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opencv/modules/calib3d/src/triangulate.cpp

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/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// Intel License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2009, Intel Corporation and others, all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's 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.
//
// * The name of Intel Corporation may not 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 Intel Corporation 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.
//
//M*/
#include "precomp.hpp"
#include "opencv2/core/core_c.h"
// cvCorrectMatches function is Copyright (C) 2009, Jostein Austvik Jacobsen.
// cvTriangulatePoints function is derived from icvReconstructPointsFor3View, originally by Valery Mosyagin.
// HZ, R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge Univ. Press, 2003.
// This method is the same as icvReconstructPointsFor3View, with only a few numbers adjusted for two-view geometry
static void
icvTriangulatePoints(CvMat* projMatr1, CvMat* projMatr2, CvMat* projPoints1, CvMat* projPoints2, CvMat* points4D)
{
if( projMatr1 == 0 || projMatr2 == 0 ||
projPoints1 == 0 || projPoints2 == 0 ||
points4D == 0)
CV_Error( CV_StsNullPtr, "Some of parameters is a NULL pointer" );
if( !CV_IS_MAT(projMatr1) || !CV_IS_MAT(projMatr2) ||
!CV_IS_MAT(projPoints1) || !CV_IS_MAT(projPoints2) ||
!CV_IS_MAT(points4D) )
CV_Error( CV_StsUnsupportedFormat, "Input parameters must be matrices" );
int numPoints = projPoints1->cols;
if( numPoints < 1 )
CV_Error( CV_StsOutOfRange, "Number of points must be more than zero" );
if( projPoints2->cols != numPoints || points4D->cols != numPoints )
CV_Error( CV_StsUnmatchedSizes, "Number of points must be the same" );
if( projPoints1->rows != 2 || projPoints2->rows != 2)
CV_Error( CV_StsUnmatchedSizes, "Number of proj points coordinates must be == 2" );
if( points4D->rows != 4 )
CV_Error( CV_StsUnmatchedSizes, "Number of world points coordinates must be == 4" );
if( projMatr1->cols != 4 || projMatr1->rows != 3 ||
projMatr2->cols != 4 || projMatr2->rows != 3)
CV_Error( CV_StsUnmatchedSizes, "Size of projection matrices must be 3x4" );
// preallocate SVD matrices on stack
cv::Matx<double, 4, 4> matrA;
cv::Matx<double, 4, 4> matrU;
cv::Matx<double, 4, 1> matrW;
cv::Matx<double, 4, 4> matrV;
CvMat* projPoints[2] = {projPoints1, projPoints2};
CvMat* projMatrs[2] = {projMatr1, projMatr2};
/* Solve system for each point */
for( int i = 0; i < numPoints; i++ )/* For each point */
{
/* Fill matrix for current point */
for( int j = 0; j < 2; j++ )/* For each view */
{
double x,y;
x = cvmGet(projPoints[j],0,i);
y = cvmGet(projPoints[j],1,i);
for( int k = 0; k < 4; k++ )
{
matrA(j*2+0, k) = x * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],0,k);
matrA(j*2+1, k) = y * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],1,k);
}
}
/* Solve system for current point */
cv::SVD::compute(matrA, matrW, matrU, matrV);
/* Copy computed point */
cvmSet(points4D,0,i,matrV(3,0));/* X */
cvmSet(points4D,1,i,matrV(3,1));/* Y */
cvmSet(points4D,2,i,matrV(3,2));/* Z */
cvmSet(points4D,3,i,matrV(3,3));/* W */
}
}
/*
* The Optimal Triangulation Method (see HZ for details)
* For each given point correspondence points1[i] <-> points2[i], and a fundamental matrix F,
* computes the corrected correspondences new_points1[i] <-> new_points2[i] that minimize the
* geometric error d(points1[i],new_points1[i])^2 + d(points2[i],new_points2[i])^2 (where d(a,b)
* is the geometric distance between points a and b) subject to the epipolar constraint
* new_points2' * F * new_points1 = 0.
*
* F_ : 3x3 fundamental matrix
* points1_ : 1xN matrix containing the first set of points
* points2_ : 1xN matrix containing the second set of points
* new_points1 : the optimized points1_. if this is NULL, the corrected points are placed back in points1_
* new_points2 : the optimized points2_. if this is NULL, the corrected points are placed back in points2_
*/
static void
icvCorrectMatches(CvMat *F_, CvMat *points1_, CvMat *points2_, CvMat *new_points1, CvMat *new_points2)
{
cv::Ptr<CvMat> tmp33;
cv::Ptr<CvMat> tmp31, tmp31_2;
cv::Ptr<CvMat> T1i, T2i;
cv::Ptr<CvMat> R1, R2;
cv::Ptr<CvMat> TFT, TFTt, RTFTR;
cv::Ptr<CvMat> U, S, V;
cv::Ptr<CvMat> e1, e2;
cv::Ptr<CvMat> polynomial;
cv::Ptr<CvMat> result;
cv::Ptr<CvMat> points1, points2;
cv::Ptr<CvMat> F;
if (!CV_IS_MAT(F_) || !CV_IS_MAT(points1_) || !CV_IS_MAT(points2_) )
CV_Error( CV_StsUnsupportedFormat, "Input parameters must be matrices" );
if (!( F_->cols == 3 && F_->rows == 3))
CV_Error( CV_StsUnmatchedSizes, "The fundamental matrix must be a 3x3 matrix");
if (!(((F_->type & CV_MAT_TYPE_MASK) >> 3) == 0 ))
CV_Error( CV_StsUnsupportedFormat, "The fundamental matrix must be a single-channel matrix" );
if (!(points1_->rows == 1 && points2_->rows == 1 && points1_->cols == points2_->cols))
CV_Error( CV_StsUnmatchedSizes, "The point-matrices must have one row, and an equal number of columns" );
if (((points1_->type & CV_MAT_TYPE_MASK) >> 3) != 1 )
CV_Error( CV_StsUnmatchedSizes, "The first set of points must contain two channels; one for x and one for y" );
if (((points2_->type & CV_MAT_TYPE_MASK) >> 3) != 1 )
CV_Error( CV_StsUnmatchedSizes, "The second set of points must contain two channels; one for x and one for y" );
if (new_points1 != NULL) {
CV_Assert(CV_IS_MAT(new_points1));
if (new_points1->cols != points1_->cols || new_points1->rows != 1)
CV_Error( CV_StsUnmatchedSizes, "The first output matrix must have the same dimensions as the input matrices" );
if (CV_MAT_CN(new_points1->type) != 2)
CV_Error( CV_StsUnsupportedFormat, "The first output matrix must have two channels; one for x and one for y" );
}
if (new_points2 != NULL) {
CV_Assert(CV_IS_MAT(new_points2));
if (new_points2->cols != points2_->cols || new_points2->rows != 1)
CV_Error( CV_StsUnmatchedSizes, "The second output matrix must have the same dimensions as the input matrices" );
if (CV_MAT_CN(new_points2->type) != 2)
CV_Error( CV_StsUnsupportedFormat, "The second output matrix must have two channels; one for x and one for y" );
}
// Make sure F uses double precision
F.reset(cvCreateMat(3,3,CV_64FC1));
cvConvert(F_, F);
// Make sure points1 uses double precision
points1.reset(cvCreateMat(points1_->rows,points1_->cols,CV_64FC2));
cvConvert(points1_, points1);
// Make sure points2 uses double precision
points2.reset(cvCreateMat(points2_->rows,points2_->cols,CV_64FC2));
cvConvert(points2_, points2);
tmp33.reset(cvCreateMat(3,3,CV_64FC1));
tmp31.reset(cvCreateMat(3,1,CV_64FC1)), tmp31_2.reset(cvCreateMat(3,1,CV_64FC1));
T1i.reset(cvCreateMat(3,3,CV_64FC1)), T2i.reset(cvCreateMat(3,3,CV_64FC1));
R1.reset(cvCreateMat(3,3,CV_64FC1)), R2.reset(cvCreateMat(3,3,CV_64FC1));
TFT.reset(cvCreateMat(3,3,CV_64FC1)), TFTt.reset(cvCreateMat(3,3,CV_64FC1)), RTFTR.reset(cvCreateMat(3,3,CV_64FC1));
U.reset(cvCreateMat(3,3,CV_64FC1));
S.reset(cvCreateMat(3,3,CV_64FC1));
V.reset(cvCreateMat(3,3,CV_64FC1));
e1.reset(cvCreateMat(3,1,CV_64FC1)), e2.reset(cvCreateMat(3,1,CV_64FC1));
double x1, y1, x2, y2;
double scale;
double f1, f2, a, b, c, d;
polynomial.reset(cvCreateMat(1,7,CV_64FC1));
result.reset(cvCreateMat(1,6,CV_64FC2));
double t_min, s_val, t, s;
for (int p = 0; p < points1->cols; ++p) {
// Replace F by T2-t * F * T1-t
x1 = points1->data.db[p*2];
y1 = points1->data.db[p*2+1];
x2 = points2->data.db[p*2];
y2 = points2->data.db[p*2+1];
cvSetZero(T1i);
cvSetReal2D(T1i,0,0,1);
cvSetReal2D(T1i,1,1,1);
cvSetReal2D(T1i,2,2,1);
cvSetReal2D(T1i,0,2,x1);
cvSetReal2D(T1i,1,2,y1);
cvSetZero(T2i);
cvSetReal2D(T2i,0,0,1);
cvSetReal2D(T2i,1,1,1);
cvSetReal2D(T2i,2,2,1);
cvSetReal2D(T2i,0,2,x2);
cvSetReal2D(T2i,1,2,y2);
cvGEMM(T2i,F,1,0,0,tmp33,CV_GEMM_A_T);
cvSetZero(TFT);
cvGEMM(tmp33,T1i,1,0,0,TFT);
// Compute the right epipole e1 from F * e1 = 0
cvSetZero(U);
cvSetZero(S);
cvSetZero(V);
cvSVD(TFT,S,U,V);
scale = sqrt(cvGetReal2D(V,0,2)*cvGetReal2D(V,0,2) + cvGetReal2D(V,1,2)*cvGetReal2D(V,1,2));
cvSetReal2D(e1,0,0,cvGetReal2D(V,0,2)/scale);
cvSetReal2D(e1,1,0,cvGetReal2D(V,1,2)/scale);
cvSetReal2D(e1,2,0,cvGetReal2D(V,2,2)/scale);
if (cvGetReal2D(e1,2,0) < 0) {
cvSetReal2D(e1,0,0,-cvGetReal2D(e1,0,0));
cvSetReal2D(e1,1,0,-cvGetReal2D(e1,1,0));
cvSetReal2D(e1,2,0,-cvGetReal2D(e1,2,0));
}
// Compute the left epipole e2 from e2' * F = 0 => F' * e2 = 0
cvSetZero(TFTt);
cvTranspose(TFT, TFTt);
cvSetZero(U);
cvSetZero(S);
cvSetZero(V);
cvSVD(TFTt,S,U,V);
cvSetZero(e2);
scale = sqrt(cvGetReal2D(V,0,2)*cvGetReal2D(V,0,2) + cvGetReal2D(V,1,2)*cvGetReal2D(V,1,2));
cvSetReal2D(e2,0,0,cvGetReal2D(V,0,2)/scale);
cvSetReal2D(e2,1,0,cvGetReal2D(V,1,2)/scale);
cvSetReal2D(e2,2,0,cvGetReal2D(V,2,2)/scale);
if (cvGetReal2D(e2,2,0) < 0) {
cvSetReal2D(e2,0,0,-cvGetReal2D(e2,0,0));
cvSetReal2D(e2,1,0,-cvGetReal2D(e2,1,0));
cvSetReal2D(e2,2,0,-cvGetReal2D(e2,2,0));
}
// Replace F by R2 * F * R1'
cvSetZero(R1);
cvSetReal2D(R1,0,0,cvGetReal2D(e1,0,0));
cvSetReal2D(R1,0,1,cvGetReal2D(e1,1,0));
cvSetReal2D(R1,1,0,-cvGetReal2D(e1,1,0));
cvSetReal2D(R1,1,1,cvGetReal2D(e1,0,0));
cvSetReal2D(R1,2,2,1);
cvSetZero(R2);
cvSetReal2D(R2,0,0,cvGetReal2D(e2,0,0));
cvSetReal2D(R2,0,1,cvGetReal2D(e2,1,0));
cvSetReal2D(R2,1,0,-cvGetReal2D(e2,1,0));
cvSetReal2D(R2,1,1,cvGetReal2D(e2,0,0));
cvSetReal2D(R2,2,2,1);
cvGEMM(R2,TFT,1,0,0,tmp33);
cvGEMM(tmp33,R1,1,0,0,RTFTR,CV_GEMM_B_T);
// Set f1 = e1(3), f2 = e2(3), a = F22, b = F23, c = F32, d = F33
f1 = cvGetReal2D(e1,2,0);
f2 = cvGetReal2D(e2,2,0);
a = cvGetReal2D(RTFTR,1,1);
b = cvGetReal2D(RTFTR,1,2);
c = cvGetReal2D(RTFTR,2,1);
d = cvGetReal2D(RTFTR,2,2);
// Form the polynomial g(t) = k6*t^6 + k5*t^5 + k4*t^4 + k3*t^3 + k2*t^2 + k1*t + k0
// from f1, f2, a, b, c and d
cvSetReal2D(polynomial,0,6,( +b*c*c*f1*f1*f1*f1*a-a*a*d*f1*f1*f1*f1*c ));
cvSetReal2D(polynomial,0,5,( +f2*f2*f2*f2*c*c*c*c+2*a*a*f2*f2*c*c-a*a*d*d*f1*f1*f1*f1+b*b*c*c*f1*f1*f1*f1+a*a*a*a ));
cvSetReal2D(polynomial,0,4,( +4*a*a*a*b+2*b*c*c*f1*f1*a+4*f2*f2*f2*f2*c*c*c*d+4*a*b*f2*f2*c*c+4*a*a*f2*f2*c*d-2*a*a*d*f1*f1*c-a*d*d*f1*f1*f1*f1*b+b*b*c*f1*f1*f1*f1*d ));
cvSetReal2D(polynomial,0,3,( +6*a*a*b*b+6*f2*f2*f2*f2*c*c*d*d+2*b*b*f2*f2*c*c+2*a*a*f2*f2*d*d-2*a*a*d*d*f1*f1+2*b*b*c*c*f1*f1+8*a*b*f2*f2*c*d ));
cvSetReal2D(polynomial,0,2,( +4*a*b*b*b+4*b*b*f2*f2*c*d+4*f2*f2*f2*f2*c*d*d*d-a*a*d*c+b*c*c*a+4*a*b*f2*f2*d*d-2*a*d*d*f1*f1*b+2*b*b*c*f1*f1*d ));
cvSetReal2D(polynomial,0,1,( +f2*f2*f2*f2*d*d*d*d+b*b*b*b+2*b*b*f2*f2*d*d-a*a*d*d+b*b*c*c ));
cvSetReal2D(polynomial,0,0,( -a*d*d*b+b*b*c*d ));
// Solve g(t) for t to get 6 roots
cvSetZero(result);
cvSolvePoly(polynomial, result, 100, 20);
// Evaluate the cost function s(t) at the real part of the 6 roots
t_min = DBL_MAX;
s_val = 1./(f1*f1) + (c*c)/(a*a+f2*f2*c*c);
for (int ti = 0; ti < 6; ++ti) {
t = result->data.db[2*ti];
s = (t*t)/(1 + f1*f1*t*t) + ((c*t + d)*(c*t + d))/((a*t + b)*(a*t + b) + f2*f2*(c*t + d)*(c*t + d));
if (s < s_val) {
s_val = s;
t_min = t;
}
}
// find the optimal x1 and y1 as the points on l1 and l2 closest to the origin
tmp31->data.db[0] = t_min*t_min*f1;
tmp31->data.db[1] = t_min;
tmp31->data.db[2] = t_min*t_min*f1*f1+1;
tmp31->data.db[0] /= tmp31->data.db[2];
tmp31->data.db[1] /= tmp31->data.db[2];
tmp31->data.db[2] /= tmp31->data.db[2];
cvGEMM(T1i,R1,1,0,0,tmp33,CV_GEMM_B_T);
cvGEMM(tmp33,tmp31,1,0,0,tmp31_2);
x1 = tmp31_2->data.db[0];
y1 = tmp31_2->data.db[1];
tmp31->data.db[0] = f2*pow(c*t_min+d,2);
tmp31->data.db[1] = -(a*t_min+b)*(c*t_min+d);
tmp31->data.db[2] = f2*f2*pow(c*t_min+d,2) + pow(a*t_min+b,2);
tmp31->data.db[0] /= tmp31->data.db[2];
tmp31->data.db[1] /= tmp31->data.db[2];
tmp31->data.db[2] /= tmp31->data.db[2];
cvGEMM(T2i,R2,1,0,0,tmp33,CV_GEMM_B_T);
cvGEMM(tmp33,tmp31,1,0,0,tmp31_2);
x2 = tmp31_2->data.db[0];
y2 = tmp31_2->data.db[1];
// Return the points in the matrix format that the user wants
points1->data.db[p*2] = x1;
points1->data.db[p*2+1] = y1;
points2->data.db[p*2] = x2;
points2->data.db[p*2+1] = y2;
}
if( new_points1 )
cvConvert( points1, new_points1 );
if( new_points2 )
cvConvert( points2, new_points2 );
}
void cv::triangulatePoints( InputArray _projMatr1, InputArray _projMatr2,
InputArray _projPoints1, InputArray _projPoints2,
OutputArray _points4D )
{
CV_INSTRUMENT_REGION();
Mat matr1 = _projMatr1.getMat(), matr2 = _projMatr2.getMat();
Mat points1 = _projPoints1.getMat(), points2 = _projPoints2.getMat();
if((points1.rows == 1 || points1.cols == 1) && points1.channels() == 2)
points1 = points1.reshape(1, static_cast<int>(points1.total())).t();
if((points2.rows == 1 || points2.cols == 1) && points2.channels() == 2)
points2 = points2.reshape(1, static_cast<int>(points2.total())).t();
CvMat cvMatr1 = cvMat(matr1), cvMatr2 = cvMat(matr2);
CvMat cvPoints1 = cvMat(points1), cvPoints2 = cvMat(points2);
_points4D.create(4, points1.cols, points1.type());
Mat cvPoints4D_ = _points4D.getMat();
CvMat cvPoints4D = cvMat(cvPoints4D_);
icvTriangulatePoints(&cvMatr1, &cvMatr2, &cvPoints1, &cvPoints2, &cvPoints4D);
}
void cv::correctMatches( InputArray _F, InputArray _points1, InputArray _points2,
OutputArray _newPoints1, OutputArray _newPoints2 )
{
CV_INSTRUMENT_REGION();
Mat F = _F.getMat();
Mat points1 = _points1.getMat(), points2 = _points2.getMat();
CvMat cvPoints1 = cvMat(points1), cvPoints2 = cvMat(points2);
CvMat cvF = cvMat(F);
_newPoints1.create(points1.size(), points1.type());
_newPoints2.create(points2.size(), points2.type());
Mat cvNewPoints1_ = _newPoints1.getMat(), cvNewPoints2_ = _newPoints2.getMat();
CvMat cvNewPoints1 = cvMat(cvNewPoints1_), cvNewPoints2 = cvMat(cvNewPoints2_);
icvCorrectMatches(&cvF, &cvPoints1, &cvPoints2, &cvNewPoints1, &cvNewPoints2);
}