From d6bf209bb3a4188009463999d212932f1cd934ae Mon Sep 17 00:00:00 2001 From: edgarriba Date: Mon, 6 Oct 2014 10:28:04 +0200 Subject: [PATCH] Updating for N=2 --- modules/calib3d/src/upnp.cpp | 628 +++++++++++++++++++---------------- modules/calib3d/src/upnp.h | 16 +- 2 files changed, 355 insertions(+), 289 deletions(-) diff --git a/modules/calib3d/src/upnp.cpp b/modules/calib3d/src/upnp.cpp index 440471a1e..66081e00c 100644 --- a/modules/calib3d/src/upnp.cpp +++ b/modules/calib3d/src/upnp.cpp @@ -2,21 +2,10 @@ #include "upnp.h" #include -void printMat(cv::Mat &mat) -{ - cout << mat.rows << "x" << mat.cols << endl; - for (int i = 0; i < mat.rows; ++i) { - cout << "["; - for (int j = 0; j < mat.cols; ++j) { - cout << mat.at(i,j) << ","; - } - cout << "];" << endl; - } -} upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints) { if (cameraMatrix.depth() == CV_32F) - init_camera_parameters(cameraMatrix); + init_camera_parameters(cameraMatrix); else init_camera_parameters(cameraMatrix); @@ -47,67 +36,67 @@ upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& i upnp::~upnp() { - if (A1) - delete[] A1; - if (A2) - delete[] A2; + if (A1) + delete[] A1; + if (A2) + delete[] A2; } double upnp::compute_pose(cv::Mat& R, cv::Mat& t) { - choose_control_points(); - compute_alphas(); + choose_control_points(); + compute_alphas(); - CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F); + CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F); - for(int i = 0; i < number_of_correspondences; i++) - { - fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]); - } + for(int i = 0; i < number_of_correspondences; i++) + { + fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]); + } - double mtm[12 * 12], d[12], ut[12 * 12]; - CvMat MtM = cvMat(12, 12, CV_64F, mtm); - CvMat D = cvMat(12, 1, CV_64F, d); - CvMat Ut = cvMat(12, 12, CV_64F, ut); + double mtm[12 * 12], d[12], ut[12 * 12]; + CvMat MtM = cvMat(12, 12, CV_64F, mtm); + CvMat D = cvMat(12, 1, CV_64F, d); + CvMat Ut = cvMat(12, 12, CV_64F, ut); - cvMulTransposed(M, &MtM, 1); - cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T); - cvReleaseMat(&M); + cvMulTransposed(M, &MtM, 1); + cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T); + cvReleaseMat(&M); - double l_6x12[6 * 12], rho[6]; - CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12); - CvMat Rho = cvMat(6, 1, CV_64F, rho); + double l_6x12[6 * 12], rho[6]; + CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12); + CvMat Rho = cvMat(6, 1, CV_64F, rho); - compute_L_6x12(ut, l_6x12); - compute_rho(rho); + compute_L_6x12(ut, l_6x12); + compute_rho(rho); - double Betas[4][4], Efs[4][1], rep_errors[4]; - double Rs[4][3][3], ts[4][3]; + double Betas[3][4], Efs[3][1], rep_errors[3]; + double Rs[3][3][3], ts[3][3]; - find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]); - gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]); - rep_errors[1] = compute_R_and_t(ut, Betas[1], Efs[1], Rs[1], ts[1]); + find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]); + gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]); + rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]); - find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]); - //gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]); - //rep_errors[2] = compute_R_and_t(ut, Betas[2], Efs[2], Rs[2], ts[2]); + find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]); + gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]); + rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]); - int N = 1; - //if (rep_errors[2] < rep_errors[1]) N = 2; - //if (rep_errors[3] < rep_errors[N]) N = 3; + int N = 1; + if (rep_errors[2] < rep_errors[1]) N = 2; - cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t); - cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R); + cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t); + cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R); + fu = fv = Efs[N][0]; - return Efs[N][0]; + return fu; } void upnp::copy_R_and_t(const double R_src[3][3], const double t_src[3], - double R_dst[3][3], double t_dst[3]) + double R_dst[3][3], double t_dst[3]) { for(int i = 0; i < 3; i++) { for(int j = 0; j < 3; j++) - R_dst[i][j] = R_src[i][j]; + R_dst[i][j] = R_src[i][j]; t_dst[i] = t_src[i]; } } @@ -177,7 +166,7 @@ void upnp::solve_for_sign(void) if (pcs[2] < 0.0) { for(int i = 0; i < 4; i++) for(int j = 0; j < 3; j++) - ccs[i][j] = -ccs[i][j]; + ccs[i][j] = -ccs[i][j]; for(int i = 0; i < number_of_correspondences; i++) { pcs[3 * i ] = -pcs[3 * i]; @@ -187,10 +176,10 @@ void upnp::solve_for_sign(void) } } -double upnp::compute_R_and_t(const double * ut, const double * betas, const double * efs, - double R[3][3], double t[3]) +double upnp::compute_R_and_t(const double * ut, const double * betas, + double R[3][3], double t[3]) { - compute_ccs(betas, efs, ut); + compute_ccs(betas, ut); compute_pcs(); solve_for_sign(); @@ -221,27 +210,27 @@ double upnp::reprojection_error(const double R[3][3], const double t[3]) void upnp::choose_control_points() { - for (int i = 0; i < 4; ++i) - cws[i][0] = cws[i][1] = cws[i][2] = 0; + for (int i = 0; i < 4; ++i) + cws[i][0] = cws[i][1] = cws[i][2] = 0; cws[0][0] = cws[1][1] = cws[2][2] = 1.; } void upnp::compute_alphas() { - cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws); - cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws.front()); - cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas.front()); + cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws); + cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws[0]); + cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas[0]); - cv::Mat CC_ = CC.clone().t(); - cv::Mat PC_ = PC.clone().t(); + cv::Mat CC_ = CC.clone().t(); + cv::Mat PC_ = PC.clone().t(); - cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F); - cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F); + cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F); + cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F); - CC_.push_back(row14); - PC_.push_back(row1n); + CC_.push_back(row14); + PC_.push_back(row1n); - ALPHAS = cv::Mat( CC_.inv() * PC_ ).t(); + ALPHAS = cv::Mat( CC_.inv() * PC_ ).t(); } void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, const double v) @@ -260,20 +249,20 @@ void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, c } } -void upnp::compute_ccs(const double * betas, const double * f, const double * ut) +void upnp::compute_ccs(const double * betas, const double * ut) { - for(int i = 0; i < 4; ++i) - ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f; + for(int i = 0; i < 4; ++i) + ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f; - int N = 4; - for(int i = 0; i < N; ++i) { - const double * v = ut + 12 * (9 + i); - for(int j = 0; j < 4; ++j) - for(int k = 0; k < 3; ++k) - ccs[j][k] += betas[i] * v[3 * j + k]; // be careful with that - } + int N = 4; + for(int i = 0; i < N; ++i) { + const double * v = ut + 12 * (9 + i); + for(int j = 0; j < 4; ++j) + for(int k = 0; k < 3; ++k) + ccs[j][k] += betas[i] * v[3 * j + k]; + } - for (int i = 0; i < 4; ++i) ccs[i][2] *= f[0]; + for (int i = 0; i < 4; ++i) ccs[i][2] *= fu; } void upnp::compute_pcs(void) @@ -289,177 +278,245 @@ void upnp::compute_pcs(void) void upnp::find_betas_and_focal_approx_1(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs) { - cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12); - cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db); + cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12); + cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db); - cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 ); - cv::Mat Dt = D.t(); + cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 ); + cv::Mat Dt = D.t(); - cv::Mat A = Dt * D; - cv::Mat b = Dt * dsq; + cv::Mat A = Dt * D; + cv::Mat b = Dt * dsq; - cv::Mat x = cv::Mat(2, 1, CV_64F); - cv::solve(A, b, x); + cv::Mat x = cv::Mat(2, 1, CV_64F); + cv::solve(A, b, x); - betas[0] = std::sqrt( std::abs( x.at(0) ) ); - betas[1] = betas[2] = betas[3] = 0; + betas[0] = std::sqrt( std::abs( x.at(0) ) ); + betas[1] = betas[2] = betas[3] = 0; - efs[0] = std::sqrt( std::abs( x.at(1) ) ) / betas[0]; + efs[0] = std::sqrt( std::abs( x.at(1) ) ) / betas[0]; } void upnp::find_betas_and_focal_approx_2(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs) { - cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12); - cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12); - cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db); + cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12); + cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12); + cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db); - cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); // OKAY + cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); - cv::Mat A = D; - cv::Mat b = dsq; + cv::Mat A = D; + cv::Mat b = dsq; - cv::Mat x = cv::Mat(6, 1, CV_64F); + double x[6]; + cv::Mat X = cv::Mat(6, 1, CV_64F, x); - cv::solve(A, b, x, cv::DECOMP_QR); + cv::solve(A, b, X, cv::DECOMP_QR); - betas[0] = std::sqrt( std::abs( x.at(0) ) ); - betas[1] = std::sqrt( std::abs( x.at(2) ) * ( x.at(2) < 0 ) ? -1 : ( x.at(2) > 0 ) ? 1 : 0 ); - betas[2] = betas[3] = 0; + double solutions[18][3]; + generate_all_possible_solutions_for_f_unk(x, solutions); + + // find solution with minimum reprojection error + double min_error = std::numeric_limits::max(); + int min_sol = 0; + for (int i = 0; i < 18; ++i) { + + betas[3] = solutions[i][0]; + betas[2] = solutions[i][1]; + betas[1] = betas[0] = 0; + fu = fv = solutions[i][2]; + + double Rs[3][3], ts[3]; + double error_i = compute_R_and_t( Ut->data.db, betas, Rs, ts); + + if( error_i < min_error) + { + min_error = error_i; + min_sol = i; + } +} + + betas[0] = solutions[min_sol][0]; + betas[1] = solutions[min_sol][1]; + betas[2] = betas[3] = 0; + + efs[0] = solutions[min_sol][2]; } cv::Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1) { - cv::Mat P = cv::Mat(6, 2, CV_64F); + cv::Mat P = cv::Mat(6, 2, CV_64F); - double m[13]; - for (int i = 1; i < 13; ++i) m[i] = M1.at(i-1); + double m[13]; + for (int i = 1; i < 13; ++i) m[i] = M1.at(i-1); - double t1 = std::pow( m[4], 2 ); - double t4 = std::pow( m[1], 2 ); - double t5 = std::pow( m[5], 2 ); - double t8 = std::pow( m[2], 2 ); - double t10 = std::pow( m[6], 2 ); - double t13 = std::pow( m[3], 2 ); - double t15 = std::pow( m[7], 2 ); - double t18 = std::pow( m[8], 2 ); - double t22 = std::pow( m[9], 2 ); - double t26 = std::pow( m[10], 2 ); - double t29 = std::pow( m[11], 2 ); - double t33 = std::pow( m[12], 2 ); + double t1 = std::pow( m[4], 2 ); + double t4 = std::pow( m[1], 2 ); + double t5 = std::pow( m[5], 2 ); + double t8 = std::pow( m[2], 2 ); + double t10 = std::pow( m[6], 2 ); + double t13 = std::pow( m[3], 2 ); + double t15 = std::pow( m[7], 2 ); + double t18 = std::pow( m[8], 2 ); + double t22 = std::pow( m[9], 2 ); + double t26 = std::pow( m[10], 2 ); + double t29 = std::pow( m[11], 2 ); + double t33 = std::pow( m[12], 2 ); - P.at(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8; - P.at(0,1) = t10 - 2 * m[6] * m[3] + t13; - P.at(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8; - P.at(1,1) = t22 - 2 * m[9] * m[3] + t13; - P.at(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8; - P.at(2,1) = t33 - 2 * m[12] * m[3] + t13; - P.at(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5; - P.at(3,1) = t22 - 2 * m[9] * m[6] + t10; - P.at(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5; - P.at(4,1) = t33 - 2 * m[12] * m[6] + t10; - P.at(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18; - P.at(5,1) = t33 - 2 * m[12] * m[9] + t22; + P.at(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8; + P.at(0,1) = t10 - 2 * m[6] * m[3] + t13; + P.at(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8; + P.at(1,1) = t22 - 2 * m[9] * m[3] + t13; + P.at(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8; + P.at(2,1) = t33 - 2 * m[12] * m[3] + t13; + P.at(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5; + P.at(3,1) = t22 - 2 * m[9] * m[6] + t10; + P.at(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5; + P.at(4,1) = t33 - 2 * m[12] * m[6] + t10; + P.at(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18; + P.at(5,1) = t33 - 2 * m[12] * m[9] + t22; - return P; + return P; } cv::Mat upnp::compute_constraint_distance_3param_6eq_6unk_f_unk(const cv::Mat& M1, const cv::Mat& M2) { - cv::Mat P = cv::Mat(6, 6, CV_64F); + cv::Mat P = cv::Mat(6, 6, CV_64F); - double m[3][13]; - for (int i = 1; i < 13; ++i) - { - m[1][i] = M1.at(i-1); - m[2][i] = M2.at(i-1); - } + double m[3][13]; + for (int i = 1; i < 13; ++i) + { + m[1][i] = M1.at(i-1); + m[2][i] = M2.at(i-1); + } - double t1 = std::pow( m[1][4], 2 ); - double t2 = std::pow( m[1][1], 2 ); - double t7 = std::pow( m[1][5], 2 ); - double t8 = std::pow( m[1][2], 2 ); - double t11 = m[1][1] * m[2][1]; - double t12 = m[1][5] * m[2][5]; - double t15 = m[1][2] * m[2][2]; - double t16 = m[1][4] * m[2][4]; - double t19 = std::pow( m[2][4], 2 ); - double t22 = std::pow( m[2][2], 2 ); - double t23 = std::pow( m[2][1], 2 ); - double t24 = std::pow( m[2][5], 2 ); - double t28 = std::pow( m[1][6], 2 ); - double t29 = std::pow( m[1][3], 2 ); - double t34 = std::pow( m[1][3], 2 ); - double t36 = m[1][6] * m[2][6]; - double t40 = std::pow( m[2][6], 2 ); - double t41 = std::pow( m[2][3], 2 ); - double t47 = std::pow( m[1][7], 2 ); - double t48 = std::pow( m[1][8], 2 ); - double t52 = m[1][7] * m[2][7]; - double t55 = m[1][8] * m[2][8]; - double t59 = std::pow( m[2][8], 2 ); - double t62 = std::pow( m[2][7], 2 ); - double t64 = std::pow( m[1][9], 2 ); - double t68 = m[1][9] * m[2][9]; - double t74 = std::pow( m[2][9], 2 ); - double t78 = std::pow( m[1][10], 2 ); - double t79 = std::pow( m[1][11], 2 ); - double t84 = m[1][10] * m[2][10]; - double t87 = m[1][11] * m[2][11]; - double t90 = std::pow( m[2][10], 2 ); - double t95 = std::pow( m[2][11], 2 ); - double t99 = std::pow( m[1][12], 2 ); - double t101 = m[1][12] * m[2][12]; - double t105 = std::pow( m[2][12], 2 ); + double t1 = std::pow( m[1][4], 2 ); + double t2 = std::pow( m[1][1], 2 ); + double t7 = std::pow( m[1][5], 2 ); + double t8 = std::pow( m[1][2], 2 ); + double t11 = m[1][1] * m[2][1]; + double t12 = m[1][5] * m[2][5]; + double t15 = m[1][2] * m[2][2]; + double t16 = m[1][4] * m[2][4]; + double t19 = std::pow( m[2][4], 2 ); + double t22 = std::pow( m[2][2], 2 ); + double t23 = std::pow( m[2][1], 2 ); + double t24 = std::pow( m[2][5], 2 ); + double t28 = std::pow( m[1][6], 2 ); + double t29 = std::pow( m[1][3], 2 ); + double t34 = std::pow( m[1][3], 2 ); + double t36 = m[1][6] * m[2][6]; + double t40 = std::pow( m[2][6], 2 ); + double t41 = std::pow( m[2][3], 2 ); + double t47 = std::pow( m[1][7], 2 ); + double t48 = std::pow( m[1][8], 2 ); + double t52 = m[1][7] * m[2][7]; + double t55 = m[1][8] * m[2][8]; + double t59 = std::pow( m[2][8], 2 ); + double t62 = std::pow( m[2][7], 2 ); + double t64 = std::pow( m[1][9], 2 ); + double t68 = m[1][9] * m[2][9]; + double t74 = std::pow( m[2][9], 2 ); + double t78 = std::pow( m[1][10], 2 ); + double t79 = std::pow( m[1][11], 2 ); + double t84 = m[1][10] * m[2][10]; + double t87 = m[1][11] * m[2][11]; + double t90 = std::pow( m[2][10], 2 ); + double t95 = std::pow( m[2][11], 2 ); + double t99 = std::pow( m[1][12], 2 ); + double t101 = m[1][12] * m[2][12]; + double t105 = std::pow( m[2][12], 2 ); - P.at(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8; - P.at(0,1) = -2 * m[2][4] * m[1][1] + 2 * t11 + 2 * t12 - 2 * m[1][4] * m[2][1] - 2 * m[2][5] * m[1][2] + 2 * t15 + 2 * t16 - 2 * m[1][5] * m[2][2]; - P.at(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2]; - P.at(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3]; - P.at(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36; - P.at(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41; + P.at(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8; + P.at(0,1) = -2 * m[2][4] * m[1][1] + 2 * t11 + 2 * t12 - 2 * m[1][4] * m[2][1] - 2 * m[2][5] * m[1][2] + 2 * t15 + 2 * t16 - 2 * m[1][5] * m[2][2]; + P.at(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2]; + P.at(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3]; + P.at(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36; + P.at(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41; - P.at(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2; - P.at(1,1) = 2 * t15 - 2 * m[1][8] * m[2][2] - 2 * m[2][8] * m[1][2] + 2 * t52 - 2 * m[1][7] * m[2][1] - 2 * m[2][7] * m[1][1] + 2 * t55 + 2 * t11; - P.at(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62; - P.at(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3]; - P.at(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3]; - P.at(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41; + P.at(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2; + P.at(1,1) = 2 * t15 - 2 * m[1][8] * m[2][2] - 2 * m[2][8] * m[1][2] + 2 * t52 - 2 * m[1][7] * m[2][1] - 2 * m[2][7] * m[1][1] + 2 * t55 + 2 * t11; + P.at(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62; + P.at(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3]; + P.at(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3]; + P.at(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41; - P.at(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1]; - P.at(2,1) = 2 * t15 - 2 * m[1][11] * m[2][2] + 2 * t84 - 2 * m[1][10] * m[2][1] - 2 * m[2][10] * m[1][1] + 2 * t87 - 2 * m[2][11] * m[1][2]+ 2 * t11; - P.at(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95; - P.at(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29; - P.at(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3]; - P.at(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3]; + P.at(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1]; + P.at(2,1) = 2 * t15 - 2 * m[1][11] * m[2][2] + 2 * t84 - 2 * m[1][10] * m[2][1] - 2 * m[2][10] * m[1][1] + 2 * t87 - 2 * m[2][11] * m[1][2]+ 2 * t11; + P.at(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95; + P.at(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29; + P.at(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3]; + P.at(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3]; - P.at(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47; - P.at(3,1) = 2 * t16 - 2 * m[1][7] * m[2][4] + 2 * t55 + 2 * t52 - 2 * m[1][8] * m[2][5] - 2 * m[2][8] * m[1][5] - 2 * m[2][7] * m[1][4] + 2 * t12; - P.at(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59; - P.at(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28; - P.at(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6]; - P.at(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6]; + P.at(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47; + P.at(3,1) = 2 * t16 - 2 * m[1][7] * m[2][4] + 2 * t55 + 2 * t52 - 2 * m[1][8] * m[2][5] - 2 * m[2][8] * m[1][5] - 2 * m[2][7] * m[1][4] + 2 * t12; + P.at(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59; + P.at(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28; + P.at(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6]; + P.at(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6]; - P.at(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5]; - P.at(4,1) = 2 * t84 - 2 * m[1][11] * m[2][5] - 2 * m[1][10] * m[2][4] + 2 * t16 - 2 * m[2][11] * m[1][5] + 2 * t87 - 2 * m[2][10] * m[1][4] + 2 * t12; - P.at(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90; - P.at(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99; - P.at(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6]; - P.at(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40; + P.at(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5]; + P.at(4,1) = 2 * t84 - 2 * m[1][11] * m[2][5] - 2 * m[1][10] * m[2][4] + 2 * t16 - 2 * m[2][11] * m[1][5] + 2 * t87 - 2 * m[2][10] * m[1][4] + 2 * t12; + P.at(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90; + P.at(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99; + P.at(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6]; + P.at(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40; - P.at(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8]; - P.at(5,1) = 2 * t84 + 2 * t87 - 2 * m[2][11] * m[1][8] - 2 * m[1][10] * m[2][7] - 2 * m[2][10] * m[1][7] + 2 * t55 + 2 * t52 - 2 * m[1][11] * m[2][8]; - P.at(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95; - P.at(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99; - P.at(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101; - P.at(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74; + P.at(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8]; + P.at(5,1) = 2 * t84 + 2 * t87 - 2 * m[2][11] * m[1][8] - 2 * m[1][10] * m[2][7] - 2 * m[2][10] * m[1][7] + 2 * t55 + 2 * t52 - 2 * m[1][11] * m[2][8]; + P.at(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95; + P.at(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99; + P.at(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101; + P.at(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74; - return P; + return P; +} + +void upnp::generate_all_possible_solutions_for_f_unk(const double betas[5], double solutions[18][3]) +{ + int matrix_to_resolve[18][9] = { + { 2, 0, 0, 1, 1, 0, 2, 0, 2 }, { 2, 0, 0, 1, 1, 0, 1, 1, 2 }, + { 2, 0, 0, 1, 1, 0, 0, 2, 2 }, { 2, 0, 0, 0, 2, 0, 2, 0, 2 }, + { 2, 0, 0, 0, 2, 0, 1, 1, 2 }, { 2, 0, 0, 0, 2, 0, 0, 2, 2 }, + { 2, 0, 0, 2, 0, 2, 1, 1, 2 }, { 2, 0, 0, 2, 0, 2, 0, 2, 2 }, + { 2, 0, 0, 1, 1, 2, 0, 2, 2 }, { 1, 1, 0, 0, 2, 0, 2, 0, 2 }, + { 1, 1, 0, 0, 2, 0, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 }, + { 1, 1, 0, 2, 0, 2, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 }, + { 1, 1, 0, 1, 1, 2, 0, 2, 2 }, { 0, 2, 0, 2, 0, 2, 1, 1, 2 }, + { 0, 2, 0, 2, 0, 2, 0, 2, 2 }, { 0, 2, 0, 1, 1, 2, 0, 2, 2 } + }; + + int combination[18][3] = { + { 1, 2, 4 }, { 1, 2, 5 }, { 1, 2, 6 }, { 1, 3, 4 }, + { 1, 3, 5 }, { 1, 3, 6 }, { 1, 4, 5 }, { 1, 4, 6 }, + { 1, 5, 6 }, { 2, 3, 4 }, { 2, 3, 5 }, { 2, 3, 6 }, + { 2, 4, 5 }, { 2, 4, 6 }, { 2, 5, 6 }, { 3, 4, 5 }, + { 3, 4, 6 }, { 3, 5, 6 } + }; + + for (int i = 0; i < 18; ++i) { + double matrix[9], independent_term[3]; + cv::Mat M = cv::Mat(3, 3, CV_64F, matrix); + cv::Mat I = cv::Mat(3, 1, CV_64F, independent_term); + cv::Mat S = cv::Mat(1, 3, CV_64F); + + for (int j = 0; j < 9; ++j) matrix[j] = (double)matrix_to_resolve[i][j]; + + independent_term[0] = std::log( std::abs( betas[ combination[i][0]-1 ] ) ); + independent_term[1] = std::log( std::abs( betas[ combination[i][1]-1 ] ) ); + independent_term[2] = std::log( std::abs( betas[ combination[i][2]-1 ] ) ); + + cv::exp( cv::Mat(M.inv() * I), S); + + solutions[i][0] = S.at(0); + solutions[i][1] = S.at(1) * sign( betas[1] ); + solutions[i][2] = std::abs( S.at(2) ); + } } void upnp::gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double betas[4], double * f) { - const int iterations_number = 100; + const int iterations_number = 50; double a[6*4], b[6], x[4]; CvMat A = cvMat(6, 4, CV_64F, a); @@ -471,41 +528,43 @@ void upnp::gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double betas[4] compute_A_and_b_gauss_newton(L_6x12->data.db, Rho->data.db, betas, &A, &B, f[0]); qr_solve(&A, &B, &X); for(int i = 0; i < 3; i++) - betas[i] += x[i]; + betas[i] += x[i]; f[0] += x[3]; } if (f[0] < 0) f[0] = -f[0]; + fu = fv = f[0]; + } void upnp::compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho, - const double betas[4], CvMat * A, CvMat * b, double const f) + const double betas[4], CvMat * A, CvMat * b, double const f) { for(int i = 0; i < 6; i++) { const double * rowL = l_6x12 + i * 12; double * rowA = A->data.db + i * 4; - rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[2] * betas[2] + f*f * ( 2 * rowL[6]*betas[0] + rowL[7]*betas[1] + rowL[8]*betas[2] ); - rowA[1] = rowL[1] * betas[0] + 2 * rowL[3] * betas[1] + rowL[4] * betas[2] + f*f * ( rowL[7]*betas[0] + 2 * rowL[9]*betas[1] + rowL[10]*betas[2] ); - rowA[2] = rowL[2] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + f*f * ( rowL[8]*betas[0] + rowL[10]*betas[1] + 2 * rowL[11]*betas[2] ); + rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[2] * betas[2] + f*f * ( 2 * rowL[6]*betas[0] + rowL[7]*betas[1] + rowL[8]*betas[2] ); + rowA[1] = rowL[1] * betas[0] + 2 * rowL[3] * betas[1] + rowL[4] * betas[2] + f*f * ( rowL[7]*betas[0] + 2 * rowL[9]*betas[1] + rowL[10]*betas[2] ); + rowA[2] = rowL[2] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + f*f * ( rowL[8]*betas[0] + rowL[10]*betas[1] + 2 * rowL[11]*betas[2] ); rowA[3] = 2*f * ( rowL[6]*betas[0]*betas[0] + rowL[7]*betas[0]*betas[1] + rowL[8]*betas[0]*betas[2] + rowL[9]*betas[1]*betas[1] + rowL[10]*betas[1]*betas[2] + rowL[11]*betas[2]*betas[2] ) ; cvmSet(b, i, 0, rho[i] - - ( - rowL[0] * betas[0] * betas[0] + - rowL[1] * betas[0] * betas[1] + - rowL[2] * betas[0] * betas[2] + - rowL[3] * betas[1] * betas[1] + - rowL[4] * betas[1] * betas[2] + - rowL[5] * betas[2] * betas[2] + - f*f * rowL[6] * betas[0] * betas[0] + - f*f * rowL[7] * betas[0] * betas[1] + - f*f * rowL[8] * betas[0] * betas[2] + - f*f * rowL[9] * betas[1] * betas[1] + - f*f * rowL[10] * betas[1] * betas[2] + - f*f * rowL[11] * betas[2] * betas[2] - )); + ( + rowL[0] * betas[0] * betas[0] + + rowL[1] * betas[0] * betas[1] + + rowL[2] * betas[0] * betas[2] + + rowL[3] * betas[1] * betas[1] + + rowL[4] * betas[1] * betas[2] + + rowL[5] * betas[2] * betas[2] + + f*f * rowL[6] * betas[0] * betas[0] + + f*f * rowL[7] * betas[0] * betas[1] + + f*f * rowL[8] * betas[0] * betas[2] + + f*f * rowL[9] * betas[1] * betas[1] + + f*f * rowL[10] * betas[1] * betas[2] + + f*f * rowL[11] * betas[2] * betas[2] + )); } } @@ -529,8 +588,8 @@ void upnp::compute_L_6x12(const double * ut, double * l_6x12) b++; if (b > 3) { - a++; - b = a + 1; + a++; + b = a + 1; } } } @@ -539,29 +598,29 @@ void upnp::compute_L_6x12(const double * ut, double * l_6x12) double * row = l_6x12 + 12 * i; row[0] = dotXY(dv[0][i], dv[0][i]); - row[1] = 2.0f * dotXY(dv[0][i], dv[1][i]); - row[2] = dotXY(dv[1][i], dv[1][i]); - row[3] = 2.0f * dotXY(dv[0][i], dv[2][i]); - row[4] = 2.0f * dotXY(dv[1][i], dv[2][i]); - row[5] = dotXY(dv[2][i], dv[2][i]); + row[1] = 2.0f * dotXY(dv[0][i], dv[1][i]); + row[2] = dotXY(dv[1][i], dv[1][i]); + row[3] = 2.0f * dotXY(dv[0][i], dv[2][i]); + row[4] = 2.0f * dotXY(dv[1][i], dv[2][i]); + row[5] = dotXY(dv[2][i], dv[2][i]); - row[6] = dotZ(dv[0][i], dv[0][i]); - row[7] = 2.0f * dotZ(dv[0][i], dv[1][i]); - row[8] = 2.0f * dotZ(dv[0][i], dv[2][i]); - row[9] = dotZ(dv[1][i], dv[1][i]); - row[10] = 2.0f * dotZ(dv[1][i], dv[2][i]); - row[11] = dotZ(dv[2][i], dv[2][i]); + row[6] = dotZ(dv[0][i], dv[0][i]); + row[7] = 2.0f * dotZ(dv[0][i], dv[1][i]); + row[8] = 2.0f * dotZ(dv[0][i], dv[2][i]); + row[9] = dotZ(dv[1][i], dv[1][i]); + row[10] = 2.0f * dotZ(dv[1][i], dv[2][i]); + row[11] = dotZ(dv[2][i], dv[2][i]); } } void upnp::compute_rho(double * rho) { - rho[0] = dist2(cws[0], cws[1]); - rho[1] = dist2(cws[0], cws[2]); - rho[2] = dist2(cws[0], cws[3]); - rho[3] = dist2(cws[1], cws[2]); - rho[4] = dist2(cws[1], cws[3]); - rho[5] = dist2(cws[2], cws[3]); + rho[0] = dist2(cws[0], cws[1]); + rho[1] = dist2(cws[0], cws[2]); + rho[2] = dist2(cws[0], cws[3]); + rho[3] = dist2(cws[1], cws[2]); + rho[4] = dist2(cws[1], cws[3]); + rho[5] = dist2(cws[2], cws[3]); } double upnp::dist2(const double * p1, const double * p2) @@ -587,6 +646,11 @@ double upnp::dotZ(const double * v1, const double * v2) return v1[2] * v2[2]; } +double upnp::sign(const double v) +{ + return ( v < 0 ) ? -1. : ( v > 0 ) ? 1. : 0.; +} + void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) { const int nr = A->rows; @@ -622,35 +686,35 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) } else { - double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta; - for(int i = k; i < nr; i++) - { - *ppAik2 *= inv_eta; - sum2 += *ppAik2 * *ppAik2; - ppAik2 += nc; - } - double sigma = sqrt(sum2); - if (*ppAkk < 0) - sigma = -sigma; - *ppAkk += sigma; - A1[k] = sigma * *ppAkk; - A2[k] = -eta * sigma; - for(int j = k + 1; j < nc; j++) - { - double * ppAik = ppAkk, sum = 0; - for(int i = k; i < nr; i++) - { - sum += *ppAik * ppAik[j - k]; - ppAik += nc; - } - double tau = sum / A1[k]; - ppAik = ppAkk; - for(int i = k; i < nr; i++) - { - ppAik[j - k] -= tau * *ppAik; - ppAik += nc; - } - } + double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta; + for(int i = k; i < nr; i++) + { + *ppAik2 *= inv_eta; + sum2 += *ppAik2 * *ppAik2; + ppAik2 += nc; + } + double sigma = sqrt(sum2); + if (*ppAkk < 0) + sigma = -sigma; + *ppAkk += sigma; + A1[k] = sigma * *ppAkk; + A2[k] = -eta * sigma; + for(int j = k + 1; j < nc; j++) + { + double * ppAik = ppAkk, sum = 0; + for(int i = k; i < nr; i++) + { + sum += *ppAik * ppAik[j - k]; + ppAik += nc; + } + double tau = sum / A1[k]; + ppAik = ppAkk; + for(int i = k; i < nr; i++) + { + ppAik[j - k] -= tau * *ppAik; + ppAik += nc; + } + } } ppAkk += nc + 1; } @@ -662,15 +726,15 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) double * ppAij = ppAjj, tau = 0; for(int i = j; i < nr; i++) { - tau += *ppAij * pb[i]; - ppAij += nc; + tau += *ppAij * pb[i]; + ppAij += nc; } tau /= A1[j]; ppAij = ppAjj; for(int i = j; i < nr; i++) { - pb[i] -= tau * *ppAij; - ppAij += nc; + pb[i] -= tau * *ppAij; + ppAij += nc; } ppAjj += nc + 1; } @@ -684,8 +748,8 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) for(int j = i + 1; j < nc; j++) { - sum += *ppAij * pX[j]; - ppAij++; + sum += *ppAij * pX[j]; + ppAij++; } pX[i] = (pb[i] - sum) / A2[i]; } diff --git a/modules/calib3d/src/upnp.h b/modules/calib3d/src/upnp.h index 39d21bf8e..9a061bd3d 100644 --- a/modules/calib3d/src/upnp.h +++ b/modules/calib3d/src/upnp.h @@ -28,12 +28,12 @@ private: { for(int i = 0; i < number_of_correspondences; i++) { - pws[3 * i ] = opoints.at(0,i).x; - pws[3 * i + 1] = opoints.at(0,i).y; - pws[3 * i + 2] = opoints.at(0,i).z; + pws[3 * i ] = opoints.at(0,i).x; + pws[3 * i + 1] = opoints.at(0,i).y; + pws[3 * i + 2] = opoints.at(0,i).z; - us[2 * i ] = ipoints.at(0,i).x; - us[2 * i + 1] = ipoints.at(0,i).y; + us[2 * i ] = ipoints.at(0,i).x; + us[2 * i + 1] = ipoints.at(0,i).y; } } @@ -41,7 +41,7 @@ private: void choose_control_points(); void compute_alphas(); void fill_M(CvMat * M, const int row, const double * alphas, const double u, const double v); - void compute_ccs(const double * betas, const double * f, const double * ut); + void compute_ccs(const double * betas, const double * ut); void compute_pcs(void); void solve_for_sign(void); @@ -52,7 +52,9 @@ private: cv::Mat compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1); cv::Mat compute_constraint_distance_3param_6eq_6unk_f_unk(const cv::Mat& M1, const cv::Mat& M2); + void generate_all_possible_solutions_for_f_unk(const double betas_[5], double solutions[18][3]); + double sign(const double v); double dot(const double * v1, const double * v2); double dotXY(const double * v1, const double * v2); double dotZ(const double * v1, const double * v2); @@ -65,7 +67,7 @@ private: void compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho, const double cb[4], CvMat * A, CvMat * b, double const f); - double compute_R_and_t(const double * ut, const double * betas, const double * efs, + double compute_R_and_t(const double * ut, const double * betas, double R[3][3], double t[3]); void estimate_R_and_t(double R[3][3], double t[3]);