Updating for N=2
This commit is contained in:
edgarriba
@@ -2,21 +2,10 @@
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#include "upnp.h"
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#include <limits>
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void printMat(cv::Mat &mat)
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{
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cout << mat.rows << "x" << mat.cols << endl;
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for (int i = 0; i < mat.rows; ++i) {
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cout << "[";
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for (int j = 0; j < mat.cols; ++j) {
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cout << mat.at<double>(i,j) << ",";
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}
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cout << "];" << endl;
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}
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}
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upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints)
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{
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if (cameraMatrix.depth() == CV_32F)
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init_camera_parameters<float>(cameraMatrix);
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init_camera_parameters<float>(cameraMatrix);
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else
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init_camera_parameters<double>(cameraMatrix);
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@@ -47,67 +36,67 @@ upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& i
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upnp::~upnp()
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{
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if (A1)
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delete[] A1;
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if (A2)
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delete[] A2;
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if (A1)
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delete[] A1;
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if (A2)
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delete[] A2;
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}
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double upnp::compute_pose(cv::Mat& R, cv::Mat& t)
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{
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choose_control_points();
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compute_alphas();
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choose_control_points();
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compute_alphas();
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CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
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CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
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for(int i = 0; i < number_of_correspondences; i++)
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{
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fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
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}
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for(int i = 0; i < number_of_correspondences; i++)
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{
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fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
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}
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double mtm[12 * 12], d[12], ut[12 * 12];
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CvMat MtM = cvMat(12, 12, CV_64F, mtm);
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CvMat D = cvMat(12, 1, CV_64F, d);
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CvMat Ut = cvMat(12, 12, CV_64F, ut);
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double mtm[12 * 12], d[12], ut[12 * 12];
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CvMat MtM = cvMat(12, 12, CV_64F, mtm);
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CvMat D = cvMat(12, 1, CV_64F, d);
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CvMat Ut = cvMat(12, 12, CV_64F, ut);
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cvMulTransposed(M, &MtM, 1);
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cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
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cvReleaseMat(&M);
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cvMulTransposed(M, &MtM, 1);
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cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
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cvReleaseMat(&M);
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double l_6x12[6 * 12], rho[6];
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CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12);
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CvMat Rho = cvMat(6, 1, CV_64F, rho);
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double l_6x12[6 * 12], rho[6];
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CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12);
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CvMat Rho = cvMat(6, 1, CV_64F, rho);
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compute_L_6x12(ut, l_6x12);
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compute_rho(rho);
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compute_L_6x12(ut, l_6x12);
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compute_rho(rho);
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double Betas[4][4], Efs[4][1], rep_errors[4];
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double Rs[4][3][3], ts[4][3];
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double Betas[3][4], Efs[3][1], rep_errors[3];
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double Rs[3][3][3], ts[3][3];
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find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]);
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gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]);
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rep_errors[1] = compute_R_and_t(ut, Betas[1], Efs[1], Rs[1], ts[1]);
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find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]);
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gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]);
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rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
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find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]);
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//gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]);
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//rep_errors[2] = compute_R_and_t(ut, Betas[2], Efs[2], Rs[2], ts[2]);
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find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]);
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gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]);
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rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
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int N = 1;
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//if (rep_errors[2] < rep_errors[1]) N = 2;
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//if (rep_errors[3] < rep_errors[N]) N = 3;
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int N = 1;
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if (rep_errors[2] < rep_errors[1]) N = 2;
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cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
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cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
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cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
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cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
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fu = fv = Efs[N][0];
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return Efs[N][0];
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return fu;
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}
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void upnp::copy_R_and_t(const double R_src[3][3], const double t_src[3],
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double R_dst[3][3], double t_dst[3])
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double R_dst[3][3], double t_dst[3])
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{
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for(int i = 0; i < 3; i++) {
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for(int j = 0; j < 3; j++)
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R_dst[i][j] = R_src[i][j];
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R_dst[i][j] = R_src[i][j];
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t_dst[i] = t_src[i];
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}
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}
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@@ -177,7 +166,7 @@ void upnp::solve_for_sign(void)
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if (pcs[2] < 0.0) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 3; j++)
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ccs[i][j] = -ccs[i][j];
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ccs[i][j] = -ccs[i][j];
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for(int i = 0; i < number_of_correspondences; i++) {
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pcs[3 * i ] = -pcs[3 * i];
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@@ -187,10 +176,10 @@ void upnp::solve_for_sign(void)
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}
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}
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double upnp::compute_R_and_t(const double * ut, const double * betas, const double * efs,
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double R[3][3], double t[3])
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double upnp::compute_R_and_t(const double * ut, const double * betas,
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double R[3][3], double t[3])
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{
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compute_ccs(betas, efs, ut);
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compute_ccs(betas, ut);
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compute_pcs();
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solve_for_sign();
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@@ -221,27 +210,27 @@ double upnp::reprojection_error(const double R[3][3], const double t[3])
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void upnp::choose_control_points()
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{
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for (int i = 0; i < 4; ++i)
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cws[i][0] = cws[i][1] = cws[i][2] = 0;
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for (int i = 0; i < 4; ++i)
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cws[i][0] = cws[i][1] = cws[i][2] = 0;
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cws[0][0] = cws[1][1] = cws[2][2] = 1.;
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}
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void upnp::compute_alphas()
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{
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cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws);
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cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws.front());
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cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas.front());
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cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws);
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cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws[0]);
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cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas[0]);
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cv::Mat CC_ = CC.clone().t();
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cv::Mat PC_ = PC.clone().t();
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cv::Mat CC_ = CC.clone().t();
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cv::Mat PC_ = PC.clone().t();
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cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F);
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cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F);
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cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F);
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cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F);
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CC_.push_back(row14);
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PC_.push_back(row1n);
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CC_.push_back(row14);
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PC_.push_back(row1n);
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ALPHAS = cv::Mat( CC_.inv() * PC_ ).t();
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ALPHAS = cv::Mat( CC_.inv() * PC_ ).t();
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}
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void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, const double v)
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@@ -260,20 +249,20 @@ void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, c
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}
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}
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void upnp::compute_ccs(const double * betas, const double * f, const double * ut)
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void upnp::compute_ccs(const double * betas, const double * ut)
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{
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for(int i = 0; i < 4; ++i)
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ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
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for(int i = 0; i < 4; ++i)
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ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
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int N = 4;
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for(int i = 0; i < N; ++i) {
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const double * v = ut + 12 * (9 + i);
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for(int j = 0; j < 4; ++j)
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for(int k = 0; k < 3; ++k)
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ccs[j][k] += betas[i] * v[3 * j + k]; // be careful with that
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}
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int N = 4;
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for(int i = 0; i < N; ++i) {
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const double * v = ut + 12 * (9 + i);
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for(int j = 0; j < 4; ++j)
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for(int k = 0; k < 3; ++k)
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ccs[j][k] += betas[i] * v[3 * j + k];
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}
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for (int i = 0; i < 4; ++i) ccs[i][2] *= f[0];
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for (int i = 0; i < 4; ++i) ccs[i][2] *= fu;
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}
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void upnp::compute_pcs(void)
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@@ -289,177 +278,245 @@ void upnp::compute_pcs(void)
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void upnp::find_betas_and_focal_approx_1(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs)
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{
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cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
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cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
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cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
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cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
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cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 );
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cv::Mat Dt = D.t();
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cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 );
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cv::Mat Dt = D.t();
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cv::Mat A = Dt * D;
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cv::Mat b = Dt * dsq;
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cv::Mat A = Dt * D;
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cv::Mat b = Dt * dsq;
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cv::Mat x = cv::Mat(2, 1, CV_64F);
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cv::solve(A, b, x);
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cv::Mat x = cv::Mat(2, 1, CV_64F);
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cv::solve(A, b, x);
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betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
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betas[1] = betas[2] = betas[3] = 0;
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betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
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betas[1] = betas[2] = betas[3] = 0;
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efs[0] = std::sqrt( std::abs( x.at<double>(1) ) ) / betas[0];
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efs[0] = std::sqrt( std::abs( x.at<double>(1) ) ) / betas[0];
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}
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void upnp::find_betas_and_focal_approx_2(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs)
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{
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cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12);
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cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
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cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
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cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12);
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cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
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cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
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cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); // OKAY
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cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 );
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cv::Mat A = D;
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cv::Mat b = dsq;
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cv::Mat A = D;
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cv::Mat b = dsq;
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cv::Mat x = cv::Mat(6, 1, CV_64F);
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double x[6];
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cv::Mat X = cv::Mat(6, 1, CV_64F, x);
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cv::solve(A, b, x, cv::DECOMP_QR);
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cv::solve(A, b, X, cv::DECOMP_QR);
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betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
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betas[1] = std::sqrt( std::abs( x.at<double>(2) ) * ( x.at<double>(2) < 0 ) ? -1 : ( x.at<double>(2) > 0 ) ? 1 : 0 );
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betas[2] = betas[3] = 0;
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double solutions[18][3];
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generate_all_possible_solutions_for_f_unk(x, solutions);
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// find solution with minimum reprojection error
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double min_error = std::numeric_limits<double>::max();
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int min_sol = 0;
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for (int i = 0; i < 18; ++i) {
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betas[3] = solutions[i][0];
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betas[2] = solutions[i][1];
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betas[1] = betas[0] = 0;
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fu = fv = solutions[i][2];
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double Rs[3][3], ts[3];
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double error_i = compute_R_and_t( Ut->data.db, betas, Rs, ts);
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if( error_i < min_error)
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{
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min_error = error_i;
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min_sol = i;
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}
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}
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betas[0] = solutions[min_sol][0];
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betas[1] = solutions[min_sol][1];
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betas[2] = betas[3] = 0;
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efs[0] = solutions[min_sol][2];
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}
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cv::Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1)
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{
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cv::Mat P = cv::Mat(6, 2, CV_64F);
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cv::Mat P = cv::Mat(6, 2, CV_64F);
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double m[13];
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for (int i = 1; i < 13; ++i) m[i] = M1.at<double>(i-1);
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double m[13];
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for (int i = 1; i < 13; ++i) m[i] = M1.at<double>(i-1);
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double t1 = std::pow( m[4], 2 );
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double t4 = std::pow( m[1], 2 );
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double t5 = std::pow( m[5], 2 );
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double t8 = std::pow( m[2], 2 );
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double t10 = std::pow( m[6], 2 );
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double t13 = std::pow( m[3], 2 );
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double t15 = std::pow( m[7], 2 );
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double t18 = std::pow( m[8], 2 );
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double t22 = std::pow( m[9], 2 );
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double t26 = std::pow( m[10], 2 );
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double t29 = std::pow( m[11], 2 );
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double t33 = std::pow( m[12], 2 );
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double t1 = std::pow( m[4], 2 );
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double t4 = std::pow( m[1], 2 );
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double t5 = std::pow( m[5], 2 );
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double t8 = std::pow( m[2], 2 );
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double t10 = std::pow( m[6], 2 );
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double t13 = std::pow( m[3], 2 );
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double t15 = std::pow( m[7], 2 );
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double t18 = std::pow( m[8], 2 );
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double t22 = std::pow( m[9], 2 );
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double t26 = std::pow( m[10], 2 );
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double t29 = std::pow( m[11], 2 );
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double t33 = std::pow( m[12], 2 );
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P.at<double>(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8;
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P.at<double>(0,1) = t10 - 2 * m[6] * m[3] + t13;
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P.at<double>(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8;
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P.at<double>(1,1) = t22 - 2 * m[9] * m[3] + t13;
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P.at<double>(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8;
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P.at<double>(2,1) = t33 - 2 * m[12] * m[3] + t13;
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P.at<double>(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5;
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P.at<double>(3,1) = t22 - 2 * m[9] * m[6] + t10;
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P.at<double>(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5;
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P.at<double>(4,1) = t33 - 2 * m[12] * m[6] + t10;
|
||||
P.at<double>(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18;
|
||||
P.at<double>(5,1) = t33 - 2 * m[12] * m[9] + t22;
|
||||
P.at<double>(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8;
|
||||
P.at<double>(0,1) = t10 - 2 * m[6] * m[3] + t13;
|
||||
P.at<double>(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8;
|
||||
P.at<double>(1,1) = t22 - 2 * m[9] * m[3] + t13;
|
||||
P.at<double>(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8;
|
||||
P.at<double>(2,1) = t33 - 2 * m[12] * m[3] + t13;
|
||||
P.at<double>(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5;
|
||||
P.at<double>(3,1) = t22 - 2 * m[9] * m[6] + t10;
|
||||
P.at<double>(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5;
|
||||
P.at<double>(4,1) = t33 - 2 * m[12] * m[6] + t10;
|
||||
P.at<double>(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18;
|
||||
P.at<double>(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<double>(i-1);
|
||||
m[2][i] = M2.at<double>(i-1);
|
||||
}
|
||||
double m[3][13];
|
||||
for (int i = 1; i < 13; ++i)
|
||||
{
|
||||
m[1][i] = M1.at<double>(i-1);
|
||||
m[2][i] = M2.at<double>(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<double>(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8;
|
||||
P.at<double>(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<double>(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2];
|
||||
P.at<double>(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3];
|
||||
P.at<double>(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36;
|
||||
P.at<double>(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41;
|
||||
P.at<double>(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8;
|
||||
P.at<double>(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<double>(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2];
|
||||
P.at<double>(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3];
|
||||
P.at<double>(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36;
|
||||
P.at<double>(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41;
|
||||
|
||||
P.at<double>(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2;
|
||||
P.at<double>(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<double>(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62;
|
||||
P.at<double>(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3];
|
||||
P.at<double>(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3];
|
||||
P.at<double>(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41;
|
||||
P.at<double>(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2;
|
||||
P.at<double>(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<double>(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62;
|
||||
P.at<double>(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3];
|
||||
P.at<double>(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3];
|
||||
P.at<double>(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41;
|
||||
|
||||
P.at<double>(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1];
|
||||
P.at<double>(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<double>(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95;
|
||||
P.at<double>(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29;
|
||||
P.at<double>(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3];
|
||||
P.at<double>(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3];
|
||||
P.at<double>(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1];
|
||||
P.at<double>(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<double>(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95;
|
||||
P.at<double>(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29;
|
||||
P.at<double>(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3];
|
||||
P.at<double>(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3];
|
||||
|
||||
P.at<double>(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47;
|
||||
P.at<double>(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<double>(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59;
|
||||
P.at<double>(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28;
|
||||
P.at<double>(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6];
|
||||
P.at<double>(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6];
|
||||
P.at<double>(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47;
|
||||
P.at<double>(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<double>(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59;
|
||||
P.at<double>(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28;
|
||||
P.at<double>(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6];
|
||||
P.at<double>(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6];
|
||||
|
||||
P.at<double>(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5];
|
||||
P.at<double>(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<double>(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90;
|
||||
P.at<double>(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99;
|
||||
P.at<double>(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6];
|
||||
P.at<double>(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40;
|
||||
P.at<double>(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5];
|
||||
P.at<double>(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<double>(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90;
|
||||
P.at<double>(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99;
|
||||
P.at<double>(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6];
|
||||
P.at<double>(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40;
|
||||
|
||||
P.at<double>(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8];
|
||||
P.at<double>(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<double>(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95;
|
||||
P.at<double>(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99;
|
||||
P.at<double>(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101;
|
||||
P.at<double>(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74;
|
||||
P.at<double>(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8];
|
||||
P.at<double>(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<double>(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95;
|
||||
P.at<double>(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99;
|
||||
P.at<double>(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101;
|
||||
P.at<double>(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<double>(0);
|
||||
solutions[i][1] = S.at<double>(1) * sign( betas[1] );
|
||||
solutions[i][2] = std::abs( S.at<double>(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];
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user