*z - x*y*(b - 1), a*y - x*z*(b - 1),
a*z - x*y*(b - 1), (b - 1)*x*x + (b - 1)*z*z + 1, -a*x - y*z*(b - 1),
-a*y - x*z*(b - 1), a*x - y*z*(b - 1), (b - 1)*x*x + (b - 1)*y*y + 1);
}
Vec3d Math::rotMat2RotVec (const Matx33d &R) {
// https://math.stackexchange.com/questions/83874/efficient-and-accurate-numerical-implementation-of-the-inverse-rodrigues-rotatio?rq=1
Vec3d rot_vec;
const double trace = R(0,0)+R(1,1)+R(2,2);
if (trace >= 3 - FLT_EPSILON) {
rot_vec = (0.5 * (trace-3)/12)*Vec3d(R(2,1)-R(1,2),
R(0,2)-R(2,0),
R(1,0)-R(0,1));
} else if (3 - FLT_EPSILON > trace && trace > -1 + FLT_EPSILON) {
double theta = acos((trace - 1) / 2);
rot_vec = (theta / (2 * sin(theta))) * Vec3d(R(2,1)-R(1,2),
R(0,2)-R(2,0),
R(1,0)-R(0,1));
} else {
int a;
if (R(0,0) > R(1,1))
a = R(0,0) > R(2,2) ? 0 : 2;
else
a = R(1,1) > R(2,2) ? 1 : 2;
Vec3d v;
int b = (a + 1) % 3, c = (a + 2) % 3;
double s = sqrt(R(a,a) - R(b,b) - R(c,c) + 1);
v[a] = s / 2;
v[b] = (R(b,a) + R(a,b)) / (2 * s);
v[c] = (R(c,a) + R(a,c)) / (2 * s);
rot_vec = M_PI * v / norm(v);
}
return rot_vec;
}
/*
* Eliminate matrix of m rows and n columns to be upper triangular.
*/
void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
for (int r = 0; r < m; r++){
double pivot = a[r*n+r];
int row_with_pivot = r;
// find the maximum pivot value among r-th column
for (int k = r+1; k < m; k++)
if (fabs(pivot) < fabs(a[k*n+r])) {
pivot = a[k*n+r];
row_with_pivot = k;
}
// if pivot value is 0 continue
if (fabs(pivot) < DBL_EPSILON)
continue;
// swap row with maximum pivot value with current row
for (int c = r; c < n; c++)
std::swap(a[row_with_pivot*n+c], a[r*n+c]);
// eliminate other rows
for (int j = r+1; j < m; j++){
const auto fac = a[j*n+r] / pivot;
for (int c = r; c < n; c++)
a[j*n+c] -= fac * a[r*n+c];
}
}
}
//////////////////////////////////////// RANDOM GENERATOR /////////////////////////////
class UniformRandomGeneratorImpl : public UniformRandomGenerator {
private:
int subset_size = 0, max_range = 0;
std::vector<int> subset;
RNG rng;
public:
explicit UniformRandomGeneratorImpl (int state) : rng(state) {}
// interval is <0; max_range);
UniformRandomGeneratorImpl (int state, int max_range_, int subset_size_) : rng(state) {
subset_size = subset_size_;
max_range = max_range_;
subset = std::vector<int>(subset_size_);
}
int getRandomNumber () override {
return rng.uniform(0, max_range);
}
int getRandomNumber (int max_rng) override {
return rng.uniform(0, max_rng);
}
// closed range
void resetGenerator (int max_range_) override {
CV_CheckGE(0, max_range_, "max range must be greater than 0");
max_range = max_range_;
}
void generateUniqueRandomSet (std::vector<int>& sample) override {
CV_CheckLE(subset_size, max_range, "RandomGenerator. Subset size must be LE than range!");
int j, num;
sample[0] = rng.uniform(0, max_range);
for (int i = 1; i < subset_size;) {
num = rng.uniform(0, max_range);
// check if value is in array
for (j = i - 1; j >= 0; j--)
if (num == sample[j])
// if so, generate again
break;
// success, value is not in array, so it is unique, add to sample.
if (j == -1) sample[i++] = num;
}
}
// interval is <0; max_range)
void generateUniqueRandomSet (std::vector<int>& sample, int max_range_) override {
/*
* necessary condition:
* if subset size is bigger than range then array cannot be unique,
* so function has infinite loop.
*/
CV_CheckLE(subset_size, max_range_, "RandomGenerator. Subset size must be LE than range!");
int num, j;
sample[0] = rng.uniform(0, max_range_);
for (int i = 1; i < subset_size;) {
num = rng.uniform(0, max_range_);
for (j = i - 1; j >= 0; j--)
if (num == sample[j])
break;
if (j == -1) sample[i++] = num;
}
}
// interval is <0, max_range)
void generateUniqueRandomSet (std::vector<int>& sample, int subset_size_, int max_range_) override {
CV_CheckLE(subset_size_, max_range_, "RandomGenerator. Subset size must be LE than range!");
int num, j;
sample[0] = rng.uniform(0, max_range_);
for (int i = 1; i < subset_size_;) {
num = rng.uniform(0, max_range_);
for (j = i - 1; j >= 0; j--)
if (num == sample[j])
break;
if (j == -1) sample[i++] = num;
}
}
const std::vector<int> &generateUniqueRandomSubset (std::vector<int> &array1, int size1) override {
CV_CheckLE(subset_size, size1, "RandomGenerator. Subset size must be LE than range!");
int temp_size1 = size1;
for (int i = 0; i < subset_size; i++) {
const int idx1 = rng.uniform(0, temp_size1);
subset[i] = array1[idx1];
std::swap(array1[idx1], array1[--temp_size1]);
}
return subset;
}
void setSubsetSize (int subset_size_) override {
subset_size = subset_size_;
}
int getSubsetSize () const override { return subset_size; }
Ptr<RandomGenerator> clone (int state) const override {
return makePtr<UniformRandomGeneratorImpl>(state, max_range, subset_size);
}
};
Ptr<UniformRandomGenerator> UniformRandomGenerator::create (int state) {
return makePtr<UniformRandomGeneratorImpl>(state);
}
Ptr<UniformRandomGenerator> UniformRandomGenerator::create
(int state, int max_range, int subset_size_) {
return makePtr<UniformRandomGeneratorImpl>(state, max_range, subset_size_);
}
// @k_minth - desired k-th minimal element. For median is half of array
// closed working interval of array <@left; @right>
float quicksort_median (std::vector<float> &array, int k_minth, int left, int right);
float quicksort_median (std::vector<float> &array, int k_minth, int left, int right) {
// length is 0, return single value
if (right - left == 0) return array[left];
// get pivot, the rightest value in array
const auto pivot = array[right];
int right_ = right - 1; // -1, not including pivot
// counter of values smaller equal than pivot
int j = left, values_less_eq_pivot = 1; // 1, inludes pivot already
for (; j <= right_;) {
if (array[j] <= pivot) {
j++;
values_less_eq_pivot++;
} else
// value is bigger than pivot, swap with right_ value
// swap values in array and decrease interval
std::swap(array[j], array[right_--]);
}
if (values_less_eq_pivot == k_minth) return pivot;
if (k_minth > values_less_eq_pivot)
return quicksort_median(array, k_minth - values_less_eq_pivot, j, right-1);
else
return quicksort_median(array, k_minth, left, j-1);
}
// find median using quicksort with complexity O(log n)
// Note, function changes order of values in array
float Utils::findMedian (std::vector<float> &array) {
const int length = static_cast<int>(array.size());
if (length % 2) {
// odd number of values
return quicksort_median (array, length/2+1, 0, length-1);
} else {
// even: return average
return (quicksort_median(array, length/2 , 0, length-1) +
quicksort_median(array, length/2+1, 0, length-1))/2;
}
}
///////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////// Radius Search Graph /////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
class RadiusSearchNeighborhoodGraphImpl : public RadiusSearchNeighborhoodGraph {
private:
std::vector<std::vector<int>> graph;
public:
RadiusSearchNeighborhoodGraphImpl (const Mat &container_, int points_size,
double radius, int flann_search_params, int num_kd_trees) {
// Radius search OpenCV works only with float data
CV_Assert(container_.type() == CV_32F);
FlannBasedMatcher flann(makePtr<flann::KDTreeIndexParams>(num_kd_trees), makePtr<flann::SearchParams>(flann_search_params));
std::vector<std::vector<DMatch>> neighbours;
flann.radiusMatch(container_, container_, neighbours, (float)radius);
// allocate graph
graph = std::vector<std::vector<int>> (points_size);
int pt = 0;
for (const auto &n : neighbours) {
auto &graph_row = graph[pt];
graph_row = std::vector<int>(n.size()-1);
int j = 0;
for (const auto &idx : n)
// skip neighbor which has the same index as requested point
if (idx.trainIdx != pt)
graph_row[j++] = idx.trainIdx;
pt++;
}
}
inline const std::vector<int> &getNeighbors(int point_idx) const override {
return graph[point_idx];
}
};
Ptr<RadiusSearchNeighborhoodGraph> RadiusSearchNeighborhoodGraph::create (const Mat &points,
int points_size, double radius_, int flann_search_params, int num_kd_trees) {
return makePtr<RadiusSearchNeighborhoodGraphImpl> (points, points_size, radius_,
flann_search_params, num_kd_trees);
}
///////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////// FLANN Graph /////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
class FlannNeighborhoodGraphImpl : public FlannNeighborhoodGraph {
private:
std::vector<std::vector<int>> graph;
std::vector<std::vector<double>> distances;
public:
FlannNeighborhoodGraphImpl (const Mat &container_, int points_size, int k_nearest_neighbors,
bool get_distances, int flann_search_params_, int num_kd_trees) {
CV_Assert(k_nearest_neighbors <= points_size);
// FLANN works only with float data
CV_Assert(container_.type() == CV_32F);
flann::Index flannIndex (container_.reshape(1), flann::KDTreeIndexParams(num_kd_trees));
Mat dists, nearest_neighbors;
flannIndex.knnSearch(container_, nearest_neighbors, dists, k_nearest_neighbors+1,
flann::SearchParams(flann_search_params_));
// first nearest neighbor of point is this point itself.
// remove this first column
nearest_neighbors.colRange(1, k_nearest_neighbors+1).copyTo (nearest_neighbors);
graph = std::vector<std::vector<int>>(points_size, std::vector<int>(k_nearest_neighbors));
const auto * const nn = (int *) nearest_neighbors.data;
const auto * const dists_ptr = (float *) dists.data;
if (get_distances)
distances = std::vector<std::vector<double>>(points_size, std::vector<double>(k_nearest_neighbors));
for (int pt = 0; pt < points_size; pt++) {
std::copy(nn + k_nearest_neighbors*pt, nn + k_nearest_neighbors*pt + k_nearest_neighbors, &graph[pt][0]);
if (get_distances)
std::copy(dists_ptr + k_nearest_neighbors*pt, dists_ptr + k_nearest_neighbors*pt + k_nearest_neighbors,
&distances[pt][0]);
}
}
const std::vector<double>& getNeighborsDistances (int idx) const override {
return distances[idx];
}
inline const std::vector<int> &getNeighbors(int point_idx) const override {
// CV_Assert(point_idx_ < num_vertices);
return graph[point_idx];
}
};
Ptr<FlannNeighborhoodGraph> FlannNeighborhoodGraph::create(const Mat &points,
int points_size, int k_nearest_neighbors_, bool get_distances,
int flann_search_params_, int num_kd_trees) {
return makePtr<FlannNeighborhoodGraphImpl>(points, points_size,
k_nearest_neighbors_, get_distances, flann_search_params_, num_kd_trees);
}
///////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////// Grid Neighborhood Graph /////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////
class GridNeighborhoodGraphImpl : public GridNeighborhoodGraph {
private:
// This struct is used for the nearest neighbors search by griding two images.
struct CellCoord {
int c1x, c1y, c2x, c2y;
CellCoord (int c1x_, int c1y_, int c2x_, int c2y_) {
c1x = c1x_; c1y = c1y_; c2x = c2x_; c2y = c2y_;
}
bool operator==(const CellCoord &o) const {
return c1x == o.c1x && c1y == o.c1y && c2x == o.c2x && c2y == o.c2y;
}
bool operator<(const CellCoord &o) const {
if (c1x < o.c1x) return true;
if (c1x == o.c1x && c1y < o.c1y) return true;
if (c1x == o.c1x && c1y == o.c1y && c2x < o.c2x) return true;
return c1x == o.c1x && c1y == o.c1y && c2x == o.c2x && c2y < o.c2y;
}
};
std::map<CellCoord, std::vector<int >> neighbors_map;
std::vector<std::vector<int>> graph;
public:
GridNeighborhoodGraphImpl (const Mat &container_, int points_size,
int cell_size_x_img1, int cell_size_y_img1, int cell_size_x_img2, int cell_size_y_img2) {
const auto * const container = (float *) container_.data;
// <int, int, int, int> -> {neighbors set}
// Key is cell position. The value is indexes of neighbors.
const float cell_sz_x1 = 1.f / (float) cell_size_x_img1,
cell_sz_y1 = 1.f / (float) cell_size_y_img1,
cell_sz_x2 = 1.f / (float) cell_size_x_img2,
cell_sz_y2 = 1.f / (float) cell_size_y_img2;
const int dimension = container_.cols;
for (int i = 0; i < points_size; i++) {
const int idx = dimension * i;
neighbors_map[CellCoord((int)(container[idx ] * cell_sz_x1),
(int)(container[idx+1] * cell_sz_y1),
(int)(container[idx+2] * cell_sz_x2),
(int)(container[idx+3] * cell_sz_y2))].emplace_back(i);
}
//--------- create a graph ----------
graph = std::vector<std::vector<int>>(points_size);
// store neighbors cells into graph (2D vector)
for (const auto &cell : neighbors_map) {
const int neighbors_in_cell = static_cast<int>(cell.second.size());
// only one point in cell -> no neighbors
if (neighbors_in_cell < 2) continue;
const std::vector<int> &neighbors = cell.second;
// ---------- fill graph -----
for (int v_in_cell : neighbors) {
// there is always at least one neighbor
auto &graph_row = graph[v_in_cell];
graph_row = std::vector<int>(neighbors_in_cell-1);
int j = 0;
for (int n : neighbors)
if (n != v_in_cell)
graph_row[j++] = n;
}
}
}
inline const std::vector<int> &getNeighbors(int point_idx) const override {
// Note, neighbors vector also includes point_idx!
// return neighbors_map[vertices_to_cells[point_idx]];
return graph[point_idx];
}
};
Ptr<GridNeighborhoodGraph> GridNeighborhoodGraph::create(const Mat &points,
int points_size, int cell_size_x_img1_, int cell_size_y_img1_,
int cell_size_x_img2_, int cell_size_y_img2_) {
return makePtr<GridNeighborhoodGraphImpl>(points, points_size,
cell_size_x_img1_, cell_size_y_img1_, cell_size_x_img2_, cell_size_y_img2_);
}
}}

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modules/calib3d/test/test_usac.cpp
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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
#include "test_precomp.hpp"
namespace opencv_test {
enum TestSolver { Homogr, Fundam, Essen, PnP, Affine};
/*
* rng -- reference to random generator
* pts1 -- 2xN image points
* pts2 -- for PnP is 3xN object points, otherwise 2xN image points.
* two_calib -- True if two cameras have different calibration.
* K1 -- intrinsic matrix of the first camera. For PnP only one camera.
* K2 -- only if two_calib is True.
* pts_size -- required size of points.
* inlier_ratio -- required inlier ratio
* noise_std -- standard deviation of Gaussian noise of image points.
* gt_inliers -- has size of number of inliers. Contains indices of inliers.
*/
static int generatePoints (cv::RNG &rng, cv::Mat &pts1, cv::Mat &pts2, cv::Mat &K1, cv::Mat &K2,
bool two_calib, int pts_size, TestSolver test_case, double inlier_ratio, double noise_std,
std::vector<int> &gt_inliers) {
auto eulerAnglesToRotationMatrix = [] (double pitch, double yaw, double roll) {
// Calculate rotation about x axis
cv::Matx33d R_x (1, 0, 0, 0, cos(roll), -sin(roll), 0, sin(roll), cos(roll));
// Calculate rotation about y axis
cv::Matx33d R_y (cos(pitch), 0, sin(pitch), 0, 1, 0, -sin(pitch), 0, cos(pitch));
// Calculate rotation about z axis
cv::Matx33d R_z (cos(yaw), -sin(yaw), 0, sin(yaw), cos(yaw), 0, 0, 0, 1);
return cv::Mat(R_z * R_y * R_x); // Combined rotation matrix
};
const double pitch_min = -CV_PI / 6, pitch_max = CV_PI / 6; // 30 degrees
const double yaw_min = -CV_PI / 6, yaw_max = CV_PI / 6;
const double roll_min = -CV_PI / 6, roll_max = CV_PI / 6;
cv::Mat R = eulerAnglesToRotationMatrix(rng.uniform(pitch_min, pitch_max),
rng.uniform(yaw_min, yaw_max), rng.uniform(roll_min, roll_max));
// generate random translation,
// if test for homography fails try to fix translation to zero vec so H is related by transl.
cv::Vec3d t (rng.uniform(-0.5f, 0.5f), rng.uniform(-0.5f, 0.5f), rng.uniform(1.0f, 2.0f));
// generate random calibration
auto getRandomCalib = [&] () {
return cv::Mat(cv::Matx33d(rng.uniform(100.0, 1000.0), 0, rng.uniform(100.0, 100.0),
0, rng.uniform(100.0, 1000.0), rng.uniform(-100.0, 100.0),
0, 0, 1.));
};
K1 = getRandomCalib();
K2 = two_calib ? getRandomCalib() : K1.clone();
auto updateTranslation = [] (const cv::Mat &pts, const cv::Mat &R_, cv::Vec3d &t_) {
// Make sure the shape is in front of the camera
cv::Mat points3d_transformed = R_ * pts + t_ * cv::Mat::ones(1, pts.cols, pts.type());
double min_dist, max_dist;
cv::minMaxIdx(points3d_transformed.row(2), &min_dist, &max_dist);
if (min_dist < 0) t_(2) -= min_dist + 1.0;
};
// compute size of inliers and outliers
const int inl_size = static_cast<int>(inlier_ratio * pts_size);
const int out_size = pts_size - inl_size;
// all points will have top 'inl_size' of their points inliers
gt_inliers.clear(); gt_inliers.reserve(inl_size);
for (int i = 0; i < inl_size; i++)
gt_inliers.emplace_back(i);
// double precision to multiply points by models
const int pts_type = CV_64F;
cv::Mat points3d;
if (test_case == TestSolver::Homogr) {
points3d.create(2, inl_size, pts_type);
rng.fill(points3d, cv::RNG::UNIFORM, 0.0, 1.0); // keep small range
// inliers must be planar points, let their 3D coordinate be 1
cv::vconcat(points3d, cv::Mat::ones(1, inl_size, points3d.type()), points3d);
} else if (test_case == TestSolver::Fundam || test_case == TestSolver::Essen) {
// create 3D points which are inliers
points3d.create(3, inl_size, pts_type);
rng.fill(points3d, cv::RNG::UNIFORM, 0.0, 1.0);
} else if (test_case == TestSolver::PnP) {
//pts1 are image points, pts2 are object points
pts2.create(3, inl_size, pts_type); // 3D inliers
rng.fill(pts2, cv::RNG::UNIFORM, 0, 1);
updateTranslation(pts2, R, t);
// project 3D points (pts2) on image plane (pts1)
pts1 = K1 * (R * pts2 + t * cv::Mat::ones(1, pts2.cols, pts2.type()));
cv::divide(pts1.row(0), pts1.row(2), pts1.row(0));
cv::divide(pts1.row(1), pts1.row(2), pts1.row(1));
// make 2D points
pts1 = pts1.rowRange(0, 2);
// create random outliers
cv::Mat pts_outliers = cv::Mat(5, out_size, pts2.type());
rng.fill(pts_outliers, cv::RNG::UNIFORM, 0, 1000);
// merge inliers with random image points = outliers
cv::hconcat(pts1, pts_outliers.rowRange(0, 2), pts1);
// merge 3D inliers with 3D outliers
cv::hconcat(pts2, pts_outliers.rowRange(2, 5), pts2);
// add Gaussian noise to image points
cv::Mat noise(pts1.rows, pts1.cols, pts1.type());
rng.fill(noise, cv::RNG::NORMAL, 0, noise_std);
pts1 += noise;
return inl_size;
} else if (test_case == TestSolver::Affine) {
} else
CV_Error(cv::Error::StsBadArg, "Unknown solver!");
if (test_case != TestSolver::PnP) {
// project 3D point on image plane
// use two relative scenes. The first camera is P1 = K1 [I | 0], the second P2 = K2 [R | t]
if (test_case != TestSolver::Affine) {
updateTranslation(points3d, R, t);
pts1 = K1 * points3d;
pts2 = K2 * (R * points3d + t * cv::Mat::ones(1, points3d.cols, points3d.type()));
// normalize by 3 coordinate
cv::divide(pts1.row(0), pts1.row(2), pts1.row(0));
cv::divide(pts1.row(1), pts1.row(2), pts1.row(1));
cv::divide(pts2.row(0), pts2.row(2), pts2.row(0));
cv::divide(pts2.row(1), pts2.row(2), pts2.row(1));
} else {
pts1 = cv::Mat(2, inl_size, pts_type);
rng.fill(pts1, cv::RNG::UNIFORM, 0, 1000);
cv::Matx33d sc(rng.uniform(1., 5.),0,0,rng.uniform(1., 4.),0,0, 0, 0, 1);
cv::Matx33d tr(1,0,rng.uniform(50., 500.),0,1,rng.uniform(50., 500.), 0, 0, 1);
const double phi = rng.uniform(0., CV_PI);
cv::Matx33d rot(cos(phi), -sin(phi),0, sin(phi), cos(phi),0, 0, 0, 1);
cv::Matx33d A = sc * tr * rot;
cv::vconcat(pts1, cv::Mat::ones(1, pts1.cols, pts1.type()), points3d);
pts2 = A * points3d;
}
// get 2D points
pts1 = pts1.rowRange(0,2); pts2 = pts2.rowRange(0,2);
// generate random outliers as 2D image points
cv::Mat pts1_outliers(pts1.rows, out_size, pts1.type()),
pts2_outliers(pts2.rows, out_size, pts2.type());
rng.fill(pts1_outliers, cv::RNG::UNIFORM, 0, 1000);
rng.fill(pts2_outliers, cv::RNG::UNIFORM, 0, 1000);
// merge inliers and outliers
cv::hconcat(pts1, pts1_outliers, pts1);
cv::hconcat(pts2, pts2_outliers, pts2);
// add normal / Gaussian noise to image points
cv::Mat noise1 (pts1.rows, pts1.cols, pts1.type()), noise2 (pts2.rows, pts2.cols, pts2.type());
rng.fill(noise1, cv::RNG::NORMAL, 0, noise_std); pts1 += noise1;
rng.fill(noise2, cv::RNG::NORMAL, 0, noise_std); pts2 += noise2;
}
return inl_size;
}
/*
* for test case = 0, 1, 2 (homography and epipolar geometry): pts1 and pts2 are 3xN
* for test_case = 3 (PnP): pts1 are 3xN and pts2 are 4xN
* all points are of the same type as model
*/
static double getError (TestSolver test_case, int pt_idx, const cv::Mat &pts1, const cv::Mat &pts2, const cv::Mat &model) {
cv::Mat pt1 = pts1.col(pt_idx), pt2 = pts2.col(pt_idx);
if (test_case == TestSolver::Homogr) { // reprojection error
// compute Euclidean distance between given and reprojected points
cv::Mat est_pt2 = model * pt1; est_pt2 /= est_pt2.at<double>(2);
if (false) {
cv::Mat est_pt1 = model.inv() * pt2; est_pt1 /= est_pt1.at<double>(2);
return (cv::norm(est_pt1 - pt1) + cv::norm(est_pt2 - pt2)) / 2;
}
return cv::norm(est_pt2 - pt2);
} else
if (test_case == TestSolver::Fundam || test_case == TestSolver::Essen) {
cv::Mat l2 = model * pt1;
cv::Mat l1 = model.t() * pt2;
if (test_case == TestSolver::Fundam) // sampson error
return fabs(pt2.dot(l2)) / sqrt(pow(l1.at<double>(0), 2) + pow(l1.at<double>(1), 2) +
pow(l2.at<double>(0), 2) + pow(l2.at<double>(1), 2));
else // symmetric geometric distance
return sqrt(pow(pt1.dot(l1),2) / (pow(l1.at<double>(0),2) + pow(l1.at<double>(1),2)) +
pow(pt2.dot(l2),2) / (pow(l2.at<double>(0),2) + pow(l2.at<double>(1),2)));
} else
if (test_case == TestSolver::PnP) { // PnP, reprojection error
cv::Mat img_pt = model * pt2; img_pt /= img_pt.at<double>(2);
return cv::norm(pt1 - img_pt);
} else
CV_Error(cv::Error::StsBadArg, "Undefined test case!");
}
/*
* inl_size -- number of ground truth inliers
* pts1 and pts2 are of the same size as from function generatePoints(...)
*/
static void checkInliersMask (TestSolver test_case, int inl_size, double thr, const cv::Mat &pts1_,
const cv::Mat &pts2_, const cv::Mat &model, const cv::Mat &mask) {
ASSERT_TRUE(!model.empty() && !mask.empty());
cv::Mat pts1 = pts1_, pts2 = pts2_;
if (pts1.type() != model.type()) {
pts1.convertTo(pts1, model.type());
pts2.convertTo(pts2, model.type());
}
// convert to homogeneous
cv::vconcat(pts1, cv::Mat::ones(1, pts1.cols, pts1.type()), pts1);
cv::vconcat(pts2, cv::Mat::ones(1, pts2.cols, pts2.type()), pts2);
thr *= 1.001; // increase a little threshold due to numerical imprecisions
const auto * const mask_ptr = mask.ptr<uchar>();
int num_found_inliers = 0;
for (int i = 0; i < pts1.cols; i++)
if (mask_ptr[i]) {
ASSERT_LT(getError(test_case, i, pts1, pts2, model), thr);
num_found_inliers++;
}
// check if RANSAC found at least 80% of inliers
ASSERT_GT(num_found_inliers, 0.8 * inl_size);
}
TEST(usac_Homography, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 1500;
cv::RNG &rng = cv::theRNG();
// do not test USAC_PARALLEL, because it is not deterministic
const std::vector<int> flags = {USAC_DEFAULT, USAC_ACCURATE, USAC_PROSAC, USAC_FAST, USAC_MAGSAC};
for (double inl_ratio = 0.1; inl_ratio < 0.91; inl_ratio += 0.1) {
cv::Mat pts1, pts2, K1, K2;
int inl_size = generatePoints(rng, pts1, pts2, K1, K2, false /*two calib*/,
pts_size, TestSolver ::Homogr, inl_ratio/*inl ratio*/, 0.1 /*noise std*/, gt_inliers);
// compute max_iters with standard upper bound rule for RANSAC with 1.5x tolerance
const double conf = 0.99, thr = 2., max_iters = 1.3 * log(1 - conf) /
log(1 - pow(inl_ratio, 4 /* sample size */));
for (auto flag : flags) {
cv::Mat mask, H = cv::findHomography(pts1, pts2,flag, thr, mask,
int(max_iters), conf);
checkInliersMask(TestSolver::Homogr, inl_size, thr, pts1, pts2, H, mask);
}
}
}
TEST(usac_Fundamental, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 2000;
cv::RNG &rng = cv::theRNG();
// start from 25% otherwise max_iters will be too big
const std::vector<int> flags = {USAC_DEFAULT, USAC_FM_8PTS, USAC_ACCURATE, USAC_PROSAC, USAC_FAST, USAC_MAGSAC};
const double conf = 0.99, thr = 1.;
for (double inl_ratio = 0.25; inl_ratio < 0.91; inl_ratio += 0.1) {
cv::Mat pts1, pts2, K1, K2;
int inl_size = generatePoints(rng, pts1, pts2, K1, K2, false /*two calib*/,
pts_size, TestSolver ::Fundam, inl_ratio, 0.1 /*noise std*/, gt_inliers);
for (auto flag : flags) {
const int sample_size = flag == USAC_FM_8PTS ? 8 : 7;
const double max_iters = 1.25 * log(1 - conf) /
log(1 - pow(inl_ratio, sample_size));
cv::Mat mask, F = cv::findFundamentalMat(pts1, pts2,flag, thr, conf,
int(max_iters), mask);
checkInliersMask(TestSolver::Fundam, inl_size, thr, pts1, pts2, F, mask);
}
}}
TEST(usac_Essential, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 1500;
cv::RNG &rng = cv::theRNG();
// findEssentilaMat has by default number of maximum iterations equal to 1000.
// It means that with 99% confidence we assume at least 34.08% of inliers
const std::vector<int> flags = {USAC_DEFAULT, USAC_ACCURATE, USAC_PROSAC, USAC_FAST, USAC_MAGSAC};
for (double inl_ratio = 0.35; inl_ratio < 0.91; inl_ratio += 0.1) {
cv::Mat pts1, pts2, K1, K2;
int inl_size = generatePoints(rng, pts1, pts2, K1, K2, false /*two calib*/,
pts_size, TestSolver ::Fundam, inl_ratio, 0.01 /*noise std, works bad with high noise*/, gt_inliers);
const double conf = 0.99, thr = 1.;
for (auto flag : flags) {
cv::Mat mask, E;
try {
E = cv::findEssentialMat(pts1, pts2, K1, flag, conf, thr, mask);
} catch (cv::Exception &e) {
if (e.code != cv::Error::StsNotImplemented)
FAIL() << "Essential matrix estimation failed!\n";
else continue;
}
// calibrate points
cv::Mat cpts1_3d, cpts2_3d;
cv::vconcat(pts1, cv::Mat::ones(1, pts1.cols, pts1.type()), cpts1_3d);
cv::vconcat(pts2, cv::Mat::ones(1, pts2.cols, pts2.type()), cpts2_3d);
cpts1_3d = K1.inv() * cpts1_3d; cpts2_3d = K1.inv() * cpts2_3d;
checkInliersMask(TestSolver::Essen, inl_size, thr / ((K1.at<double>(0,0) + K1.at<double>(1,1)) / 2),
cpts1_3d.rowRange(0,2), cpts2_3d.rowRange(0,2), E, mask);
}
}
}
TEST(usac_P3P, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 3000;
cv::Mat img_pts, obj_pts, K1, K2;
cv::RNG &rng = cv::theRNG();
const std::vector<int> flags = {USAC_DEFAULT, USAC_ACCURATE, USAC_PROSAC, USAC_FAST, USAC_MAGSAC};
for (double inl_ratio = 0.1; inl_ratio < 0.91; inl_ratio += 0.1) {
int inl_size = generatePoints(rng, img_pts, obj_pts, K1, K2, false /*two calib*/,
pts_size, TestSolver ::PnP, inl_ratio, 0.15 /*noise std*/, gt_inliers);
const double conf = 0.99, thr = 2., max_iters = 1.3 * log(1 - conf) /
log(1 - pow(inl_ratio, 3 /* sample size */));
for (auto flag : flags) {
cv::Mat rvec, tvec, mask, R, P;
CV_Assert(cv::solvePnPRansac(obj_pts, img_pts, K1, cv::noArray(), rvec, tvec,
false, (int)max_iters, (float)thr, conf, mask, flag));
cv::Rodrigues(rvec, R);
cv::hconcat(K1 * R, K1 * tvec, P);
checkInliersMask(TestSolver ::PnP, inl_size, thr, img_pts, obj_pts, P, mask);
}
}
}
TEST (usac_Affine2D, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 2000;
cv::Mat pts1, pts2, K1, K2;
cv::RNG &rng = cv::theRNG();
const std::vector<int> flags = {USAC_DEFAULT, USAC_ACCURATE, USAC_PROSAC, USAC_FAST, USAC_MAGSAC};
for (double inl_ratio = 0.1; inl_ratio < 0.91; inl_ratio += 0.1) {
int inl_size = generatePoints(rng, pts1, pts2, K1, K2, false /*two calib*/,
pts_size, TestSolver ::Affine, inl_ratio, 0.15 /*noise std*/, gt_inliers);
const double conf = 0.99, thr = 2., max_iters = 1.3 * log(1 - conf) /
log(1 - pow(inl_ratio, 3 /* sample size */));
for (auto flag : flags) {
cv::Mat mask, A = cv::estimateAffine2D(pts1, pts2, mask, flag, thr, (size_t)max_iters, conf, 0);
cv::vconcat(A, cv::Mat(cv::Matx13d(0,0,1)), A);
checkInliersMask(TestSolver::Homogr /*use homography error*/, inl_size, thr, pts1, pts2, A, mask);
}
}
}
TEST(usac_testUsacParams, accuracy) {
std::vector<int> gt_inliers;
const int pts_size = 1500;
cv::RNG &rng = cv::theRNG();
const cv::UsacParams usac_params = cv::UsacParams();
cv::Mat pts1, pts2, K1, K2, mask, model, rvec, tvec, R;
int inl_size;
auto getInlierRatio = [] (int max_iters, int sample_size, double conf) {
return std::pow(1 - exp(log(1 - conf)/(double)max_iters), 1 / (double)sample_size);
};
cv::Vec4d dist_coeff (0, 0, 0, 0); // test with 0 distortion
// Homography matrix
inl_size = generatePoints(rng, pts1, pts2, K1, K2, false, pts_size, TestSolver::Homogr,
getInlierRatio(usac_params.maxIterations, 4, usac_params.confidence), 0.1, gt_inliers);
model = cv::findHomography(pts1, pts2, mask, usac_params);
checkInliersMask(TestSolver::Homogr, inl_size, usac_params.threshold, pts1, pts2, model, mask);
// Fundamental matrix
inl_size = generatePoints(rng, pts1, pts2, K1, K2, false, pts_size, TestSolver::Fundam,
getInlierRatio(usac_params.maxIterations, 7, usac_params.confidence), 0.1, gt_inliers);
model = cv::findFundamentalMat(pts1, pts2, mask, usac_params);
checkInliersMask(TestSolver::Fundam, inl_size, usac_params.threshold, pts1, pts2, model, mask);
// Essential matrix
inl_size = generatePoints(rng, pts1, pts2, K1, K2, true, pts_size, TestSolver::Essen,
getInlierRatio(usac_params.maxIterations, 5, usac_params.confidence), 0.01, gt_inliers);
try {
model = cv::findEssentialMat(pts1, pts2, K1, K2, dist_coeff, dist_coeff, mask, usac_params);
cv::Mat cpts1_3d, cpts2_3d;
cv::vconcat(pts1, cv::Mat::ones(1, pts1.cols, pts1.type()), cpts1_3d);
cv::vconcat(pts2, cv::Mat::ones(1, pts2.cols, pts2.type()), cpts2_3d);
cpts1_3d = K1.inv() * cpts1_3d; cpts2_3d = K2.inv() * cpts2_3d;
checkInliersMask(TestSolver::Essen, inl_size, usac_params.threshold /
((K1.at<double>(0,0) + K1.at<double>(1,1) + K2.at<double>(0,0) + K2.at<double>(1,1)) / 4),
cpts1_3d.rowRange(0,2), cpts2_3d.rowRange(0,2), model, mask);
} catch (cv::Exception &e) {
if (e.code != cv::Error::StsNotImplemented)
FAIL() << "Essential matrix estimation failed!\n";
// CV_Error(cv::Error::StsError, "Essential matrix estimation failed!");
}
// P3P
inl_size = generatePoints(rng, pts1, pts2, K1, K2, false, pts_size, TestSolver::PnP,
getInlierRatio(usac_params.maxIterations, 3, usac_params.confidence), 0.01, gt_inliers);
CV_Assert(cv::solvePnPRansac(pts2, pts1, K1, dist_coeff, rvec, tvec, mask, usac_params));
cv::Rodrigues(rvec, R); cv::hconcat(K1 * R, K1 * tvec, model);
checkInliersMask(TestSolver::PnP, inl_size, usac_params.threshold, pts1, pts2, model, mask);
// P6P
inl_size = generatePoints(rng, pts1, pts2, K1, K2, false, pts_size, TestSolver::PnP,
getInlierRatio(usac_params.maxIterations, 6, usac_params.confidence), 0.1, gt_inliers);
cv::Mat K_est;
CV_Assert(cv::solvePnPRansac(pts2, pts1, K_est, dist_coeff, rvec, tvec, mask, usac_params));
cv::Rodrigues(rvec, R); cv::hconcat(K_est * R, K_est * tvec, model);
checkInliersMask(TestSolver::PnP, inl_size, usac_params.threshold, pts1, pts2, model, mask);
// Affine2D
inl_size = generatePoints(rng, pts1, pts2, K1, K2, false, pts_size, TestSolver::Affine,
getInlierRatio(usac_params.maxIterations, 3, usac_params.confidence), 0.1, gt_inliers);
model = cv::estimateAffine2D(pts1, pts2, mask, usac_params);
cv::vconcat(model, cv::Mat(cv::Matx13d(0,0,1)), model);
checkInliersMask(TestSolver::Homogr, inl_size, usac_params.threshold, pts1, pts2, model, mask);
}
}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html
#include "opencv2/calib3d.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#include <vector>
#include <iostream>
using namespace cv;
int main(int args, char** argv) {
std::string img_name1, img_name2;
if (args < 3) {
CV_Error(Error::StsBadArg,
"Path to two images \nFor example: "
"./epipolar_lines img1.jpg img2.jpg");
} else {
img_name1 = argv[1];
img_name2 = argv[2];
}
Mat image1 = imread(img_name1);
Mat image2 = imread(img_name2);
Mat descriptors1, descriptors2;
std::vector<KeyPoint> keypoints1, keypoints2;
Ptr<SIFT> detector = SIFT::create();
detector->detect(image1, keypoints1);
detector->detect(image2, keypoints2);
detector->compute(image1, keypoints1, descriptors1);
detector->compute(image2, keypoints2, descriptors2);
FlannBasedMatcher matcher(makePtr<flann::KDTreeIndexParams>(5), makePtr<flann::SearchParams>(32));
// get k=2 best match that we can apply ratio test explained by D.Lowe
std::vector<std::vector<DMatch>> matches_vector;
matcher.knnMatch(descriptors1, descriptors2, matches_vector, 2);
std::vector<Point2d> pts1, pts2;
pts1.reserve(matches_vector.size()); pts2.reserve(matches_vector.size());
for (const auto &m : matches_vector) {
// compare best and second match using Lowe ratio test
if (m[0].distance / m[1].distance < 0.75) {
pts1.emplace_back(keypoints1[m[0].queryIdx].pt);
pts2.emplace_back(keypoints2[m[0].trainIdx].pt);
}
}
std::cout << "Number of points " << pts1.size() << '\n';
Mat inliers;
const auto begin_time = std::chrono::steady_clock::now();
const Mat F = findFundamentalMat(pts1, pts2, RANSAC, 1., 0.99, 2000, inliers);
std::cout << "RANSAC fundamental matrix time " << static_cast<int>(std::chrono::duration_cast<std::chrono::microseconds>
(std::chrono::steady_clock::now() - begin_time).count()) << "\n";
Mat points1 = Mat((int)pts1.size(), 2, CV_64F, pts1.data());
Mat points2 = Mat((int)pts2.size(), 2, CV_64F, pts2.data());
vconcat(points1.t(), Mat::ones(1, points1.rows, points1.type()), points1);
vconcat(points2.t(), Mat::ones(1, points2.rows, points2.type()), points2);
RNG rng;
const int circle_sz = 3, line_sz = 1, max_lines = 300;
std::vector<int> pts_shuffle (points1.cols);
for (int i = 0; i < points1.cols; i++)
pts_shuffle[i] = i;
randShuffle(pts_shuffle);
int plot_lines = 0, num_inliers = 0;
double mean_err = 0;
for (int pt : pts_shuffle) {
if (inliers.at<uchar>(pt)) {
const Scalar col (rng.uniform(0,256), rng.uniform(0,256), rng.uniform(0,256));
const Mat l2 = F * points1.col(pt);
const Mat l1 = F.t() * points2.col(pt);
double a1 = l1.at<double>(0), b1 = l1.at<double>(1), c1 = l1.at<double>(2);
double a2 = l2.at<double>(0), b2 = l2.at<double>(1), c2 = l2.at<double>(2);
const double mag1 = sqrt(a1*a1 + b1*b1), mag2 = (a2*a2 + b2*b2);
a1 /= mag1; b1 /= mag1; c1 /= mag1; a2 /= mag2; b2 /= mag2; c2 /= mag2;
if (plot_lines++ < max_lines) {
line(image1, Point2d(0, -c1/b1),
Point2d((double)image1.cols, -(a1*image1.cols+c1)/b1), col, line_sz);
line(image2, Point2d(0, -c2/b2),
Point2d((double)image2.cols, -(a2*image2.cols+c2)/b2), col, line_sz);
}
circle (image1, pts1[pt], circle_sz, col, -1);
circle (image2, pts2[pt], circle_sz, col, -1);
mean_err += (fabs(points1.col(pt).dot(l2)) / mag2 + fabs(points2.col(pt).dot(l1) / mag1)) / 2;
num_inliers++;
}
}
std::cout << "Mean distance from tentative inliers to epipolar lines " << mean_err/num_inliers
<< " number of inliers " << num_inliers << "\n";
// concatenate two images
hconcat(image1, image2, image1);
const int new_img_size = 1200 * 800; // for example
// resize with the same aspect ratio
resize(image1, image1, Size((int) sqrt ((double) image1.cols * new_img_size / image1.rows),
(int)sqrt ((double) image1.rows * new_img_size / image1.cols)));
imshow("epipolar lines, image 1, 2", image1);
imwrite("epipolar_lines.png", image1);
waitKey(0);
}

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// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html
#include "opencv2/calib3d.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#include <vector>
#include <iostream>
#include <fstream>
using namespace cv;
static double getError2EpipLines (const Mat &F, const Mat &pts1, const Mat &pts2, const Mat &mask) {
Mat points1, points2;
vconcat(pts1, Mat::ones(1, pts1.cols, pts1.type()), points1);
vconcat(pts2, Mat::ones(1, pts2.cols, pts2.type()), points2);
double mean_error = 0;
for (int pt = 0; pt < (int) mask.total(); pt++)
if (mask.at<uchar>(pt)) {
const Mat l2 = F * points1.col(pt);
const Mat l1 = F.t() * points2.col(pt);
mean_error += (fabs(points1.col(pt).dot(l1)) / sqrt(pow(l1.at<double>(0), 2) + pow(l1.at<double>(1), 2)) +
fabs(points2.col(pt).dot(l2) / sqrt(pow(l2.at<double>(0), 2) + pow(l2.at<double>(1), 2)))) / 2;
}
return mean_error / mask.total();
}
static int sgn(double val) { return (0 < val) - (val < 0); }
/*
* @points3d - vector of Point3 or Mat of size Nx3
* @planes - vector of found planes
* @labels - vector of size point3d. Every point which has non-zero label is classified to this plane.
*/
static void getPlanes (InputArray points3d_, std::vector<int> &labels, std::vector<Vec4d> &planes, int desired_num_planes, double thr_, double conf_, int max_iters_) {
Mat points3d = points3d_.getMat();
points3d.convertTo(points3d, CV_64F); // convert points to have double precision
if (points3d_.isVector())
points3d = Mat((int)points3d.total(), 3, CV_64F, points3d.data);
else {
if (points3d.type() != CV_64F)
points3d = points3d.reshape(1, (int)points3d.total()); // convert point to have 1 channel
if (points3d.rows < points3d.cols)
transpose(points3d, points3d); // transpose so points will be in rows
CV_CheckEQ(points3d.cols, 3, "Invalid dimension of point");
}
/*
* 3D plane fitting with RANSAC
* @best_model contains coefficients [a b c d] s.t. ax + by + cz = d
*
*/
auto plane_ransac = [] (const Mat &pts, double thr, double conf, int max_iters, Vec4d &best_model, std::vector<bool> &inliers) {
const int pts_size = pts.rows, max_lo_inliers = 15, max_lo_iters = 10;
int best_inls = 0;
if (pts_size < 3) return false;
RNG rng;
const auto * const points = (double *) pts.data;
std::vector<int> min_sample(3);
inliers = std::vector<bool>(pts_size);
const double log_conf = log(1-conf);
Vec4d model, lo_model;
std::vector<int> random_pool (pts_size);
for (int p = 0; p < pts_size; p++)
random_pool[p] = p;
// estimate plane coefficients using covariance matrix
auto estimate = [&] (const std::vector<int> &sample, Vec4d &model_) {
// https://www.ilikebigbits.com/2017_09_25_plane_from_points_2.html
const int n = static_cast<int>(sample.size());
if (n < 3) return false;
double sum_x = 0, sum_y = 0, sum_z = 0;
for (int s : sample) {
sum_x += points[3*s ];
sum_y += points[3*s+1];
sum_z += points[3*s+2];
}
const double c_x = sum_x / n, c_y = sum_y / n, c_z = sum_z / n;
double xx = 0, yy = 0, zz = 0, xy = 0, xz = 0, yz = 0;
for (int s : sample) {
const double x_ = points[3*s] - c_x, y_ = points[3*s+1] - c_y, z_ = points[3*s+2] - c_z;
xx += x_*x_; yy += y_*y_; zz += z_*z_; xy = x_*y_; yz += y_*z_; xz += x_*z_;
}
xx /= n; yy /= n; zz /= n; xy /= n; yz /= n; xz /= n;
Vec3d weighted_normal(0,0,0);
const double det_x = yy*zz - yz*yz, det_y = xx*zz - xz*xz, det_z = xx*yy - xy*xy;
Vec3d axis_x (det_x, xz*xz-xy*zz, xy*yz-xz*yy);
Vec3d axis_y (xz*yz-xy*zz, det_y, xy*xz-yz*xx);
Vec3d axis_z (xy*yz-xz*yy, xy*xz-yz*xx, det_z);
weighted_normal += axis_x * det_x * det_x;
weighted_normal += sgn(weighted_normal.dot(axis_y)) * axis_y * det_y * det_y;
weighted_normal += sgn(weighted_normal.dot(axis_z)) * axis_z * det_z * det_z;
weighted_normal /= norm(weighted_normal);
if (std::isinf(weighted_normal(0)) ||
std::isinf(weighted_normal(1)) ||
std::isinf(weighted_normal(2))) return false;
// find plane model from normal and centroid
model_ = Vec4d(weighted_normal(0), weighted_normal(1), weighted_normal(2),
weighted_normal.dot(Vec3d(c_x, c_y, c_z)));
return true;
};
// calculate number of inliers
auto getInliers = [&] (const Vec4d &model_) {
const double a = model_(0), b = model_(1), c = model_(2), d = model_(3);
int num_inliers = 0;
std::fill(inliers.begin(), inliers.end(), false);
for (int p = 0; p < pts_size; p++) {
inliers[p] = fabs(a * points[3*p] + b * points[3*p+1] + c * points[3*p+2] - d) < thr;
if (inliers[p]) num_inliers++;
if (num_inliers + pts_size - p < best_inls) break;
}
return num_inliers;
};
// main RANSAC loop
for (int iters = 0; iters < max_iters; iters++) {
// find minimal sample: 3 points
min_sample[0] = rng.uniform(0, pts_size);
min_sample[1] = rng.uniform(0, pts_size);
min_sample[2] = rng.uniform(0, pts_size);
if (! estimate(min_sample, model))
continue;
int num_inliers = getInliers(model);
if (num_inliers > best_inls) {
// store so-far-the-best
std::vector<bool> best_inliers = inliers;
// do Local Optimization
for (int lo_iter = 0; lo_iter < max_lo_iters; lo_iter++) {
std::vector<int> inliers_idx; inliers_idx.reserve(max_lo_inliers);
randShuffle(random_pool);
for (int p : random_pool) {
if (best_inliers[p]) {
inliers_idx.emplace_back(p);
if ((int)inliers_idx.size() >= max_lo_inliers)
break;
}
}
if (! estimate(inliers_idx, lo_model))
continue;
int lo_inls = getInliers(lo_model);
if (best_inls < lo_inls) {
best_model = lo_model;
best_inls = lo_inls;
best_inliers = inliers;
}
}
if (best_inls < num_inliers) {
best_model = model;
best_inls = num_inliers;
}
// update max iters
// because points are quite noisy we need more iterations
const double max_hyp = 3 * log_conf / log(1 - pow(double(best_inls) / pts_size, 3));
if (! std::isinf(max_hyp) && max_hyp < max_iters)
max_iters = static_cast<int>(max_hyp);
}
}
getInliers(best_model);
return best_inls != 0;
};
labels = std::vector<int>(points3d.rows, 0);
Mat pts3d_plane_fit = points3d.clone();
// keep array of indices of points corresponding to original points3d
std::vector<int> to_orig_pts_arr(pts3d_plane_fit.rows);
for (int i = 0; i < (int) to_orig_pts_arr.size(); i++)
to_orig_pts_arr[i] = i;
for (int num_planes = 1; num_planes <= desired_num_planes; num_planes++) {
Vec4d model;
std::vector<bool> inl;
if (!plane_ransac(pts3d_plane_fit, thr_, conf_, max_iters_, model, inl))
break;
planes.emplace_back(model);
const int pts3d_size = pts3d_plane_fit.rows;
pts3d_plane_fit = Mat();
pts3d_plane_fit.reserve(points3d.rows);
int cnt = 0;
for (int p = 0; p < pts3d_size; p++) {
if (! inl[p]) {
// if point is not inlier to found plane - add it to next run
to_orig_pts_arr[cnt] = to_orig_pts_arr[p];
pts3d_plane_fit.push_back(points3d.row(to_orig_pts_arr[cnt]));
cnt++;
} else labels[to_orig_pts_arr[p]] = num_planes; // otherwise label this point
}
}
}
int main(int args, char** argv) {
std::string data_file, image_dir;
if (args < 3) {
CV_Error(Error::StsBadArg,
"Path to data file and directory to image files are missing!\nData file must have"
" format:\n--------------\n image_name_1\nimage_name_2\nk11 k12 k13\n0 k22 k23\n"
"0 0 1\n--------------\nIf image_name_{1,2} are not in the same directory as "
"the data file then add argument with directory to image files.\nFor example: "
"./essential_mat_reconstr essential_mat_data.txt ./");
} else {
data_file = argv[1];
image_dir = argv[2];
}
std::ifstream file(data_file, std::ios_base::in);
CV_CheckEQ(file.is_open(), true, "Data file is not found!");
std::string filename1, filename2;
std::getline(file, filename1);
std::getline(file, filename2);
Mat image1 = imread(image_dir+filename1);
Mat image2 = imread(image_dir+filename2);
CV_CheckEQ(image1.empty(), false, "Image 1 is not found!");
CV_CheckEQ(image2.empty(), false, "Image 2 is not found!");
// read calibration
Matx33d K;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
file >> K(i,j);
file.close();
Mat descriptors1, descriptors2;
std::vector<KeyPoint> keypoints1, keypoints2;
// detect points with SIFT
Ptr<SIFT> detector = SIFT::create();
detector->detect(image1, keypoints1);
detector->detect(image2, keypoints2);
detector->compute(image1, keypoints1, descriptors1);
detector->compute(image2, keypoints2, descriptors2);
FlannBasedMatcher matcher(makePtr<flann::KDTreeIndexParams>(5), makePtr<flann::SearchParams>(32));
// get k=2 best match that we can apply ratio test explained by D.Lowe
std::vector<std::vector<DMatch>> matches_vector;
matcher.knnMatch(descriptors1, descriptors2, matches_vector, 2);
// filter keypoints with Lowe ratio test
std::vector<Point2d> pts1, pts2;
pts1.reserve(matches_vector.size()); pts2.reserve(matches_vector.size());
for (const auto &m : matches_vector) {
// compare best and second match using Lowe ratio test
if (m[0].distance / m[1].distance < 0.75) {
pts1.emplace_back(keypoints1[m[0].queryIdx].pt);
pts2.emplace_back(keypoints2[m[0].trainIdx].pt);
}
}
Mat inliers;
const int pts_size = (int) pts1.size();
const auto begin_time = std::chrono::steady_clock::now();
// fine essential matrix
const Mat E = findEssentialMat(pts1, pts2, Mat(K), RANSAC, 0.99, 1.0, inliers);
std::cout << "RANSAC essential matrix time " << std::chrono::duration_cast<std::chrono::microseconds>
(std::chrono::steady_clock::now() - begin_time).count() <<
"mcs.\nNumber of inliers " << countNonZero(inliers) << "\n";
Mat points1 = Mat((int)pts1.size(), 2, CV_64F, pts1.data());
Mat points2 = Mat((int)pts2.size(), 2, CV_64F, pts2.data());
points1 = points1.t(); points2 = points2.t();
std::cout << "Mean error to epipolar lines " <<
getError2EpipLines(K.inv().t() * E * K.inv(), points1, points2, inliers) << "\n";
// decompose essential into rotation and translation
Mat R1, R2, t;
decomposeEssentialMat(E, R1, R2, t);
// Create two relative pose
// P1 = K [ I | 0 ]
// P2 = K [R{1,2} | {+-}t]
Mat P1;
hconcat(K, Vec3d::zeros(), P1);
std::vector<Mat> P2s(4);
hconcat(K * R1, K * t, P2s[0]);
hconcat(K * R1, -K * t, P2s[1]);
hconcat(K * R2, K * t, P2s[2]);
hconcat(K * R2, -K * t, P2s[3]);
// find objects point by enumerating over 4 different projection matrices of second camera
// vector to keep object points
std::vector<std::vector<Vec3d>> obj_pts_per_cam(4);
// vector to keep indices of image points corresponding to object points
std::vector<std::vector<int>> img_idxs_per_cam(4);
int cam_idx = 0, best_cam_idx = 0, max_obj_pts = 0;
for (const auto &P2 : P2s) {
obj_pts_per_cam[cam_idx].reserve(pts_size);
img_idxs_per_cam[cam_idx].reserve(pts_size);
for (int i = 0; i < pts_size; i++) {
// process only inliers
if (! inliers.at<uchar>(i))
continue;
Vec4d obj_pt;
// find object point using triangulation
triangulatePoints(P1, P2, points1.col(i), points2.col(i), obj_pt);
obj_pt /= obj_pt(3); // normalize 4d point
if (obj_pt(2) > 0) { // check if projected point has positive depth
obj_pts_per_cam[cam_idx].emplace_back(Vec3d(obj_pt(0), obj_pt(1), obj_pt(2)));
img_idxs_per_cam[cam_idx].emplace_back(i);
}
}
if (max_obj_pts < (int) obj_pts_per_cam[cam_idx].size()) {
max_obj_pts = (int) obj_pts_per_cam[cam_idx].size();
best_cam_idx = cam_idx;
}
cam_idx++;
}
std::cout << "Number of object points " << max_obj_pts << "\n";
const int circle_sz = 7;
// draw image points that are inliers on two images
std::vector<int> labels;
std::vector<Vec4d> planes;
getPlanes (obj_pts_per_cam[best_cam_idx], labels, planes, 4, 0.002, 0.99, 10000);
const int num_found_planes = (int) planes.size();
RNG rng;
std::vector<Scalar> plane_colors (num_found_planes);
for (int pl = 0; pl < num_found_planes; pl++)
plane_colors[pl] = Scalar (rng.uniform(0,256), rng.uniform(0,256), rng.uniform(0,256));
for (int obj_pt = 0; obj_pt < max_obj_pts; obj_pt++) {
const int pt = img_idxs_per_cam[best_cam_idx][obj_pt];
if (labels[obj_pt] > 0) { // plot plane points
circle (image1, pts1[pt], circle_sz, plane_colors[labels[obj_pt]-1], -1);
circle (image2, pts2[pt], circle_sz, plane_colors[labels[obj_pt]-1], -1);
} else { // plot inliers
circle (image1, pts1[pt], circle_sz, Scalar(0,0,0), -1);
circle (image2, pts2[pt], circle_sz, Scalar(0,0,0), -1);
}
}
// concatenate two images
hconcat(image1, image2, image1);
const int new_img_size = 1200 * 800; // for example
// resize with the same aspect ratio
resize(image1, image1, Size((int)sqrt ((double) image1.cols * new_img_size / image1.rows),
(int)sqrt ((double) image1.rows * new_img_size / image1.cols)));
imshow("image 1-2", image1);
imwrite("planes.png", image1);
waitKey(0);
}

5
samples/data/essential_mat_data.txt
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leuvenA.jpg
leuvenB.jpg
651.4462353114224 0 376.27522319223914
0 653.7348054191838 280.1106539526218
0 0 1

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137
samples/python/essential_mat_reconstr.py
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import numpy as np, cv2 as cv, matplotlib.pyplot as plt, time, sys, os
from mpl_toolkits.mplot3d import axes3d, Axes3D
def getEpipolarError(F, pts1_, pts2_, inliers):
pts1 = np.concatenate((pts1_.T, np.ones((1, pts1_.shape[0]))))[:,inliers]
pts2 = np.concatenate((pts2_.T, np.ones((1, pts2_.shape[0]))))[:,inliers]
lines2 = np.dot(F , pts1)
lines1 = np.dot(F.T, pts2)
return np.median((np.abs(np.sum(pts1 * lines1, axis=0)) / np.sqrt(lines1[0,:]**2 + lines1[1,:]**2) +
np.abs(np.sum(pts2 * lines2, axis=0)) / np.sqrt(lines2[0,:]**2 + lines2[1,:]**2))/2)
if __name__ == '__main__':
if len(sys.argv) < 3:
print("Path to data file and directory to image files are missing!\nData file must have"
" format:\n--------------\n image_name_1\nimage_name_2\nk11 k12 k13\n0 k22 k23\n"
"0 0 1\n--------------\nIf image_name_{1,2} are not in the same directory as "
"the data file then add argument with directory to image files.\nFor example: "
"python essential_mat_reconstr.py essential_mat_data.txt ./")
exit(1)
else:
data_file = sys.argv[1]
image_dir = sys.argv[2]
if not os.path.isfile(data_file):
print('Incorrect path to data file!')
exit(1)
with open(data_file, 'r') as f:
image1 = cv.imread(image_dir+f.readline()[:-1]) # remove '\n'
image2 = cv.imread(image_dir+f.readline()[:-1])
K = np.array([[float(x) for x in f.readline().split(' ')],
[float(x) for x in f.readline().split(' ')],
[float(x) for x in f.readline().split(' ')]])
if image1 is None or image2 is None:
print('Incorrect directory to images!')
exit(1)
if K.shape != (3,3):
print('Intrinsic matrix has incorrect format!')
exit(1)
print('find keypoints and compute descriptors')
detector = cv.SIFT_create(nfeatures=20000)
keypoints1, descriptors1 = detector.detectAndCompute(cv.cvtColor(image1, cv.COLOR_BGR2GRAY), None)
keypoints2, descriptors2 = detector.detectAndCompute(cv.cvtColor(image2, cv.COLOR_BGR2GRAY), None)
matcher = cv.FlannBasedMatcher(dict(algorithm=0, trees=5), dict(checks=32))
print('match with FLANN, size of descriptors', descriptors1.shape, descriptors2.shape)
matches_vector = matcher.knnMatch(descriptors1, descriptors2, k=2)
print('find good keypoints')
pts1 = []; pts2 = []
for m in matches_vector:
# compare best and second match using Lowe ratio test
if m[0].distance / m[1].distance < 0.75:
pts1.append(keypoints1[m[0].queryIdx].pt)
pts2.append(keypoints2[m[0].trainIdx].pt)
pts1 = np.array(pts1); pts2 = np.array(pts2)
print('points size', pts1.shape[0])
print('Essential matrix RANSAC')
start = time.time()
E, inliers = cv.findEssentialMat(pts1, pts2, K, cv.RANSAC, 0.999, 1.0)
print('RANSAC time', time.time() - start, 'seconds')
print('Median error to epipolar lines', getEpipolarError
(np.dot(np.linalg.inv(K).T, np.dot(E, np.linalg.inv(K))), pts1, pts2, inliers.squeeze()),
'number of inliers', inliers.sum())
print('Decompose essential matrix')
R1, R2, t = cv.decomposeEssentialMat(E)
# Assume relative pose. Fix the first camera
P1 = np.concatenate((K, np.zeros((3,1))), axis=1) # K [I | 0]
P2s = [np.dot(K, np.concatenate((R1, t), axis=1)), # K[R1 | t]
np.dot(K, np.concatenate((R1, -t), axis=1)), # K[R1 | -t]
np.dot(K, np.concatenate((R2, t), axis=1)), # K[R2 | t]
np.dot(K, np.concatenate((R2, -t), axis=1))] # K[R2 | -t]
obj_pts_per_cam = []
# enumerate over all P2 projection matrices
for cam_idx, P2 in enumerate(P2s):
obj_pts = []
for i, (pt1, pt2) in enumerate(zip(pts1, pts2)):
if not inliers[i]:
continue
# find object point by triangulation of image points by projection matrices
obj_pt = cv.triangulatePoints(P1, P2, pt1, pt2)
obj_pt /= obj_pt[3]
# check if reprojected point has positive depth
if obj_pt[2] > 0:
obj_pts.append([obj_pt[0], obj_pt[1], obj_pt[2]])
obj_pts_per_cam.append(obj_pts)
best_cam_idx = np.array([len(obj_pts_per_cam[0]),len(obj_pts_per_cam[1]),
len(obj_pts_per_cam[2]),len(obj_pts_per_cam[3])]).argmax()
max_pts = len(obj_pts_per_cam[best_cam_idx])
print('Number of object points', max_pts)
# filter object points to have reasonable depth
MAX_DEPTH = 6.
obj_pts = []
for pt in obj_pts_per_cam[best_cam_idx]:
if pt[2] < MAX_DEPTH:
obj_pts.append(pt)
obj_pts = np.array(obj_pts).reshape(len(obj_pts), 3)
# visualize image points
for i, (pt1, pt2) in enumerate(zip(pts1, pts2)):
if inliers[i]:
cv.circle(image1, (int(pt1[0]), int(pt1[1])), 7, (255,0,0), -1)
cv.circle(image2, (int(pt2[0]), int(pt2[1])), 7, (255,0,0), -1)
# concatenate two images
image1 = np.concatenate((image1, image2), axis=1)
# resize concatenated image
new_img_size = 1200. * 800.
image1 = cv.resize(image1, (int(np.sqrt(image1.shape[1] * new_img_size / image1.shape[0])),
int(np.sqrt (image1.shape[0] * new_img_size / image1.shape[1]))))
# plot object points
fig = plt.figure(figsize=(13.0, 11.0))
ax = fig.add_subplot(111, projection='3d')
ax.set_aspect('equal')
ax.scatter(obj_pts[:,0], obj_pts[:,1], obj_pts[:,2], c='r', marker='o', s=3)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('depth')
ax.view_init(azim=-80, elev=110)
# save figures
cv.imshow("matches", image1)
cv.imwrite('matches_E.png', image1)
plt.savefig('reconstruction_3D.png')
cv.waitKey(0)
plt.show()
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