From 84475ef1de1120efbc5d786832c83224b0723a2d Mon Sep 17 00:00:00 2001 From: edgarriba Date: Thu, 2 Oct 2014 16:43:50 +0200 Subject: [PATCH] UPNP code for N=1 --- modules/calib3d/src/upnp.cpp | 699 +++++++++++++++++++++++++++++++++++++++++++ modules/calib3d/src/upnp.h | 88 ++++++ 2 files changed, 787 insertions(+) create mode 100644 modules/calib3d/src/upnp.cpp create mode 100644 modules/calib3d/src/upnp.h diff --git a/modules/calib3d/src/upnp.cpp b/modules/calib3d/src/upnp.cpp new file mode 100644 index 0000000..6683681 --- /dev/null +++ b/modules/calib3d/src/upnp.cpp @@ -0,0 +1,699 @@ +#include "precomp.hpp" +#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); + else + init_camera_parameters(cameraMatrix); + + number_of_correspondences = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F)); + + pws.resize(3 * number_of_correspondences); + us.resize(2 * number_of_correspondences); + + if (opoints.depth() == ipoints.depth()) + { + if (opoints.depth() == CV_32F) + init_points(opoints, ipoints); + else + init_points(opoints, ipoints); + } + else if (opoints.depth() == CV_32F) + init_points(opoints, ipoints); + else + init_points(opoints, ipoints); + + alphas.resize(4 * number_of_correspondences); + pcs.resize(3 * number_of_correspondences); + + max_nr = 0; + A1 = NULL; + A2 = NULL; +} + +upnp::~upnp() +{ + if (A1) + delete[] A1; + if (A2) + delete[] A2; +} + +void upnp::compute_pose(cv::Mat& R, cv::Mat& t) +{ + choose_control_points(); + compute_alphas(); + + 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]); + } + + 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); + //check_positive_eigenvectors(ut); // same result + 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); + + 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]; + + 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_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]); + + int N = 1; + //if (rep_errors[2] < rep_errors[1]) N = 2; + //if (rep_errors[3] < rep_errors[N]) N = 3; + + cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t); + cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R); +} + +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]) +{ + for(int i = 0; i < 3; i++) { + for(int j = 0; j < 3; j++) + R_dst[i][j] = R_src[i][j]; + t_dst[i] = t_src[i]; + } +} + +void upnp::estimate_R_and_t(double R[3][3], double t[3]) +{ + double pc0[3], pw0[3]; + + pc0[0] = pc0[1] = pc0[2] = 0.0; + pw0[0] = pw0[1] = pw0[2] = 0.0; + + for(int i = 0; i < number_of_correspondences; i++) { + const double * pc = &pcs[3 * i]; + const double * pw = &pws[3 * i]; + + for(int j = 0; j < 3; j++) { + pc0[j] += pc[j]; + pw0[j] += pw[j]; + } + } + for(int j = 0; j < 3; j++) { + pc0[j] /= number_of_correspondences; + pw0[j] /= number_of_correspondences; + } + + double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3]; + CvMat ABt = cvMat(3, 3, CV_64F, abt); + CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d); + CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u); + CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v); + + cvSetZero(&ABt); + for(int i = 0; i < number_of_correspondences; i++) { + double * pc = &pcs[3 * i]; + double * pw = &pws[3 * i]; + + for(int j = 0; j < 3; j++) { + abt[3 * j ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]); + abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]); + abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]); + } + } + + cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A); + + for(int i = 0; i < 3; i++) + for(int j = 0; j < 3; j++) + R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j); + + const double det = + R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] - + R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1]; + + if (det < 0) { + R[2][0] = -R[2][0]; + R[2][1] = -R[2][1]; + R[2][2] = -R[2][2]; + } + + t[0] = pc0[0] - dot(R[0], pw0); + t[1] = pc0[1] - dot(R[1], pw0); + t[2] = pc0[2] - dot(R[2], pw0); +} + +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]; + + for(int i = 0; i < number_of_correspondences; i++) { + pcs[3 * i ] = -pcs[3 * i]; + pcs[3 * i + 1] = -pcs[3 * i + 1]; + pcs[3 * i + 2] = -pcs[3 * i + 2]; + } + } +} + +void upnp::check_positive_eigenvectors(double * ut) +{ + for (int i = 0; i < 12; ++i) + if (ut[12 * i] < 0.0) { + for (int j = 0; j < 12; ++j)ut[12 * i + j] = -ut[12 * i + j]; + } +} + +double upnp::compute_R_and_t(const double * ut, const double * betas, const double * efs, + double R[3][3], double t[3]) +{ + compute_ccs(betas, efs, ut); + compute_pcs(); + + solve_for_sign(); + + estimate_R_and_t(R, t); + + return reprojection_error(R, t); +} + +double upnp::reprojection_error(const double R[3][3], const double t[3]) +{ + double sum2 = 0.0; + + for(int i = 0; i < number_of_correspondences; i++) { + double * pw = &pws[3 * i]; + double Xc = dot(R[0], pw) + t[0]; + double Yc = dot(R[1], pw) + t[1]; + double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]); + double ue = uc + fu * Xc * inv_Zc; + double ve = vc + fv * Yc * inv_Zc; + double u = us[2 * i], v = us[2 * i + 1]; + + sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) ); + } + + return sum2 / number_of_correspondences; +} + +void upnp::choose_control_points() +{ + 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_ = 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); + + CC_.push_back(row14); + PC_.push_back(row1n); + + 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) +{ + double * M1 = M->data.db + row * 12; + double * M2 = M1 + 12; + + for(int i = 0; i < 4; i++) { + M1[3 * i ] = as[i] * fu; + M1[3 * i + 1] = 0.0; + M1[3 * i + 2] = as[i] * (uc - u); + + M2[3 * i ] = 0.0; + M2[3 * i + 1] = as[i] * fv; + M2[3 * i + 2] = as[i] * (vc - v); + } +} + +void upnp::compute_ccs(const double * betas, const double * f, const double * ut) +{ + 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 + } + + for (int i = 0; i < 4; ++i) ccs[i][2] *= f[0]; +} + +void upnp::compute_pcs(void) +{ + for(int i = 0; i < number_of_correspondences; i++) { + double * a = &alphas[0] + 4 * i; + double * pc = &pcs[0] + 3 * i; + + for(int j = 0; j < 3; j++) + pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j]; + } +} + +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 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 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; + + 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 D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); // OKAY + + cv::Mat A = D; + cv::Mat b = dsq; + + cv::Mat x = cv::Mat(6, 1, CV_64F); + + 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; +} + +cv::Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1) +{ + 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 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; + + 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); + + 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 ); + + 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(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(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; + + return P; +} + +void upnp::gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double betas[4], double * f) +{ + const int iterations_number = 100; + + double a[6*4], b[6], x[4]; + CvMat A = cvMat(6, 4, CV_64F, a); + CvMat B = cvMat(6, 1, CV_64F, b); + CvMat X = cvMat(4, 1, CV_64F, x); + + for(int k = 0; k < iterations_number; k++) + { + 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]; + f[0] += x[3]; + } + + if (f[0] < 0) f[0] = -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) +{ + + 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[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] + )); + } +} + +void upnp::compute_L_6x12(const double * ut, double * l_6x12) +{ + int N = 3; + const double * v[N]; + + v[0] = ut + 12 * 9; + v[1] = ut + 12 * 10; + v[2] = ut + 12 * 11; + + double dv[N][6][3]; + + for(int i = 0; i < N; i++) { + int a = 0, b = 1; + for(int j = 0; j < 6; j++) { + dv[i][j][0] = v[i][3 * a ] - v[i][3 * b]; + dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1]; + dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2]; + + b++; + if (b > 3) { + a++; + b = a + 1; + } + } + } + + for(int i = 0; i < 6; i++) { + 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[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]); +} + +double upnp::dist2(const double * p1, const double * p2) +{ + return + (p1[0] - p2[0]) * (p1[0] - p2[0]) + + (p1[1] - p2[1]) * (p1[1] - p2[1]) + + (p1[2] - p2[2]) * (p1[2] - p2[2]); +} + +double upnp::dot(const double * v1, const double * v2) +{ + return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2]; +} + +double upnp::dotXY(const double * v1, const double * v2) +{ + return v1[0] * v2[0] + v1[1] * v2[1]; +} + +double upnp::dotZ(const double * v1, const double * v2) +{ + return v1[2] * v2[2]; +} + +void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) +{ + const int nr = A->rows; + const int nc = A->cols; + + if (max_nr != 0 && max_nr < nr) + { + delete [] A1; + delete [] A2; + } + if (max_nr < nr) + { + max_nr = nr; + A1 = new double[nr]; + A2 = new double[nr]; + } + + double * pA = A->data.db, * ppAkk = pA; + for(int k = 0; k < nc; k++) + { + double * ppAik1 = ppAkk, eta = fabs(*ppAik1); + for(int i = k + 1; i < nr; i++) + { + double elt = fabs(*ppAik1); + if (eta < elt) eta = elt; + ppAik1 += nc; + } + if (eta == 0) + { + A1[k] = A2[k] = 0.0; + //cerr << "God damnit, A is singular, this shouldn't happen." << endl; + return; + } + 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; + } + } + } + ppAkk += nc + 1; + } + + // b <- Qt b + double * ppAjj = pA, * pb = b->data.db; + for(int j = 0; j < nc; j++) + { + double * ppAij = ppAjj, tau = 0; + for(int i = j; i < nr; i++) + { + tau += *ppAij * pb[i]; + ppAij += nc; + } + tau /= A1[j]; + ppAij = ppAjj; + for(int i = j; i < nr; i++) + { + pb[i] -= tau * *ppAij; + ppAij += nc; + } + ppAjj += nc + 1; + } + + // X = R-1 b + double * pX = X->data.db; + pX[nc - 1] = pb[nc - 1] / A2[nc - 1]; + for(int i = nc - 2; i >= 0; i--) + { + double * ppAij = pA + i * nc + (i + 1), sum = 0; + + for(int j = i + 1; j < nc; j++) + { + 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 new file mode 100644 index 0000000..fce22bf --- /dev/null +++ b/modules/calib3d/src/upnp.h @@ -0,0 +1,88 @@ +#ifndef UPNP_H_ +#define UPNP_H_ + +#include "precomp.hpp" +#include "opencv2/core/core_c.h" +#include + +using namespace std; + +class upnp +{ +public: + upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints); + ~upnp(); + + void compute_pose(cv::Mat& R, cv::Mat& t); +private: + template + void init_camera_parameters(const cv::Mat& cameraMatrix) + { + uc = cameraMatrix.at (0, 2); + vc = cameraMatrix.at (1, 2); + fu = 1; + fv = 1; + } + template + void init_points(const cv::Mat& opoints, const cv::Mat& ipoints) + { + 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; + + us[2 * i ] = ipoints.at(0,i).x; + us[2 * i + 1] = ipoints.at(0,i).y; + } + } + + double reprojection_error(const double R[3][3], const double t[3]); + 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_pcs(void); + + void solve_for_sign(void); + void check_positive_eigenvectors(double * ut); + + void find_betas_and_focal_approx_1(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs); + void find_betas_and_focal_approx_2(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs); + void qr_solve(CvMat * A, CvMat * b, CvMat * X); + + 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); + + double dot(const double * v1, const double * v2); + double dotXY(const double * v1, const double * v2); + double dotZ(const double * v1, const double * v2); + double dist2(const double * p1, const double * p2); + + void compute_rho(double * rho); + void compute_L_6x12(const double * ut, double * l_6x12); + + void gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double current_betas[4], double * efs); + 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 R[3][3], double t[3]); + + void estimate_R_and_t(double R[3][3], double t[3]); + + void copy_R_and_t(const double R_dst[3][3], const double t_dst[3], + double R_src[3][3], double t_src[3]); + + + double uc, vc, fu, fv; + + std::vector pws, us, alphas, pcs; + int number_of_correspondences; + + double cws[4][3], ccs[4][3]; + int max_nr; + double * A1, * A2; +}; + +#endif // UPNP_H_ -- 2.7.4