/*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" // 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 CV_IMPL void cvTriangulatePoints(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; 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" ); CvMat matrA; double matrA_dat[24]; matrA = cvMat(6,4,CV_64F,matrA_dat); //CvMat matrU; CvMat matrW; CvMat matrV; //double matrU_dat[9*9]; double matrW_dat[6*4]; double matrV_dat[4*4]; //matrU = cvMat(6,6,CV_64F,matrU_dat); matrW = cvMat(6,4,CV_64F,matrW_dat); matrV = cvMat(4,4,CV_64F,matrV_dat); CvMat* projPoints[2]; CvMat* projMatrs[2]; projPoints[0] = projPoints1; projPoints[1] = projPoints2; projMatrs[0] = projMatr1; projMatrs[1] = projMatr2; /* Solve system for each point */ int i,j; for( i = 0; i < numPoints; i++ )/* For each point */ { /* Fill matrix for current point */ for( 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++ ) { cvmSet(&matrA, j*3+0, k, x * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],0,k) ); cvmSet(&matrA, j*3+1, k, y * cvmGet(projMatrs[j],2,k) - cvmGet(projMatrs[j],1,k) ); cvmSet(&matrA, j*3+2, k, x * cvmGet(projMatrs[j],1,k) - y * cvmGet(projMatrs[j],0,k) ); } } /* Solve system for current point */ { cvSVD(&matrA,&matrW,0,&matrV,CV_SVD_V_T); /* Copy computed point */ cvmSet(points4D,0,i,cvmGet(&matrV,3,0));/* X */ cvmSet(points4D,1,i,cvmGet(&matrV,3,1));/* Y */ cvmSet(points4D,2,i,cvmGet(&matrV,3,2));/* Z */ cvmSet(points4D,3,i,cvmGet(&matrV,3,3));/* W */ } } #if 0 double err = 0; /* Points was reconstructed. Try to reproject points */ /* We can compute reprojection error if need */ { int i; CvMat point3D; double point3D_dat[4]; point3D = cvMat(4,1,CV_64F,point3D_dat); CvMat point2D; double point2D_dat[3]; point2D = cvMat(3,1,CV_64F,point2D_dat); for( i = 0; i < numPoints; i++ ) { double W = cvmGet(points4D,3,i); point3D_dat[0] = cvmGet(points4D,0,i)/W; point3D_dat[1] = cvmGet(points4D,1,i)/W; point3D_dat[2] = cvmGet(points4D,2,i)/W; point3D_dat[3] = 1; /* !!! Project this point for each camera */ for( int currCamera = 0; currCamera < 2; currCamera++ ) { cvMatMul(projMatrs[currCamera], &point3D, &point2D); float x,y; float xr,yr,wr; x = (float)cvmGet(projPoints[currCamera],0,i); y = (float)cvmGet(projPoints[currCamera],1,i); wr = (float)point2D_dat[2]; xr = (float)(point2D_dat[0]/wr); yr = (float)(point2D_dat[1]/wr); float deltaX,deltaY; deltaX = (float)fabs(x-xr); deltaY = (float)fabs(y-yr); err += deltaX*deltaX + deltaY*deltaY; } } } #endif } /* * 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_ : 2xN matrix containing the first set of points * points2_ : 2xN 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_ */ CV_IMPL void cvCorrectMatches(CvMat *F_, CvMat *points1_, CvMat *points2_, CvMat *new_points1, CvMat *new_points2) { cv::Ptr tmp33; cv::Ptr tmp31, tmp31_2; cv::Ptr T1i, T2i; cv::Ptr R1, R2; cv::Ptr TFT, TFTt, RTFTR; cv::Ptr U, S, V; cv::Ptr e1, e2; cv::Ptr polynomial; cv::Ptr result; cv::Ptr points1, points2; cv::Ptr 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 two rows, 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 = cvCreateMat(3,3,CV_64FC1); cvConvert(F_, F); // Make sure points1 uses double precision points1 = cvCreateMat(points1_->rows,points1_->cols,CV_64FC2); cvConvert(points1_, points1); // Make sure points2 uses double precision points2 = cvCreateMat(points2_->rows,points2_->cols,CV_64FC2); cvConvert(points2_, points2); tmp33 = cvCreateMat(3,3,CV_64FC1); tmp31 = cvCreateMat(3,1,CV_64FC1), tmp31_2 = cvCreateMat(3,1,CV_64FC1); T1i = cvCreateMat(3,3,CV_64FC1), T2i = cvCreateMat(3,3,CV_64FC1); R1 = cvCreateMat(3,3,CV_64FC1), R2 = cvCreateMat(3,3,CV_64FC1); TFT = cvCreateMat(3,3,CV_64FC1), TFTt = cvCreateMat(3,3,CV_64FC1), RTFTR = cvCreateMat(3,3,CV_64FC1); U = cvCreateMat(3,3,CV_64FC1); S = cvCreateMat(3,3,CV_64FC1); V = cvCreateMat(3,3,CV_64FC1); e1 = cvCreateMat(3,1,CV_64FC1), e2 = cvCreateMat(3,1,CV_64FC1); double x1, y1, x2, y2; double scale; double f1, f2, a, b, c, d; polynomial = cvCreateMat(1,7,CV_64FC1); result = 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*t⁶ + k5*t⁵ + k4*t⁴ + k3*t³ + k2*t² + 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 ); }