/*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) 2000, Intel Corporation, 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 "_cv.h" /* This is stright forward port v2 of Matlab calibration engine by Jean-Yves Bouguet that is (in a large extent) based on the paper: Z. Zhang. "A flexible new technique for camera calibration". IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334, 2000. The 1st initial port was done by Valery Mosyagin. */ static void icvGaussNewton( const CvMat* J, const CvMat* err, CvMat* delta, CvMat* JtJ=0, CvMat* JtErr=0, CvMat* JtJW=0, CvMat* JtJV=0 ) { CvMat* _temp_JtJ = 0; CvMat* _temp_JtErr = 0; CvMat* _temp_JtJW = 0; CvMat* _temp_JtJV = 0; CV_FUNCNAME( "icvGaussNewton" ); __BEGIN__; if( !CV_IS_MAT(J) || !CV_IS_MAT(err) || !CV_IS_MAT(delta) ) CV_ERROR( CV_StsBadArg, "Some of required arguments is not a valid matrix" ); if( !JtJ ) { CV_CALL( _temp_JtJ = cvCreateMat( J->cols, J->cols, J->type )); JtJ = _temp_JtJ; } else if( !CV_IS_MAT(JtJ) ) CV_ERROR( CV_StsBadArg, "JtJ is not a valid matrix" ); if( !JtErr ) { CV_CALL( _temp_JtErr = cvCreateMat( J->cols, 1, J->type )); JtErr = _temp_JtErr; } else if( !CV_IS_MAT(JtErr) ) CV_ERROR( CV_StsBadArg, "JtErr is not a valid matrix" ); if( !JtJW ) { CV_CALL( _temp_JtJW = cvCreateMat( J->cols, 1, J->type )); JtJW = _temp_JtJW; } else if( !CV_IS_MAT(JtJW) ) CV_ERROR( CV_StsBadArg, "JtJW is not a valid matrix" ); if( !JtJV ) { CV_CALL( _temp_JtJV = cvCreateMat( J->cols, J->cols, J->type )); JtJV = _temp_JtJV; } else if( !CV_IS_MAT(JtJV) ) CV_ERROR( CV_StsBadArg, "JtJV is not a valid matrix" ); cvMulTransposed( J, JtJ, 1 ); cvGEMM( J, err, 1, 0, 0, JtErr, CV_GEMM_A_T ); cvSVD( JtJ, JtJW, 0, JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); cvSVBkSb( JtJW, JtJV, JtJV, JtErr, delta, CV_SVD_U_T + CV_SVD_V_T ); __END__; if( _temp_JtJ || _temp_JtErr || _temp_JtJW || _temp_JtJV ) { cvReleaseMat( &_temp_JtJ ); cvReleaseMat( &_temp_JtErr ); cvReleaseMat( &_temp_JtJW ); cvReleaseMat( &_temp_JtJV ); } } /*static double calc_repr_err( const double* object_points, int o_step, const double* image_points, const double* h, int count ) { double err = 0; for( int i = 0; i < count; i++ ) { double X = object_points[i*o_step], Y = object_points[i*o_step + 1]; double x0 = image_points[i*2], y0 = image_points[i*2 + 1]; double d = 1./(h[6]*X + h[7]*Y + h[8]); double x = (h[0]*X + h[1]*Y + h[2])*d; double y = (h[3]*X + h[4]*Y + h[5])*d; err += fabs(x - x0) + fabs(y - y0); } return err; }*/ // finds perspective transformation H between the object plane and image plane, // so that (sxi,syi,s) ~ H*(Xi,Yi,1) CV_IMPL void cvFindHomography( const CvMat* object_points, const CvMat* image_points, CvMat* __H ) { CvMat *_m = 0, *_M = 0; CvMat *_L = 0; CV_FUNCNAME( "cvFindHomography" ); __BEGIN__; int h_type; int i, k, count, count2; CvPoint2D64f *m, *M; CvPoint2D64f cm = {0,0}, sm = {0,0}; double inv_Hnorm[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 1 }; double H[9]; CvMat _inv_Hnorm = cvMat( 3, 3, CV_64FC1, inv_Hnorm ); CvMat _H = cvMat( 3, 3, CV_64FC1, H ); double LtL[9*9], LW[9], LV[9*9]; CvMat* _Lp; double* L; CvMat _LtL = cvMat( 9, 9, CV_64FC1, LtL ); CvMat _LW = cvMat( 9, 1, CV_64FC1, LW ); CvMat _LV = cvMat( 9, 9, CV_64FC1, LV ); CvMat _Hrem = cvMat( 3, 3, CV_64FC1, LV + 8*9 ); if( !CV_IS_MAT(image_points) || !CV_IS_MAT(object_points) || !CV_IS_MAT(__H) ) CV_ERROR( CV_StsBadArg, "one of arguments is not a valid matrix" ); h_type = CV_MAT_TYPE(__H->type); if( h_type != CV_32FC1 && h_type != CV_64FC1 ) CV_ERROR( CV_StsUnsupportedFormat, "Homography matrix must have 32fC1 or 64fC1 type" ); if( __H->rows != 3 || __H->cols != 3 ) CV_ERROR( CV_StsBadSize, "Homography matrix must be 3x3" ); count = MAX(image_points->cols, image_points->rows); count2 = MAX(object_points->cols, object_points->rows); if( count != count2 ) CV_ERROR( CV_StsUnmatchedSizes, "Numbers of image and object points do not match" ); CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); CV_CALL( cvConvertPointsHomogenious( image_points, _m )); m = (CvPoint2D64f*)_m->data.ptr; CV_CALL( _M = cvCreateMat( 1, count, CV_64FC2 )); CV_CALL( cvConvertPointsHomogenious( object_points, _M )); M = (CvPoint2D64f*)_M->data.ptr; // calculate the normalization transformation Hnorm. for( i = 0; i < count; i++ ) cm.x += m[i].x, cm.y += m[i].y; cm.x /= count; cm.y /= count; for( i = 0; i < count; i++ ) { double x = m[i].x - cm.x; double y = m[i].y - cm.y; sm.x += fabs(x); sm.y += fabs(y); } sm.x /= count; sm.y /= count; inv_Hnorm[0] = sm.x; inv_Hnorm[4] = sm.y; inv_Hnorm[2] = cm.x; inv_Hnorm[5] = cm.y; sm.x = 1./sm.x; sm.y = 1./sm.y; CV_CALL( _Lp = _L = cvCreateMat( 2*count, 9, CV_64FC1 ) ); L = _L->data.db; for( i = 0; i < count; i++, L += 18 ) { double x = -(m[i].x - cm.x)*sm.x, y = -(m[i].y - cm.y)*sm.y; L[0] = L[9 + 3] = M[i].x; L[1] = L[9 + 4] = M[i].y; L[2] = L[9 + 5] = 1; L[9 + 0] = L[9 + 1] = L[9 + 2] = L[3] = L[4] = L[5] = 0; L[6] = x*M[i].x; L[7] = x*M[i].y; L[8] = x; L[9 + 6] = y*M[i].x; L[9 + 7] = y*M[i].y; L[9 + 8] = y; } if( count > 4 ) { cvMulTransposed( _L, &_LtL, 1 ); _Lp = &_LtL; } _LW.rows = MIN(count*2, 9); cvSVD( _Lp, &_LW, 0, &_LV, CV_SVD_MODIFY_A + CV_SVD_V_T ); cvScale( &_Hrem, &_Hrem, 1./_Hrem.data.db[8] ); cvMatMul( &_inv_Hnorm, &_Hrem, &_H ); if( count > 4 ) { // reuse the available storage for jacobian and other vars CvMat _J = cvMat( 2*count, 8, CV_64FC1, _L->data.db ); CvMat _err = cvMat( 2*count, 1, CV_64FC1, _L->data.db + 2*count*8 ); CvMat _JtJ = cvMat( 8, 8, CV_64FC1, LtL ); CvMat _JtErr = cvMat( 8, 1, CV_64FC1, LtL + 8*8 ); CvMat _JtJW = cvMat( 8, 1, CV_64FC1, LW ); CvMat _JtJV = cvMat( 8, 8, CV_64FC1, LV ); CvMat _Hinnov = cvMat( 8, 1, CV_64FC1, LV + 8*8 ); for( k = 0; k < 10; k++ ) { double* J = _J.data.db, *err = _err.data.db; for( i = 0; i < count; i++, J += 16, err += 2 ) { double di = 1./(H[6]*M[i].x + H[7]*M[i].y + 1.); double _xi = (H[0]*M[i].x + H[1]*M[i].y + H[2])*di; double _yi = (H[3]*M[i].x + H[4]*M[i].y + H[5])*di; err[0] = m[i].x - _xi; err[1] = m[i].y - _yi; J[0] = M[i].x*di; J[1] = M[i].y*di; J[2] = di; J[8+3] = M[i].x; J[8+4] = M[i].y; J[8+5] = di; J[6] = -J[0]*_xi; J[7] = -J[1]*_xi; J[8+6] = -J[8+3]*_yi; J[8+7] = -J[8+4]*_yi; J[3] = J[4] = J[5] = J[8+0] = J[8+1] = J[8+2] = 0.; } icvGaussNewton( &_J, &_err, &_Hinnov, &_JtJ, &_JtErr, &_JtJW, &_JtJV ); for( i = 0; i < 8; i++ ) H[i] += _Hinnov.data.db[i]; } } cvConvert( &_H, __H ); __END__; cvReleaseMat( &_m ); cvReleaseMat( &_M ); cvReleaseMat( &_L ); } CV_IMPL int cvRodrigues2( const CvMat* src, CvMat* dst, CvMat* jacobian ) { int result = 0; CV_FUNCNAME( "cvRogrigues2" ); __BEGIN__; int depth, elem_size; int i, k; double J[27]; CvMat _J = cvMat( 3, 9, CV_64F, J ); if( !CV_IS_MAT(src) ) CV_ERROR( !src ? CV_StsNullPtr : CV_StsBadArg, "Input argument is not a valid matrix" ); if( !CV_IS_MAT(dst) ) CV_ERROR( !dst ? CV_StsNullPtr : CV_StsBadArg, "The first output argument is not a valid matrix" ); depth = CV_MAT_DEPTH(src->type); elem_size = CV_ELEM_SIZE(depth); if( depth != CV_32F && depth != CV_64F ) CV_ERROR( CV_StsUnsupportedFormat, "The matrices must have 32f or 64f data type" ); if( !CV_ARE_DEPTHS_EQ(src, dst) ) CV_ERROR( CV_StsUnmatchedFormats, "All the matrices must have the same data type" ); if( jacobian ) { if( !CV_IS_MAT(jacobian) ) CV_ERROR( CV_StsBadArg, "Jacobian is not a valid matrix" ); if( !CV_ARE_DEPTHS_EQ(src, jacobian) || CV_MAT_CN(jacobian->type) != 1 ) CV_ERROR( CV_StsUnmatchedFormats, "Jacobian must have 32fC1 or 64fC1 datatype" ); if( (jacobian->rows != 9 || jacobian->cols != 3) && (jacobian->rows != 3 || jacobian->cols != 9)) CV_ERROR( CV_StsBadSize, "Jacobian must be 3x9 or 9x3" ); } if( src->cols == 1 || src->rows == 1 ) { double rx, ry, rz, theta; int step = src->rows > 1 ? src->step / elem_size : 1; if( src->rows + src->cols*CV_MAT_CN(src->type) - 1 != 3 ) CV_ERROR( CV_StsBadSize, "Input matrix must be 1x3, 3x1 or 3x3" ); if( dst->rows != 3 || dst->cols != 3 || CV_MAT_CN(dst->type) != 1 ) CV_ERROR( CV_StsBadSize, "Output matrix must be 3x3, single-channel floating point matrix" ); if( depth == CV_32F ) { rx = src->data.fl[0]; ry = src->data.fl[step]; rz = src->data.fl[step*2]; } else { rx = src->data.db[0]; ry = src->data.db[step]; rz = src->data.db[step*2]; } theta = sqrt(rx*rx + ry*ry + rz*rz); if( theta < DBL_EPSILON ) { cvSetIdentity( dst ); if( jacobian ) { memset( J, 0, sizeof(J) ); J[5] = J[15] = J[19] = -1; J[7] = J[11] = J[21] = 1; } } else { const double I[] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 }; double c = cos(theta); double s = sin(theta); double c1 = 1. - c; double itheta = theta ? 1./theta : 0.; rx *= itheta; ry *= itheta; rz *= itheta; double rrt[] = { rx*rx, rx*ry, rx*rz, rx*ry, ry*ry, ry*rz, rx*rz, ry*rz, rz*rz }; double _r_x_[] = { 0, -rz, ry, rz, 0, -rx, -ry, rx, 0 }; double R[9]; CvMat _R = cvMat( 3, 3, CV_64F, R ); // R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x] // where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0] for( k = 0; k < 9; k++ ) R[k] = c*I[k] + c1*rrt[k] + s*_r_x_[k]; cvConvert( &_R, dst ); if( jacobian ) { double drrt[] = { rx+rx, ry, rz, ry, 0, 0, rz, 0, 0, 0, rx, 0, rx, ry+ry, rz, 0, rz, 0, 0, 0, rx, 0, 0, ry, rx, ry, rz+rz }; double d_r_x_[] = { 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0 }; for( i = 0; i < 3; i++ ) { double ri = i == 0 ? rx : i == 1 ? ry : rz; double a0 = -s*ri, a1 = (s - 2*c1*itheta)*ri, a2 = c1*itheta; double a3 = (c - s*itheta)*ri, a4 = s*itheta; for( k = 0; k < 9; k++ ) J[i*9+k] = a0*I[k] + a1*rrt[k] + a2*drrt[i*9+k] + a3*_r_x_[k] + a4*d_r_x_[i*9+k]; } } } } else if( src->cols == 3 && src->rows == 3 ) { double R[9], U[9], V[9], W[3], rx, ry, rz; CvMat _R = cvMat( 3, 3, CV_64F, R ); CvMat _U = cvMat( 3, 3, CV_64F, U ); CvMat _V = cvMat( 3, 3, CV_64F, V ); CvMat _W = cvMat( 3, 1, CV_64F, W ); double theta, s, c; int step = dst->rows > 1 ? dst->step / elem_size : 1; if( (dst->rows != 1 || dst->cols*CV_MAT_CN(dst->type) != 3) && (dst->rows != 3 || dst->cols != 1 || CV_MAT_CN(dst->type) != 1)) CV_ERROR( CV_StsBadSize, "Output matrix must be 1x3 or 3x1" ); cvConvert( src, &_R ); if( !cvCheckArr( &_R, CV_CHECK_RANGE+CV_CHECK_QUIET, -100, 100 ) ) { cvZero(dst); if( jacobian ) cvZero(jacobian); EXIT; } cvSVD( &_R, &_W, &_U, &_V, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T ); cvGEMM( &_U, &_V, 1, 0, 0, &_R, CV_GEMM_A_T ); rx = R[7] - R[5]; ry = R[2] - R[6]; rz = R[3] - R[1]; s = sqrt((rx*rx + ry*ry + rz*rz)*0.25); c = (R[0] + R[4] + R[8] - 1)*0.5; c = c > 1. ? 1. : c < -1. ? -1. : c; theta = acos(c); if( s < 1e-5 ) { double t; if( c > 0 ) rx = ry = rz = 0; else { t = (R[0] + 1)*0.5; rx = theta*sqrt(MAX(t,0.)); t = (R[4] + 1)*0.5; ry = theta*sqrt(MAX(t,0.))*(R[1] < 0 ? -1. : 1.); t = (R[8] + 1)*0.5; rz = theta*sqrt(MAX(t,0.))*(R[2] < 0 ? -1. : 1.); } if( jacobian ) { memset( J, 0, sizeof(J) ); if( c > 0 ) { J[5] = J[15] = J[19] = -0.5; J[7] = J[11] = J[21] = 0.5; } } } else { double vth = 1/(2*s); if( jacobian ) { double t, dtheta_dtr = -1./s; // var1 = [vth;theta] // var = [om1;var1] = [om1;vth;theta] double dvth_dtheta = -vth*c/s; double d1 = 0.5*dvth_dtheta*dtheta_dtr; double d2 = 0.5*dtheta_dtr; // dvar1/dR = dvar1/dtheta*dtheta/dR = [dvth/dtheta; 1] * dtheta/dtr * dtr/dR double dvardR[5*9] = { 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, d1, 0, 0, 0, d1, 0, 0, 0, d1, d2, 0, 0, 0, d2, 0, 0, 0, d2 }; // var2 = [om;theta] double dvar2dvar[] = { vth, 0, 0, rx, 0, 0, vth, 0, ry, 0, 0, 0, vth, rz, 0, 0, 0, 0, 0, 1 }; double domegadvar2[] = { theta, 0, 0, rx*vth, 0, theta, 0, ry*vth, 0, 0, theta, rz*vth }; CvMat _dvardR = cvMat( 5, 9, CV_64FC1, dvardR ); CvMat _dvar2dvar = cvMat( 4, 5, CV_64FC1, dvar2dvar ); CvMat _domegadvar2 = cvMat( 3, 4, CV_64FC1, domegadvar2 ); double t0[3*5]; CvMat _t0 = cvMat( 3, 5, CV_64FC1, t0 ); cvMatMul( &_domegadvar2, &_dvar2dvar, &_t0 ); cvMatMul( &_t0, &_dvardR, &_J ); // transpose every row of _J (treat the rows as 3x3 matrices) CV_SWAP(J[1], J[3], t); CV_SWAP(J[2], J[6], t); CV_SWAP(J[5], J[7], t); CV_SWAP(J[10], J[12], t); CV_SWAP(J[11], J[15], t); CV_SWAP(J[14], J[16], t); CV_SWAP(J[19], J[21], t); CV_SWAP(J[20], J[24], t); CV_SWAP(J[23], J[25], t); } vth *= theta; rx *= vth; ry *= vth; rz *= vth; } if( depth == CV_32F ) { dst->data.fl[0] = (float)rx; dst->data.fl[step] = (float)ry; dst->data.fl[step*2] = (float)rz; } else { dst->data.db[0] = rx; dst->data.db[step] = ry; dst->data.db[step*2] = rz; } } if( jacobian ) { if( depth == CV_32F ) { if( jacobian->rows == _J.rows ) cvConvert( &_J, jacobian ); else { float Jf[3*9]; CvMat _Jf = cvMat( _J.rows, _J.cols, CV_32FC1, Jf ); cvConvert( &_J, &_Jf ); cvTranspose( &_Jf, jacobian ); } } else if( jacobian->rows == _J.rows ) cvCopy( &_J, jacobian ); else cvTranspose( &_J, jacobian ); } result = 1; __END__; return result; } CV_IMPL void cvProjectPoints2( const CvMat* obj_points, const CvMat* r_vec, const CvMat* t_vec, const CvMat* A, const CvMat* dist_coeffs, CvMat* img_points, CvMat* dpdr, CvMat* dpdt, CvMat* dpdf, CvMat* dpdc, CvMat* dpdk ) { CvMat *_M = 0, *_m = 0; CvMat *_dpdr = 0, *_dpdt = 0, *_dpdc = 0, *_dpdf = 0, *_dpdk = 0; CV_FUNCNAME( "cvProjectPoints2" ); __BEGIN__; int i, j, count; int calc_derivatives; const CvPoint3D64f* M; CvPoint2D64f* m; double r[3], R[9], dRdr[27], t[3], a[9], k[4] = {0,0,0,0}, fx, fy, cx, cy; CvMat _r, _t, _a = cvMat( 3, 3, CV_64F, a ), _k; CvMat _R = cvMat( 3, 3, CV_64F, R ), _dRdr = cvMat( 3, 9, CV_64F, dRdr ); double *dpdr_p = 0, *dpdt_p = 0, *dpdk_p = 0, *dpdf_p = 0, *dpdc_p = 0; int dpdr_step = 0, dpdt_step = 0, dpdk_step = 0, dpdf_step = 0, dpdc_step = 0; if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(r_vec) || !CV_IS_MAT(t_vec) || !CV_IS_MAT(A) || /*!CV_IS_MAT(dist_coeffs) ||*/ !CV_IS_MAT(img_points) ) CV_ERROR( CV_StsBadArg, "One of required arguments is not a valid matrix" ); count = MAX(obj_points->rows, obj_points->cols); if( CV_IS_CONT_MAT(obj_points->type) && CV_MAT_DEPTH(obj_points->type) == CV_64F && (obj_points->rows == 1 && CV_MAT_CN(obj_points->type) == 3 || obj_points->rows == count && CV_MAT_CN(obj_points->type)*obj_points->cols == 3)) _M = (CvMat*)obj_points; else { CV_CALL( _M = cvCreateMat( 1, count, CV_64FC3 )); CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); } if( CV_IS_CONT_MAT(img_points->type) && CV_MAT_DEPTH(img_points->type) == CV_64F && (img_points->rows == 1 && CV_MAT_CN(img_points->type) == 2 || img_points->rows == count && CV_MAT_CN(img_points->type)*img_points->cols == 2)) _m = img_points; else CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); M = (CvPoint3D64f*)_M->data.db; m = (CvPoint2D64f*)_m->data.db; if( CV_MAT_DEPTH(r_vec->type) != CV_64F && CV_MAT_DEPTH(r_vec->type) != CV_32F || (r_vec->rows != 1 && r_vec->cols != 1 || r_vec->rows*r_vec->cols*CV_MAT_CN(r_vec->type) != 3) && (r_vec->rows != 3 && r_vec->cols != 3 || CV_MAT_CN(r_vec->type) != 1)) CV_ERROR( CV_StsBadArg, "Rotation must be represented by 1x3 or 3x1 " "floating-point rotation vector, or 3x3 rotation matrix" ); if( r_vec->rows == 3 && r_vec->cols == 3 ) { _r = cvMat( 3, 1, CV_64FC1, r ); CV_CALL( cvRodrigues2( r_vec, &_r )); CV_CALL( cvRodrigues2( &_r, &_R, &_dRdr )); cvCopy( r_vec, &_R ); } else { _r = cvMat( r_vec->rows, r_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(r_vec->type)), r ); CV_CALL( cvConvert( r_vec, &_r )); CV_CALL( cvRodrigues2( &_r, &_R, &_dRdr ) ); } if( CV_MAT_DEPTH(t_vec->type) != CV_64F && CV_MAT_DEPTH(t_vec->type) != CV_32F || t_vec->rows != 1 && t_vec->cols != 1 || t_vec->rows*t_vec->cols*CV_MAT_CN(t_vec->type) != 3 ) CV_ERROR( CV_StsBadArg, "Translation vector must be 1x3 or 3x1 floating-point vector" ); _t = cvMat( t_vec->rows, t_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(t_vec->type)), t ); CV_CALL( cvConvert( t_vec, &_t )); if( CV_MAT_TYPE(A->type) != CV_64FC1 && CV_MAT_TYPE(A->type) != CV_32FC1 || A->rows != 3 || A->cols != 3 ) CV_ERROR( CV_StsBadArg, "Instrinsic parameters must be 3x3 floating-point matrix" ); CV_CALL( cvConvert( A, &_a )); fx = a[0]; fy = a[4]; cx = a[2]; cy = a[5]; if( dist_coeffs ) { if( !CV_IS_MAT(dist_coeffs) || CV_MAT_DEPTH(dist_coeffs->type) != CV_64F && CV_MAT_DEPTH(dist_coeffs->type) != CV_32F || dist_coeffs->rows != 1 && dist_coeffs->cols != 1 || dist_coeffs->rows*dist_coeffs->cols*CV_MAT_CN(dist_coeffs->type) != 4 ) CV_ERROR( CV_StsBadArg, "Distortion coefficients must be 1x4 or 4x1 floating-point vector" ); _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(dist_coeffs->type)), k ); CV_CALL( cvConvert( dist_coeffs, &_k )); } if( dpdr ) { if( !CV_IS_MAT(dpdr) || CV_MAT_TYPE(dpdr->type) != CV_32FC1 && CV_MAT_TYPE(dpdr->type) != CV_64FC1 || dpdr->rows != count*2 || dpdr->cols != 3 ) CV_ERROR( CV_StsBadArg, "dp/drot must be 2Nx3 floating-point matrix" ); if( CV_MAT_TYPE(dpdr->type) == CV_64FC1 ) _dpdr = dpdr; else CV_CALL( _dpdr = cvCreateMat( 2*count, 3, CV_64FC1 )); dpdr_p = _dpdr->data.db; dpdr_step = _dpdr->step/sizeof(dpdr_p[0]); } if( dpdt ) { if( !CV_IS_MAT(dpdt) || CV_MAT_TYPE(dpdt->type) != CV_32FC1 && CV_MAT_TYPE(dpdt->type) != CV_64FC1 || dpdt->rows != count*2 || dpdt->cols != 3 ) CV_ERROR( CV_StsBadArg, "dp/dT must be 2Nx3 floating-point matrix" ); if( CV_MAT_TYPE(dpdt->type) == CV_64FC1 ) _dpdt = dpdt; else CV_CALL( _dpdt = cvCreateMat( 2*count, 3, CV_64FC1 )); dpdt_p = _dpdt->data.db; dpdt_step = _dpdt->step/sizeof(dpdt_p[0]); } if( dpdf ) { if( !CV_IS_MAT(dpdf) || CV_MAT_TYPE(dpdf->type) != CV_32FC1 && CV_MAT_TYPE(dpdf->type) != CV_64FC1 || dpdf->rows != count*2 || dpdf->cols != 2 ) CV_ERROR( CV_StsBadArg, "dp/df must be 2Nx2 floating-point matrix" ); if( CV_MAT_TYPE(dpdf->type) == CV_64FC1 ) _dpdf = dpdf; else CV_CALL( _dpdf = cvCreateMat( 2*count, 2, CV_64FC1 )); dpdf_p = _dpdf->data.db; dpdf_step = _dpdf->step/sizeof(dpdf_p[0]); } if( dpdc ) { if( !CV_IS_MAT(dpdc) || CV_MAT_TYPE(dpdc->type) != CV_32FC1 && CV_MAT_TYPE(dpdc->type) != CV_64FC1 || dpdc->rows != count*2 || dpdc->cols != 2 ) CV_ERROR( CV_StsBadArg, "dp/dc must be 2Nx2 floating-point matrix" ); if( CV_MAT_TYPE(dpdc->type) == CV_64FC1 ) _dpdc = dpdc; else CV_CALL( _dpdc = cvCreateMat( 2*count, 2, CV_64FC1 )); dpdc_p = _dpdc->data.db; dpdc_step = _dpdc->step/sizeof(dpdc_p[0]); } if( dpdk ) { if( !CV_IS_MAT(dpdk) || CV_MAT_TYPE(dpdk->type) != CV_32FC1 && CV_MAT_TYPE(dpdk->type) != CV_64FC1 || dpdk->rows != count*2 || (dpdk->cols != 4 && dpdk->cols != 2) ) CV_ERROR( CV_StsBadArg, "dp/df must be 2Nx4 or 2Nx2 floating-point matrix" ); if( !dist_coeffs ) CV_ERROR( CV_StsNullPtr, "dist_coeffs is NULL while dpdk is not" ); if( CV_MAT_TYPE(dpdk->type) == CV_64FC1 ) _dpdk = dpdk; else CV_CALL( _dpdk = cvCreateMat( dpdk->rows, dpdk->cols, CV_64FC1 )); dpdk_p = _dpdk->data.db; dpdk_step = _dpdk->step/sizeof(dpdk_p[0]); } calc_derivatives = dpdr || dpdt || dpdf || dpdc || dpdk; for( i = 0; i < count; i++ ) { double X = M[i].x, Y = M[i].y, Z = M[i].z; double x = R[0]*X + R[1]*Y + R[2]*Z + t[0]; double y = R[3]*X + R[4]*Y + R[5]*Z + t[1]; double z = R[6]*X + R[7]*Y + R[8]*Z + t[2]; double r2, r4, a1, a2, a3, cdist; double xd, yd; z = z ? 1./z : 1; x *= z; y *= z; r2 = x*x + y*y; r4 = r2*r2; a1 = 2*x*y; a2 = r2 + 2*x*x; a3 = r2 + 2*y*y; cdist = 1 + k[0]*r2 + k[1]*r4; xd = x*cdist + k[2]*a1 + k[3]*a2; yd = y*cdist + k[2]*a3 + k[3]*a1; m[i].x = xd*fx + cx; m[i].y = yd*fy + cy; if( calc_derivatives ) { if( dpdc_p ) { dpdc_p[0] = 1; dpdc_p[1] = 0; dpdc_p[dpdc_step] = 0; dpdc_p[dpdc_step+1] = 1; dpdc_p += dpdc_step*2; } if( dpdf_p ) { dpdf_p[0] = xd; dpdf_p[1] = 0; dpdf_p[dpdf_step] = 0; dpdf_p[dpdf_step+1] = yd; dpdf_p += dpdf_step*2; } if( dpdk_p ) { dpdk_p[0] = fx*x*r2; dpdk_p[1] = fx*x*r4; dpdk_p[dpdk_step] = fy*y*r2; dpdk_p[dpdk_step+1] = fy*y*r4; if( _dpdk->cols > 2 ) { dpdk_p[2] = fx*a1; dpdk_p[3] = fx*a2; dpdk_p[dpdk_step+2] = fy*a3; dpdk_p[dpdk_step+3] = fy*a1; } dpdk_p += dpdk_step*2; } if( dpdt_p ) { double dxdt[] = { z, 0, -x*z }, dydt[] = { 0, z, -y*z }; for( j = 0; j < 3; j++ ) { double dr2dt = 2*x*dxdt[j] + 2*y*dydt[j]; double dcdist_dt = k[0]*dr2dt + 2*k[1]*r2*dr2dt; double da1dt = 2*(x*dydt[j] + y*dxdt[j]); double dmxdt = fx*(dxdt[j]*cdist + x*dcdist_dt + k[2]*da1dt + k[3]*(dr2dt + 2*x*dxdt[j])); double dmydt = fy*(dydt[j]*cdist + y*dcdist_dt + k[2]*(dr2dt + 2*y*dydt[j]) + k[3]*da1dt); dpdt_p[j] = dmxdt; dpdt_p[dpdt_step+j] = dmydt; } dpdt_p += dpdt_step*2; } if( dpdr_p ) { double dx0dr[] = { X*dRdr[0] + Y*dRdr[1] + Z*dRdr[2], X*dRdr[9] + Y*dRdr[10] + Z*dRdr[11], X*dRdr[18] + Y*dRdr[19] + Z*dRdr[20] }; double dy0dr[] = { X*dRdr[3] + Y*dRdr[4] + Z*dRdr[5], X*dRdr[12] + Y*dRdr[13] + Z*dRdr[14], X*dRdr[21] + Y*dRdr[22] + Z*dRdr[23] }; double dz0dr[] = { X*dRdr[6] + Y*dRdr[7] + Z*dRdr[8], X*dRdr[15] + Y*dRdr[16] + Z*dRdr[17], X*dRdr[24] + Y*dRdr[25] + Z*dRdr[26] }; for( j = 0; j < 3; j++ ) { double dxdr = z*(dx0dr[j] - x*dz0dr[j]); double dydr = z*(dy0dr[j] - y*dz0dr[j]); double dr2dr = 2*x*dxdr + 2*y*dydr; double dcdist_dr = k[0]*dr2dr + 2*k[1]*r2*dr2dr; double da1dr = 2*(x*dydr + y*dxdr); double dmxdr = fx*(dxdr*cdist + x*dcdist_dr + k[2]*da1dr + k[3]*(dr2dr + 2*x*dxdr)); double dmydr = fy*(dydr*cdist + y*dcdist_dr + k[2]*(dr2dr + 2*y*dydr) + k[3]*da1dr); dpdr_p[j] = dmxdr; dpdr_p[dpdr_step+j] = dmydr; } dpdr_p += dpdr_step*2; } } } if( _m != img_points ) cvConvertPointsHomogenious( _m, img_points ); if( _dpdr != dpdr ) cvConvert( _dpdr, dpdr ); if( _dpdt != dpdt ) cvConvert( _dpdt, dpdt ); if( _dpdf != dpdf ) cvConvert( _dpdf, dpdf ); if( _dpdc != dpdc ) cvConvert( _dpdc, dpdc ); if( _dpdk != dpdk ) cvConvert( _dpdk, dpdk ); __END__; if( _M != obj_points ) cvReleaseMat( &_M ); if( _m != img_points ) cvReleaseMat( &_m ); if( _dpdr != dpdr ) cvReleaseMat( &_dpdr ); if( _dpdt != dpdt ) cvReleaseMat( &_dpdt ); if( _dpdf != dpdf ) cvReleaseMat( &_dpdf ); if( _dpdc != dpdc ) cvReleaseMat( &_dpdc ); if( _dpdk != dpdk ) cvReleaseMat( &_dpdk ); } CV_IMPL void cvFindExtrinsicCameraParams2( const CvMat* obj_points, const CvMat* img_points, const CvMat* A, const CvMat* dist_coeffs, CvMat* r_vec, CvMat* t_vec ) { const int max_iter = 20; CvMat *_M = 0, *_Mxy = 0, *_m = 0, *_mn = 0, *_L = 0, *_J = 0; CV_FUNCNAME( "cvFindExtrinsicCameraParams2" ); __BEGIN__; int i, j, count; double a[9], k[4] = { 0, 0, 0, 0 }, R[9], ifx, ify, cx, cy; double Mc[3] = {0, 0, 0}, MM[9], U[9], V[9], W[3]; double JtJ[6*6], JtErr[6], JtJW[6], JtJV[6*6], delta[6], param[6]; CvPoint3D64f* M = 0; CvPoint2D64f *m = 0, *mn = 0; CvMat _a = cvMat( 3, 3, CV_64F, a ); CvMat _R = cvMat( 3, 3, CV_64F, R ); CvMat _r = cvMat( 3, 1, CV_64F, param ); CvMat _t = cvMat( 3, 1, CV_64F, param + 3 ); CvMat _Mc = cvMat( 1, 3, CV_64F, Mc ); CvMat _MM = cvMat( 3, 3, CV_64F, MM ); CvMat _U = cvMat( 3, 3, CV_64F, U ); CvMat _V = cvMat( 3, 3, CV_64F, V ); CvMat _W = cvMat( 3, 1, CV_64F, W ); CvMat _JtJ = cvMat( 6, 6, CV_64F, JtJ ); CvMat _JtErr = cvMat( 6, 1, CV_64F, JtErr ); CvMat _JtJW = cvMat( 6, 1, CV_64F, JtJW ); CvMat _JtJV = cvMat( 6, 6, CV_64F, JtJV ); CvMat _delta = cvMat( 6, 1, CV_64F, delta ); CvMat _param = cvMat( 6, 1, CV_64F, param ); CvMat _dpdr, _dpdt; if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(img_points) || !CV_IS_MAT(A) || !CV_IS_MAT(r_vec) || !CV_IS_MAT(t_vec) ) CV_ERROR( CV_StsBadArg, "One of required arguments is not a valid matrix" ); count = MAX(obj_points->cols, obj_points->rows); CV_CALL( _M = cvCreateMat( 1, count, CV_64FC3 )); CV_CALL( _Mxy = cvCreateMat( 1, count, CV_64FC2 )); CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); CV_CALL( _mn = cvCreateMat( 1, count, CV_64FC2 )); M = (CvPoint3D64f*)_M->data.db; m = (CvPoint2D64f*)_m->data.db; mn = (CvPoint2D64f*)_mn->data.db; CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); CV_CALL( cvConvertPointsHomogenious( img_points, _m )); CV_CALL( cvConvert( A, &_a )); if( dist_coeffs ) { CvMat _k; if( !CV_IS_MAT(dist_coeffs) || CV_MAT_DEPTH(dist_coeffs->type) != CV_64F && CV_MAT_DEPTH(dist_coeffs->type) != CV_32F || dist_coeffs->rows != 1 && dist_coeffs->cols != 1 || dist_coeffs->rows*dist_coeffs->cols*CV_MAT_CN(dist_coeffs->type) != 4 ) CV_ERROR( CV_StsBadArg, "Distortion coefficients must be 1x4 or 4x1 floating-point vector" ); _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(dist_coeffs->type)), k ); CV_CALL( cvConvert( dist_coeffs, &_k )); } if( CV_MAT_DEPTH(r_vec->type) != CV_64F && CV_MAT_DEPTH(r_vec->type) != CV_32F || r_vec->rows != 1 && r_vec->cols != 1 || r_vec->rows*r_vec->cols*CV_MAT_CN(r_vec->type) != 3 ) CV_ERROR( CV_StsBadArg, "Rotation vector must be 1x3 or 3x1 floating-point vector" ); if( CV_MAT_DEPTH(t_vec->type) != CV_64F && CV_MAT_DEPTH(t_vec->type) != CV_32F || t_vec->rows != 1 && t_vec->cols != 1 || t_vec->rows*t_vec->cols*CV_MAT_CN(t_vec->type) != 3 ) CV_ERROR( CV_StsBadArg, "Translation vector must be 1x3 or 3x1 floating-point vector" ); ifx = 1./a[0]; ify = 1./a[4]; cx = a[2]; cy = a[5]; // normalize image points // (unapply the intrinsic matrix transformation and distortion) for( i = 0; i < count; i++ ) { double x = (m[i].x - cx)*ifx, y = (m[i].y - cy)*ify, x0 = x, y0 = y; // compensate distortion iteratively if( dist_coeffs ) for( j = 0; j < 5; j++ ) { double r2 = x*x + y*y; double icdist = 1./(1 + k[0]*r2 + k[1]*r2*r2); double delta_x = 2*k[2]*x*y + k[3]*(r2 + 2*x*x); double delta_y = k[2]*(r2 + 2*y*y) + 2*k[3]*x*y; x = (x0 - delta_x)*icdist; y = (y0 - delta_y)*icdist; } mn[i].x = x; mn[i].y = y; // calc mean(M) Mc[0] += M[i].x; Mc[1] += M[i].y; Mc[2] += M[i].z; } Mc[0] /= count; Mc[1] /= count; Mc[2] /= count; cvReshape( _M, _M, 1, count ); cvMulTransposed( _M, &_MM, 1, &_Mc ); cvSVD( &_MM, &_W, 0, &_V, CV_SVD_MODIFY_A + CV_SVD_V_T ); // initialize extrinsic parameters if( W[2]/W[1] < 1e-3 || count < 4 ) { // a planar structure case (all M's lie in the same plane) double tt[3], h[9], h1_norm, h2_norm; CvMat* R_transform = &_V; CvMat T_transform = cvMat( 3, 1, CV_64F, tt ); CvMat _H = cvMat( 3, 3, CV_64F, h ); CvMat _h1, _h2, _h3; if( V[2]*V[2] + V[5]*V[5] < 1e-10 ) cvSetIdentity( R_transform ); if( cvDet(R_transform) < 0 ) cvScale( R_transform, R_transform, -1 ); cvGEMM( R_transform, &_Mc, -1, 0, 0, &T_transform, CV_GEMM_B_T ); for( i = 0; i < count; i++ ) { const double* Rp = R_transform->data.db; const double* Tp = T_transform.data.db; const double* src = _M->data.db + i*3; double* dst = _Mxy->data.db + i*2; dst[0] = Rp[0]*src[0] + Rp[1]*src[1] + Rp[2]*src[2] + Tp[0]; dst[1] = Rp[3]*src[0] + Rp[4]*src[1] + Rp[5]*src[2] + Tp[1]; } cvFindHomography( _Mxy, _mn, &_H ); cvGetCol( &_H, &_h1, 0 ); _h2 = _h1; _h2.data.db++; _h3 = _h2; _h3.data.db++; h1_norm = sqrt(h[0]*h[0] + h[3]*h[3] + h[6]*h[6]); h2_norm = sqrt(h[1]*h[1] + h[4]*h[4] + h[7]*h[7]); cvScale( &_h1, &_h1, 1./h1_norm ); cvScale( &_h2, &_h2, 1./h2_norm ); cvScale( &_h3, &_t, 2./(h1_norm + h2_norm)); cvCrossProduct( &_h1, &_h2, &_h3 ); cvRodrigues2( &_H, &_r ); cvRodrigues2( &_r, &_H ); cvMatMulAdd( &_H, &T_transform, &_t, &_t ); cvMatMul( &_H, R_transform, &_R ); cvRodrigues2( &_R, &_r ); } else { // non-planar structure. Use DLT method double* L; double LL[12*12], LW[12], LV[12*12], sc; CvMat _LL = cvMat( 12, 12, CV_64F, LL ); CvMat _LW = cvMat( 12, 1, CV_64F, LW ); CvMat _LV = cvMat( 12, 12, CV_64F, LV ); CvMat _RRt, _RR, _tt; CV_CALL( _L = cvCreateMat( 2*count, 12, CV_64F )); L = _L->data.db; for( i = 0; i < count; i++, L += 24 ) { double x = -mn[i].x, y = -mn[i].y; L[0] = L[16] = M[i].x; L[1] = L[17] = M[i].y; L[2] = L[18] = M[i].z; L[3] = L[19] = 1.; L[4] = L[5] = L[6] = L[7] = 0.; L[12] = L[13] = L[14] = L[15] = 0.; L[8] = x*M[i].x; L[9] = x*M[i].y; L[10] = x*M[i].z; L[11] = x; L[20] = y*M[i].x; L[21] = y*M[i].y; L[22] = y*M[i].z; L[23] = y; } cvMulTransposed( _L, &_LL, 1 ); cvSVD( &_LL, &_LW, 0, &_LV, CV_SVD_MODIFY_A + CV_SVD_V_T ); _RRt = cvMat( 3, 4, CV_64F, LV + 11*12 ); cvGetCols( &_RRt, &_RR, 0, 3 ); cvGetCol( &_RRt, &_tt, 3 ); if( cvDet(&_RR) < 0 ) cvScale( &_RRt, &_RRt, -1 ); sc = cvNorm(&_RR); cvSVD( &_RR, &_W, &_U, &_V, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T ); cvGEMM( &_U, &_V, 1, 0, 0, &_R, CV_GEMM_A_T ); cvScale( &_tt, &_t, cvNorm(&_R)/sc ); cvRodrigues2( &_R, &_r ); cvReleaseMat( &_L ); } CV_CALL( _J = cvCreateMat( 2*count, 6, CV_64FC1 )); cvGetCols( _J, &_dpdr, 0, 3 ); cvGetCols( _J, &_dpdt, 3, 6 ); // refine extrinsic parameters using iterative algorithm for( i = 0; i < max_iter; i++ ) { double n1, n2; cvReshape( _mn, _mn, 2, 1 ); cvProjectPoints2( _M, &_r, &_t, &_a, dist_coeffs, _mn, &_dpdr, &_dpdt, 0, 0, 0 ); cvSub( _m, _mn, _mn ); cvReshape( _mn, _mn, 1, 2*count ); cvMulTransposed( _J, &_JtJ, 1 ); cvGEMM( _J, _mn, 1, 0, 0, &_JtErr, CV_GEMM_A_T ); cvSVD( &_JtJ, &_JtJW, 0, &_JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); if( JtJW[5]/JtJW[0] < 1e-12 ) break; cvSVBkSb( &_JtJW, &_JtJV, &_JtJV, &_JtErr, &_delta, CV_SVD_U_T + CV_SVD_V_T ); cvAdd( &_delta, &_param, &_param ); n1 = cvNorm( &_delta ); n2 = cvNorm( &_param ); if( n1/n2 < 1e-10 ) break; } _r = cvMat( r_vec->rows, r_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(r_vec->type)), param ); _t = cvMat( t_vec->rows, t_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(t_vec->type)), param + 3 ); cvConvert( &_r, r_vec ); cvConvert( &_t, t_vec ); __END__; cvReleaseMat( &_M ); cvReleaseMat( &_Mxy ); cvReleaseMat( &_m ); cvReleaseMat( &_mn ); cvReleaseMat( &_L ); cvReleaseMat( &_J ); } static void icvInitIntrinsicParams2D( const CvMat* obj_points, const CvMat* img_points, const CvMat* point_counts, CvSize image_size, CvMat* intrinsic_matrix, double aspect_ratio ) { CvMat *_A = 0, *_b = 0; CV_FUNCNAME( "icvInitIntrinsicParams2D" ); __BEGIN__; int i, j, pos, img_count; double a[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 1 }; double H[9], AtA[4], AtAW[2], AtAV[4], Atb[2], f[2]; CvMat _a = cvMat( 3, 3, CV_64F, a ); CvMat _H = cvMat( 3, 3, CV_64F, H ); CvMat _AtA = cvMat( 2, 2, CV_64F, AtA ); CvMat _AtAW = cvMat( 2, 1, CV_64F, AtAW ); CvMat _AtAV = cvMat( 2, 2, CV_64F, AtAV ); CvMat _Atb = cvMat( 2, 1, CV_64F, Atb ); CvMat _f = cvMat( 2, 1, CV_64F, f ); assert( CV_MAT_TYPE(point_counts->type) == CV_32SC1 && CV_IS_MAT_CONT(point_counts->type) ); img_count = point_counts->rows + point_counts->cols - 1; if( CV_MAT_TYPE(obj_points->type) != CV_32FC3 && CV_MAT_TYPE(obj_points->type) != CV_64FC3 || CV_MAT_TYPE(img_points->type) != CV_32FC2 && CV_MAT_TYPE(img_points->type) != CV_64FC2 ) CV_ERROR( CV_StsUnsupportedFormat, "Both object points and image points must be 2D" ); if( obj_points->rows != 1 || img_points->rows != 1 ) CV_ERROR( CV_StsBadSize, "object points and image points must be a single-row matrices" ); CV_CALL( _A = cvCreateMat( 2*img_count, 2, CV_64F )); CV_CALL( _b = cvCreateMat( 2*img_count, 1, CV_64F )); a[2] = (image_size.width - 1)*0.5; a[5] = (image_size.height - 1)*0.5; // extract vanishing points in order to obtain initial value for the focal length for( i = 0, pos = 0; i < img_count; i++ ) { double* Ap = _A->data.db + i*4; double* bp = _b->data.db + i*2; int count = point_counts->data.i[i]; double h[3], v[3], d1[3], d2[3]; double n[4] = {0,0,0,0}; CvMat _m, _M; cvGetCols( obj_points, &_M, pos, pos + count ); cvGetCols( img_points, &_m, pos, pos + count ); pos += count; CV_CALL( cvFindHomography( &_M, &_m, &_H )); H[0] -= H[6]*a[2]; H[1] -= H[7]*a[2]; H[2] -= H[8]*a[2]; H[3] -= H[6]*a[5]; H[4] -= H[7]*a[5]; H[5] -= H[8]*a[5]; for( j = 0; j < 3; j++ ) { double t0 = H[j*3], t1 = H[j*3+1]; h[j] = t0; v[j] = t1; d1[j] = (t0 + t1)*0.5; d2[j] = (t0 - t1)*0.5; n[0] += t0*t0; n[1] += t1*t1; n[2] += d1[j]*d1[j]; n[3] += d2[j]*d2[j]; } for( j = 0; j < 4; j++ ) n[j] = 1./sqrt(n[j]); for( j = 0; j < 3; j++ ) { h[j] *= n[0]; v[j] *= n[1]; d1[j] *= n[2]; d2[j] *= n[3]; } Ap[0] = h[0]*v[0]; Ap[1] = h[1]*v[1]; Ap[2] = d1[0]*d2[0]; Ap[3] = d1[1]*d2[1]; bp[0] = -h[2]*v[2]; bp[1] = -d1[2]*d2[2]; } // while it is not about gradient descent search, // the formula is the same: f = inv(At*A)*At*b icvGaussNewton( _A, _b, &_f, &_AtA, &_Atb, &_AtAW, &_AtAV ); a[0] = sqrt(fabs(1./f[0])); a[4] = sqrt(fabs(1./f[1])); if( aspect_ratio != 0 ) { double tf = (a[0] + a[4])/(aspect_ratio + 1.); a[0] = aspect_ratio*tf; a[4] = tf; } cvConvert( &_a, intrinsic_matrix ); __END__; cvReleaseMat( &_A ); cvReleaseMat( &_b ); } /* finds intrinsic and extrinsic camera parameters from a few views of known calibration pattern */ CV_IMPL void cvCalibrateCamera2( const CvMat* obj_points, const CvMat* img_points, const CvMat* point_counts, CvSize image_size, CvMat* A, CvMat* dist_coeffs, CvMat* r_vecs, CvMat* t_vecs, int flags ) { double alpha_smooth = 0.4; CvMat *counts = 0, *_M = 0, *_m = 0; CvMat *_Ji = 0, *_Je = 0, *_JtJ = 0, *_JtErr = 0, *_JtJW = 0, *_JtJV = 0; CvMat *_param = 0, *_param_innov = 0, *_err = 0; CV_FUNCNAME( "cvCalibrateCamera2" ); __BEGIN__; double a[9]; CvMat _a = cvMat( 3, 3, CV_64F, a ), _k; CvMat _Mi, _mi, _ri, _ti, _part; CvMat _dpdr, _dpdt, _dpdf, _dpdc, _dpdk; CvMat _sr_part = cvMat( 1, 3, CV_64F ), _st_part = cvMat( 1, 3, CV_64F ), _r_part, _t_part; int i, j, pos, iter, img_count, count = 0, max_count = 0, total = 0, param_count; int r_depth = 0, t_depth = 0, r_step = 0, t_step = 0, cn, dims; int output_r_matrices = 0; double aspect_ratio = 0.; if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(img_points) || !CV_IS_MAT(point_counts) || !CV_IS_MAT(A) || !CV_IS_MAT(dist_coeffs) ) CV_ERROR( CV_StsBadArg, "One of required vector arguments is not a valid matrix" ); if( image_size.width <= 0 || image_size.height <= 0 ) CV_ERROR( CV_StsOutOfRange, "image width and height must be positive" ); if( CV_MAT_TYPE(point_counts->type) != CV_32SC1 || point_counts->rows != 1 && point_counts->cols != 1 ) CV_ERROR( CV_StsUnsupportedFormat, "the array of point counters must be 1-dimensional integer vector" ); CV_CALL( counts = cvCreateMat( point_counts->rows, point_counts->width, CV_32SC1 )); cvCopy( point_counts, counts ); img_count = counts->rows + counts->cols - 1; if( r_vecs ) { r_depth = CV_MAT_DEPTH(r_vecs->type); r_step = r_vecs->rows == 1 ? 3*CV_ELEM_SIZE(r_depth) : r_vecs->step; cn = CV_MAT_CN(r_vecs->type); if( !CV_IS_MAT(r_vecs) || r_depth != CV_32F && r_depth != CV_64F || (r_vecs->rows != img_count || r_vecs->cols*cn != 3 && r_vecs->cols*cn != 9) && (r_vecs->rows != 1 || r_vecs->cols != img_count || cn != 3) ) CV_ERROR( CV_StsBadArg, "the output array of rotation vectors must be 3-channel " "1xn or nx1 array or 1-channel nx3 or nx9 array, where n is the number of views" ); output_r_matrices = r_vecs->rows == img_count && r_vecs->cols*cn == 9; } if( t_vecs ) { t_depth = CV_MAT_DEPTH(t_vecs->type); t_step = t_vecs->rows == 1 ? 3*CV_ELEM_SIZE(t_depth) : t_vecs->step; cn = CV_MAT_CN(t_vecs->type); if( !CV_IS_MAT(t_vecs) || t_depth != CV_32F && t_depth != CV_64F || (t_vecs->rows != img_count || t_vecs->cols*cn != 3) && (t_vecs->rows != 1 || t_vecs->cols != img_count || cn != 3) ) CV_ERROR( CV_StsBadArg, "the output array of translation vectors must be 3-channel " "1xn or nx1 array or 1-channel nx3 array, where n is the number of views" ); } if( CV_MAT_TYPE(A->type) != CV_32FC1 && CV_MAT_TYPE(A->type) != CV_64FC1 || A->rows != 3 || A->cols != 3 ) CV_ERROR( CV_StsBadArg, "Intrinsic parameters must be 3x3 floating-point matrix" ); if( CV_MAT_TYPE(dist_coeffs->type) != CV_32FC1 && CV_MAT_TYPE(dist_coeffs->type) != CV_64FC1 || (dist_coeffs->rows != 4 || dist_coeffs->cols != 1) && (dist_coeffs->cols != 4 || dist_coeffs->rows != 1)) CV_ERROR( CV_StsBadArg, "Distortion coefficients must be 4x1 or 1x4 floating-point matrix" ); for( i = 0; i < img_count; i++ ) { int temp_count = counts->data.i[i]; if( temp_count < 4 ) { char buf[100]; sprintf( buf, "The number of points in the view #%d is <4", i ); CV_ERROR( CV_StsOutOfRange, buf ); } max_count = MAX( max_count, temp_count ); total += temp_count; } dims = CV_MAT_CN(obj_points->type)*(obj_points->rows == 1 ? 1 : obj_points->cols); if( CV_MAT_DEPTH(obj_points->type) != CV_32F && CV_MAT_DEPTH(obj_points->type) != CV_64F || (obj_points->rows != total || dims != 3 && dims != 2) && (obj_points->rows != 1 || obj_points->cols != total || (dims != 3 && dims != 2)) ) CV_ERROR( CV_StsBadArg, "Object points must be 1xn or nx1, 2- or 3-channel matrix, " "or nx3 or nx2 single-channel matrix" ); cn = CV_MAT_CN(img_points->type); if( CV_MAT_DEPTH(img_points->type) != CV_32F && CV_MAT_DEPTH(img_points->type) != CV_64F || (img_points->rows != total || img_points->cols*cn != 2) && (img_points->rows != 1 || img_points->cols != total || cn != 2) ) CV_ERROR( CV_StsBadArg, "Image points must be 1xn or nx1, 2-channel matrix, " "or nx2 single-channel matrix" ); CV_CALL( _M = cvCreateMat( 1, total, CV_64FC3 )); CV_CALL( _m = cvCreateMat( 1, total, CV_64FC2 )); CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); CV_CALL( cvConvertPointsHomogenious( img_points, _m )); param_count = 8 + img_count*6; CV_CALL( _param = cvCreateMat( param_count, 1, CV_64FC1 )); CV_CALL( _param_innov = cvCreateMat( param_count, 1, CV_64FC1 )); CV_CALL( _JtJ = cvCreateMat( param_count, param_count, CV_64FC1 )); CV_CALL( _JtErr = cvCreateMat( param_count, 1, CV_64FC1 )); CV_CALL( _JtJW = cvCreateMat( param_count, 1, CV_64FC1 )); CV_CALL( _JtJV = cvCreateMat( param_count, param_count, CV_64FC1 )); CV_CALL( _Ji = cvCreateMat( max_count*2, 8, CV_64FC1 )); CV_CALL( _Je = cvCreateMat( max_count*2, 6, CV_64FC1 )); CV_CALL( _err = cvCreateMat( max_count*2, 1, CV_64FC1 )); cvGetCols( _Je, &_dpdr, 0, 3 ); cvGetCols( _Je, &_dpdt, 3, 6 ); cvGetCols( _Ji, &_dpdf, 0, 2 ); cvGetCols( _Ji, &_dpdc, 2, 4 ); cvGetCols( _Ji, &_dpdk, 4, flags & CV_CALIB_ZERO_TANGENT_DIST ? 6 : 8 ); cvZero( _Ji ); // 1. initialize intrinsic parameters if( flags & CV_CALIB_USE_INTRINSIC_GUESS ) { cvConvert( A, &_a ); if( a[0] <= 0 || a[4] <= 0 ) CV_ERROR( CV_StsOutOfRange, "Focal length (fx and fy) must be positive" ); if( a[2] < 0 || a[2] >= image_size.width || a[5] < 0 || a[5] >= image_size.height ) CV_ERROR( CV_StsOutOfRange, "Principal point must be within the image" ); if( fabs(a[1]) > 1e-5 ) CV_ERROR( CV_StsOutOfRange, "Non-zero skew is not supported by the function" ); if( fabs(a[3]) > 1e-5 || fabs(a[6]) > 1e-5 || fabs(a[7]) > 1e-5 || fabs(a[8]-1) > 1e-5 ) CV_ERROR( CV_StsOutOfRange, "The intrinsic matrix must have [fx 0 cx; 0 fy cy; 0 0 1] shape" ); a[1] = a[3] = a[6] = a[7] = 0.; a[8] = 1.; if( flags & CV_CALIB_FIX_ASPECT_RATIO ) aspect_ratio = a[0]/a[4]; } else { if( dims == 3 ) { CvScalar mean, sdv; cvAvgSdv( _M, &mean, &sdv ); if( fabs(mean.val[2]) > 1e-5 && fabs(mean.val[2] - 1) > 1e-5 || fabs(sdv.val[2]) > 1e-5 ) CV_ERROR( CV_StsBadArg, "For non-planar calibration rigs the initial intrinsic matrix must be specified" ); } for( i = 0; i < total; i++ ) ((CvPoint3D64f*)(_M->data.db + i*3))->z = 0.; if( flags & CV_CALIB_FIX_ASPECT_RATIO ) { aspect_ratio = cvmGet(A,0,0); aspect_ratio /= cvmGet(A,1,1); if( aspect_ratio < 0.01 || aspect_ratio > 100 ) CV_ERROR( CV_StsOutOfRange, "The specified aspect ratio (=a(0,0)/a(1,1)) is incorrect" ); } icvInitIntrinsicParams2D( _M, _m, counts, image_size, &_a, aspect_ratio ); } _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, CV_64FC1, _param->data.db + 4 ); cvZero( &_k ); // 2. initialize extrinsic parameters for( i = 0, pos = 0; i < img_count; i++, pos += count ) { count = counts->data.i[i]; _ri = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 ); _ti = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 + 3 ); cvGetCols( _M, &_Mi, pos, pos + count ); cvGetCols( _m, &_mi, pos, pos + count ); cvFindExtrinsicCameraParams2( &_Mi, &_mi, &_a, &_k, &_ri, &_ti ); } _param->data.db[0] = a[0]; _param->data.db[1] = a[4]; _param->data.db[2] = a[2]; _param->data.db[3] = a[5]; // 3. run the optimization for( iter = 0; iter < 30; iter++ ) { double* jj = _JtJ->data.db; double change; for( i = 0, pos = 0; i < img_count; i++, pos += count ) { count = counts->data.i[i]; _ri = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6); _ti = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 + 3); cvGetCols( _M, &_Mi, pos, pos + count ); _mi = cvMat( count*2, 1, CV_64FC1, _m->data.db + pos*2 ); _dpdr.rows = _dpdt.rows = _dpdf.rows = _dpdc.rows = _dpdk.rows = count*2; _err->cols = 1; _err->rows = count*2; cvReshape( _err, _err, 2, count ); cvProjectPoints2( &_Mi, &_ri, &_ti, &_a, &_k, _err, &_dpdr, &_dpdt, &_dpdf, flags & CV_CALIB_FIX_PRINCIPAL_POINT ? 0 : &_dpdc, &_dpdk ); // alter dpdf in case if only one of the focal // parameters (fy) is independent variable if( flags & CV_CALIB_FIX_ASPECT_RATIO ) for( j = 0; j < count; j++ ) { double* dpdf_j = (double*)(_dpdf.data.ptr + j*_dpdf.step*2); dpdf_j[1] = dpdf_j[0]*aspect_ratio; dpdf_j[0] = 0.; } cvReshape( _err, _err, 1, count*2 ); cvSub( &_mi, _err, _err ); _Je->rows = _Ji->rows = count*2; cvGetSubRect( _JtJ, &_part, cvRect(0,0,8,8) ); cvGEMM( _Ji, _Ji, 1, &_part, i > 0, &_part, CV_GEMM_A_T ); cvGetSubRect( _JtJ, &_part, cvRect(8+i*6,8+i*6,6,6) ); cvMulTransposed( _Je, &_part, 1 ); cvGetSubRect( _JtJ, &_part, cvRect(8+i*6,0,6,8) ); cvGEMM( _Ji, _Je, 1, 0, 0, &_part, CV_GEMM_A_T ); cvGetRows( _JtErr, &_part, 0, 8 ); cvGEMM( _Ji, _err, 1, &_part, i > 0, &_part, CV_GEMM_A_T ); cvGetRows( _JtErr, &_part, 8 + i*6, 8 + (i+1)*6 ); cvGEMM( _Je, _err, 1, 0, 0, &_part, CV_GEMM_A_T ); } // make the matrix JtJ exactly symmetrical and add missing zeros for( i = 0; i < param_count; i++ ) { int mj = i < 8 ? param_count : ((i - 8)/6)*6 + 14; for( j = i+1; j < mj; j++ ) jj[j*param_count + i] = jj[i*param_count + j]; for( ; j < param_count; j++ ) jj[j*param_count + i] = jj[i*param_count + j] = 0; } cvSVD( _JtJ, _JtJW, 0, _JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); cvSVBkSb( _JtJW, _JtJV, _JtJV, _JtErr, _param_innov, CV_SVD_U_T + CV_SVD_V_T ); cvScale( _param_innov, _param_innov, 1. - pow(1. - alpha_smooth, iter + 1.) ); cvGetRows( _param_innov, &_part, 0, 4 ); change = cvNorm( &_part ); cvGetRows( _param, &_part, 0, 4 ); change /= cvNorm( &_part ); if( flags & CV_CALIB_FIX_PRINCIPAL_POINT ) _param_innov->data.db[2] = _param_innov->data.db[3] = 0.; if( flags & CV_CALIB_ZERO_TANGENT_DIST ) _param_innov->data.db[6] = _param_innov->data.db[7] = 0.; cvAdd( _param, _param_innov, _param ); if( flags & CV_CALIB_FIX_ASPECT_RATIO ) _param->data.db[0] = _param->data.db[1]*aspect_ratio; a[0] = _param->data.db[0]; a[4] = _param->data.db[1]; a[2] = _param->data.db[2]; a[5] = _param->data.db[3]; if( change < FLT_EPSILON ) break; } cvConvert( &_a, A ); cvConvert( &_k, dist_coeffs ); _r_part = cvMat( output_r_matrices ? 3 : 1, 3, r_depth ); _t_part = cvMat( 1, 3, t_depth ); for( i = 0; i < img_count; i++ ) { if( r_vecs ) { _sr_part.data.db = _param->data.db + 8 + i*6; _r_part.data.ptr = r_vecs->data.ptr + i*r_step; if( !output_r_matrices ) cvConvert( &_sr_part, &_r_part ); else { cvRodrigues2( &_sr_part, &_a ); cvConvert( &_a, &_r_part ); } } if( t_vecs ) { _st_part.data.db = _param->data.db + 8 + i*6 + 3; _t_part.data.ptr = t_vecs->data.ptr + i*t_step; cvConvert( &_st_part, &_t_part ); } } __END__; cvReleaseMat( &counts ); cvReleaseMat( &_M ); cvReleaseMat( &_m ); cvReleaseMat( &_param ); cvReleaseMat( &_param_innov ); cvReleaseMat( &_JtJ ); cvReleaseMat( &_JtErr ); cvReleaseMat( &_JtJW ); cvReleaseMat( &_JtJV ); cvReleaseMat( &_Ji ); cvReleaseMat( &_Je ); cvReleaseMat( &_err ); } /* End of file. */