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/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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//
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// Intel License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2009, Intel Corporation and others, all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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#include "precomp.hpp"
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// cvCorrectMatches function is Copyright (C) 2009, Jostein Austvik Jacobsen.
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// cvTriangulatePoints function is derived from icvReconstructPointsFor3View, originally by Valery Mosyagin.
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// HZ, R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge Univ. Press, 2003.
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// This method is the same as icvReconstructPointsFor3View, with only a few numbers adjusted for two-view geometry
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CV_IMPL void
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cvTriangulatePoints(CvMat* projMatr1, CvMat* projMatr2, CvMat* projPoints1, CvMat* projPoints2, CvMat* points4D)
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{
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if( projMatr1 == 0 || projMatr2 == 0 ||
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projPoints1 == 0 || projPoints2 == 0 ||
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points4D == 0)
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CV_Error( CV_StsNullPtr, "Some of parameters is a NULL pointer" );
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if( !CV_IS_MAT(projMatr1) || !CV_IS_MAT(projMatr2) ||
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!CV_IS_MAT(projPoints1) || !CV_IS_MAT(projPoints2) ||
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!CV_IS_MAT(points4D) )
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CV_Error( CV_StsUnsupportedFormat, "Input parameters must be matrices" );
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int numPoints;
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numPoints = projPoints1->cols;
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if( numPoints < 1 )
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CV_Error( CV_StsOutOfRange, "Number of points must be more than zero" );
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if( projPoints2->cols != numPoints || points4D->cols != numPoints )
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CV_Error( CV_StsUnmatchedSizes, "Number of points must be the same" );
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if( projPoints1->rows != 2 || projPoints2->rows != 2)
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CV_Error( CV_StsUnmatchedSizes, "Number of proj points coordinates must be == 2" );
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if( points4D->rows != 4 )
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CV_Error( CV_StsUnmatchedSizes, "Number of world points coordinates must be == 4" );
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if( projMatr1->cols != 4 || projMatr1->rows != 3 ||
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projMatr2->cols != 4 || projMatr2->rows != 3)
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CV_Error( CV_StsUnmatchedSizes, "Size of projection matrices must be 3x4" );
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CvMat matrA;
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double matrA_dat[24];
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matrA = cvMat(6,4,CV_64F,matrA_dat);
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//CvMat matrU;
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CvMat matrW;
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CvMat matrV;
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//double matrU_dat[9*9];
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double matrW_dat[6*4];
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double matrV_dat[4*4];
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//matrU = cvMat(6,6,CV_64F,matrU_dat);
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matrW = cvMat(6,4,CV_64F,matrW_dat);
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matrV = cvMat(4,4,CV_64F,matrV_dat);
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CvMat* projPoints[2];
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CvMat* projMatrs[2];
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projPoints[0] = projPoints1;
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projPoints[1] = projPoints2;
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projMatrs[0] = projMatr1;
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projMatrs[1] = projMatr2;
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/* Solve system for each point */
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int i,j;
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for( i = 0; i < numPoints; i++ )/* For each point */
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{
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/* Fill matrix for current point */
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for( j = 0; j < 2; j++ )/* For each view */
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{
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double x,y;
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x = cvmGet(projPoints[j],0,i);
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y = cvmGet(projPoints[j],1,i);
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for( int k = 0; k < 4; k++ )
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{
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cvmSet(&matrA, j*3+0, k, x * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],0,k) );
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cvmSet(&matrA, j*3+1, k, y * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],1,k) );
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cvmSet(&matrA, j*3+2, k, x * cvmGet(projMatrs[j],1,k) - y * cvmGet(projMatrs[j],0,k) );
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}
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}
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/* Solve system for current point */
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{
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cvSVD(&matrA,&matrW,0,&matrV,CV_SVD_V_T);
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/* Copy computed point */
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cvmSet(points4D,0,i,cvmGet(&matrV,3,0));/* X */
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cvmSet(points4D,1,i,cvmGet(&matrV,3,1));/* Y */
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cvmSet(points4D,2,i,cvmGet(&matrV,3,2));/* Z */
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cvmSet(points4D,3,i,cvmGet(&matrV,3,3));/* W */
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}
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}
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#if 0
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double err = 0;
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/* Points was reconstructed. Try to reproject points */
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/* We can compute reprojection error if need */
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{
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int i;
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CvMat point3D;
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double point3D_dat[4];
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point3D = cvMat(4,1,CV_64F,point3D_dat);
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CvMat point2D;
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double point2D_dat[3];
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point2D = cvMat(3,1,CV_64F,point2D_dat);
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for( i = 0; i < numPoints; i++ )
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{
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double W = cvmGet(points4D,3,i);
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point3D_dat[0] = cvmGet(points4D,0,i)/W;
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point3D_dat[1] = cvmGet(points4D,1,i)/W;
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point3D_dat[2] = cvmGet(points4D,2,i)/W;
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point3D_dat[3] = 1;
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/* !!! Project this point for each camera */
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for( int currCamera = 0; currCamera < 2; currCamera++ )
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{
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cvMatMul(projMatrs[currCamera], &point3D, &point2D);
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float x,y;
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float xr,yr,wr;
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x = (float)cvmGet(projPoints[currCamera],0,i);
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y = (float)cvmGet(projPoints[currCamera],1,i);
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wr = (float)point2D_dat[2];
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xr = (float)(point2D_dat[0]/wr);
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yr = (float)(point2D_dat[1]/wr);
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float deltaX,deltaY;
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deltaX = (float)fabs(x-xr);
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deltaY = (float)fabs(y-yr);
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err += deltaX*deltaX + deltaY*deltaY;
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}
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}
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}
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#endif
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}
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/*
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* The Optimal Triangulation Method (see HZ for details)
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* For each given point correspondence points1[i] <-> points2[i], and a fundamental matrix F,
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* computes the corrected correspondences new_points1[i] <-> new_points2[i] that minimize the
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* geometric error d(points1[i],new_points1[i])^2 + d(points2[i],new_points2[i])^2 (where d(a,b)
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* is the geometric distance between points a and b) subject to the epipolar constraint
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* new_points2' * F * new_points1 = 0.
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*
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* F_ : 3x3 fundamental matrix
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* points1_ : 1xN matrix containing the first set of points
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* points2_ : 1xN matrix containing the second set of points
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* new_points1 : the optimized points1_. if this is NULL, the corrected points are placed back in points1_
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* new_points2 : the optimized points2_. if this is NULL, the corrected points are placed back in points2_
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*/
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CV_IMPL void
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cvCorrectMatches(CvMat *F_, CvMat *points1_, CvMat *points2_, CvMat *new_points1, CvMat *new_points2)
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{
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cv::Ptr<CvMat> tmp33;
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cv::Ptr<CvMat> tmp31, tmp31_2;
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cv::Ptr<CvMat> T1i, T2i;
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cv::Ptr<CvMat> R1, R2;
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cv::Ptr<CvMat> TFT, TFTt, RTFTR;
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cv::Ptr<CvMat> U, S, V;
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cv::Ptr<CvMat> e1, e2;
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cv::Ptr<CvMat> polynomial;
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cv::Ptr<CvMat> result;
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cv::Ptr<CvMat> points1, points2;
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cv::Ptr<CvMat> F;
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if (!CV_IS_MAT(F_) || !CV_IS_MAT(points1_) || !CV_IS_MAT(points2_) )
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CV_Error( CV_StsUnsupportedFormat, "Input parameters must be matrices" );
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if (!( F_->cols == 3 && F_->rows == 3))
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CV_Error( CV_StsUnmatchedSizes, "The fundamental matrix must be a 3x3 matrix");
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if (!(((F_->type & CV_MAT_TYPE_MASK) >> 3) == 0 ))
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CV_Error( CV_StsUnsupportedFormat, "The fundamental matrix must be a single-channel matrix" );
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if (!(points1_->rows == 1 && points2_->rows == 1 && points1_->cols == points2_->cols))
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CV_Error( CV_StsUnmatchedSizes, "The point-matrices must have one row, and an equal number of columns" );
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if (((points1_->type & CV_MAT_TYPE_MASK) >> 3) != 1 )
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CV_Error( CV_StsUnmatchedSizes, "The first set of points must contain two channels; one for x and one for y" );
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if (((points2_->type & CV_MAT_TYPE_MASK) >> 3) != 1 )
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CV_Error( CV_StsUnmatchedSizes, "The second set of points must contain two channels; one for x and one for y" );
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if (new_points1 != NULL) {
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CV_Assert(CV_IS_MAT(new_points1));
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if (new_points1->cols != points1_->cols || new_points1->rows != 1)
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CV_Error( CV_StsUnmatchedSizes, "The first output matrix must have the same dimensions as the input matrices" );
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if (CV_MAT_CN(new_points1->type) != 2)
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CV_Error( CV_StsUnsupportedFormat, "The first output matrix must have two channels; one for x and one for y" );
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}
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if (new_points2 != NULL) {
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CV_Assert(CV_IS_MAT(new_points2));
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if (new_points2->cols != points2_->cols || new_points2->rows != 1)
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CV_Error( CV_StsUnmatchedSizes, "The second output matrix must have the same dimensions as the input matrices" );
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if (CV_MAT_CN(new_points2->type) != 2)
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CV_Error( CV_StsUnsupportedFormat, "The second output matrix must have two channels; one for x and one for y" );
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}
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// Make sure F uses double precision
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F = cvCreateMat(3,3,CV_64FC1);
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cvConvert(F_, F);
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// Make sure points1 uses double precision
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points1 = cvCreateMat(points1_->rows,points1_->cols,CV_64FC2);
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cvConvert(points1_, points1);
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// Make sure points2 uses double precision
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points2 = cvCreateMat(points2_->rows,points2_->cols,CV_64FC2);
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cvConvert(points2_, points2);
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tmp33 = cvCreateMat(3,3,CV_64FC1);
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tmp31 = cvCreateMat(3,1,CV_64FC1), tmp31_2 = cvCreateMat(3,1,CV_64FC1);
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T1i = cvCreateMat(3,3,CV_64FC1), T2i = cvCreateMat(3,3,CV_64FC1);
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R1 = cvCreateMat(3,3,CV_64FC1), R2 = cvCreateMat(3,3,CV_64FC1);
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TFT = cvCreateMat(3,3,CV_64FC1), TFTt = cvCreateMat(3,3,CV_64FC1), RTFTR = cvCreateMat(3,3,CV_64FC1);
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U = cvCreateMat(3,3,CV_64FC1);
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S = cvCreateMat(3,3,CV_64FC1);
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V = cvCreateMat(3,3,CV_64FC1);
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e1 = cvCreateMat(3,1,CV_64FC1), e2 = cvCreateMat(3,1,CV_64FC1);
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double x1, y1, x2, y2;
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double scale;
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double f1, f2, a, b, c, d;
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polynomial = cvCreateMat(1,7,CV_64FC1);
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result = cvCreateMat(1,6,CV_64FC2);
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double t_min, s_val, t, s;
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for (int p = 0; p < points1->cols; ++p) {
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// Replace F by T2-t * F * T1-t
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x1 = points1->data.db[p*2];
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y1 = points1->data.db[p*2+1];
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x2 = points2->data.db[p*2];
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y2 = points2->data.db[p*2+1];
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cvSetZero(T1i);
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cvSetReal2D(T1i,0,0,1);
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cvSetReal2D(T1i,1,1,1);
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cvSetReal2D(T1i,2,2,1);
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cvSetReal2D(T1i,0,2,x1);
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cvSetReal2D(T1i,1,2,y1);
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cvSetZero(T2i);
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cvSetReal2D(T2i,0,0,1);
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cvSetReal2D(T2i,1,1,1);
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cvSetReal2D(T2i,2,2,1);
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cvSetReal2D(T2i,0,2,x2);
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cvSetReal2D(T2i,1,2,y2);
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cvGEMM(T2i,F,1,0,0,tmp33,CV_GEMM_A_T);
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cvSetZero(TFT);
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cvGEMM(tmp33,T1i,1,0,0,TFT);
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// Compute the right epipole e1 from F * e1 = 0
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cvSetZero(U);
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cvSetZero(S);
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cvSetZero(V);
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cvSVD(TFT,S,U,V);
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scale = sqrt(cvGetReal2D(V,0,2)*cvGetReal2D(V,0,2) + cvGetReal2D(V,1,2)*cvGetReal2D(V,1,2));
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cvSetReal2D(e1,0,0,cvGetReal2D(V,0,2)/scale);
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cvSetReal2D(e1,1,0,cvGetReal2D(V,1,2)/scale);
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cvSetReal2D(e1,2,0,cvGetReal2D(V,2,2)/scale);
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if (cvGetReal2D(e1,2,0) < 0) {
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cvSetReal2D(e1,0,0,-cvGetReal2D(e1,0,0));
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cvSetReal2D(e1,1,0,-cvGetReal2D(e1,1,0));
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cvSetReal2D(e1,2,0,-cvGetReal2D(e1,2,0));
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}
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// Compute the left epipole e2 from e2' * F = 0 => F' * e2 = 0
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cvSetZero(TFTt);
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cvTranspose(TFT, TFTt);
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cvSetZero(U);
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cvSetZero(S);
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cvSetZero(V);
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cvSVD(TFTt,S,U,V);
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cvSetZero(e2);
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scale = sqrt(cvGetReal2D(V,0,2)*cvGetReal2D(V,0,2) + cvGetReal2D(V,1,2)*cvGetReal2D(V,1,2));
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cvSetReal2D(e2,0,0,cvGetReal2D(V,0,2)/scale);
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cvSetReal2D(e2,1,0,cvGetReal2D(V,1,2)/scale);
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cvSetReal2D(e2,2,0,cvGetReal2D(V,2,2)/scale);
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if (cvGetReal2D(e2,2,0) < 0) {
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cvSetReal2D(e2,0,0,-cvGetReal2D(e2,0,0));
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cvSetReal2D(e2,1,0,-cvGetReal2D(e2,1,0));
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cvSetReal2D(e2,2,0,-cvGetReal2D(e2,2,0));
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}
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// Replace F by R2 * F * R1'
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cvSetZero(R1);
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cvSetReal2D(R1,0,0,cvGetReal2D(e1,0,0));
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cvSetReal2D(R1,0,1,cvGetReal2D(e1,1,0));
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cvSetReal2D(R1,1,0,-cvGetReal2D(e1,1,0));
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cvSetReal2D(R1,1,1,cvGetReal2D(e1,0,0));
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cvSetReal2D(R1,2,2,1);
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cvSetZero(R2);
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cvSetReal2D(R2,0,0,cvGetReal2D(e2,0,0));
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cvSetReal2D(R2,0,1,cvGetReal2D(e2,1,0));
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cvSetReal2D(R2,1,0,-cvGetReal2D(e2,1,0));
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cvSetReal2D(R2,1,1,cvGetReal2D(e2,0,0));
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cvSetReal2D(R2,2,2,1);
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cvGEMM(R2,TFT,1,0,0,tmp33);
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cvGEMM(tmp33,R1,1,0,0,RTFTR,CV_GEMM_B_T);
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// Set f1 = e1(3), f2 = e2(3), a = F22, b = F23, c = F32, d = F33
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f1 = cvGetReal2D(e1,2,0);
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f2 = cvGetReal2D(e2,2,0);
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a = cvGetReal2D(RTFTR,1,1);
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b = cvGetReal2D(RTFTR,1,2);
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c = cvGetReal2D(RTFTR,2,1);
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d = cvGetReal2D(RTFTR,2,2);
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// Form the polynomial g(t) = k6*t⁶ + k5*t⁵ + k4*t⁴ + k3*t³ + k2*t² + k1*t + k0
|
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// from f1, f2, a, b, c and d
|
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cvSetReal2D(polynomial,0,6,( +b*c*c*f1*f1*f1*f1*a-a*a*d*f1*f1*f1*f1*c ));
|
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|
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 ));
|
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|
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 )
|
|
|
|
{
|
|
|
|
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, points1.total()).t();
|
|
|
|
|
|
|
|
if((points2.rows == 1 || points2.cols == 1) && points2.channels() == 2)
|
|
|
|
points2 = points2.reshape(1, points2.total()).t();
|
|
|
|
|
|
|
|
CvMat cvMatr1 = matr1, cvMatr2 = matr2;
|
|
|
|
CvMat cvPoints1 = points1, cvPoints2 = points2;
|
|
|
|
|
|
|
|
_points4D.create(4, points1.cols, points1.type());
|
|
|
|
CvMat cvPoints4D = _points4D.getMat();
|
|
|
|
|
|
|
|
cvTriangulatePoints(&cvMatr1, &cvMatr2, &cvPoints1, &cvPoints2, &cvPoints4D);
|
|
|
|
}
|
|
|
|
|
|
|
|
void cv::correctMatches( InputArray _F, InputArray _points1, InputArray _points2,
|
|
|
|
OutputArray _newPoints1, OutputArray _newPoints2 )
|
|
|
|
{
|
|
|
|
Mat F = _F.getMat();
|
|
|
|
Mat points1 = _points1.getMat(), points2 = _points2.getMat();
|
|
|
|
|
|
|
|
CvMat cvPoints1 = points1, cvPoints2 = points2;
|
|
|
|
CvMat cvF = F;
|
|
|
|
|
|
|
|
_newPoints1.create(points1.size(), points1.type());
|
|
|
|
_newPoints2.create(points2.size(), points2.type());
|
|
|
|
CvMat cvNewPoints1 = _newPoints1.getMat(), cvNewPoints2 = _newPoints2.getMat();
|
|
|
|
|
|
|
|
cvCorrectMatches(&cvF, &cvPoints1, &cvPoints2, &cvNewPoints1, &cvNewPoints2);
|
|
|
|
}
|