From c5d8ec4ac04128fcb59c85317ede4e71b87bf408 Mon Sep 17 00:00:00 2001 From: Alexander Shishkov Date: Tue, 20 Dec 2011 11:33:12 +0000 Subject: [PATCH] first version of ePnP code --- .../calib3d/include/opencv2/calib3d/calib3d.hpp | 4 +- modules/calib3d/src/epnp.cpp | 744 +++++++++++++++++++++ modules/calib3d/src/epnp.h | 73 ++ 3 files changed, 820 insertions(+), 1 deletion(-) create mode 100644 modules/calib3d/src/epnp.cpp create mode 100644 modules/calib3d/src/epnp.h diff --git a/modules/calib3d/include/opencv2/calib3d/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d/calib3d.hpp index fae3111..889be59 100644 --- a/modules/calib3d/include/opencv2/calib3d/calib3d.hpp +++ b/modules/calib3d/include/opencv2/calib3d/calib3d.hpp @@ -393,7 +393,6 @@ CVAPI(void) cvReprojectImageTo3D( const CvArr* disparityImage, } ////////////////////////////////////////////////////////////////////////////////////////// - class CV_EXPORTS CvLevMarq { public: @@ -432,6 +431,9 @@ public: namespace cv { +CV_EXPORTS_W double ePnP( InputArray _opoints, InputArray _ipoints, + InputArray _cameraMatrix, InputArray _distCoeffs, + OutputArray _rvec, OutputArray _tvec); //! converts rotation vector to rotation matrix or vice versa using Rodrigues transformation CV_EXPORTS_W void Rodrigues(InputArray src, OutputArray dst, OutputArray jacobian=noArray()); diff --git a/modules/calib3d/src/epnp.cpp b/modules/calib3d/src/epnp.cpp new file mode 100644 index 0000000..cbbea01 --- /dev/null +++ b/modules/calib3d/src/epnp.cpp @@ -0,0 +1,744 @@ +#include +using namespace std; +#include "precomp.hpp" +#include "epnp.h" + +namespace cv +{ +double ePnP( InputArray _opoints, InputArray _ipoints, + InputArray _cameraMatrix, InputArray _distCoeffs, + OutputArray _rvec, OutputArray _tvec) +{ + Mat opoints = _opoints.getMat(), ipoints = _ipoints.getMat(); + int npoints = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F)); + CV_Assert( npoints >= 0 && npoints == std::max(ipoints.checkVector(2, CV_32F), ipoints.checkVector(2, CV_64F)) ); + Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat(); + + Mat undistortedPoints; + undistortPoints(ipoints, undistortedPoints, cameraMatrix, distCoeffs); + + epnp PnP; + PnP.set_internal_parameters(cameraMatrix.at (0, 2), cameraMatrix.at (1, 2), cameraMatrix.at (0, 0), cameraMatrix.at (1, 1)); + PnP.set_maximum_number_of_correspondences(npoints); + PnP.reset_correspondences(); + for(int i = 0; i < npoints; i++) { + PnP.add_correspondence(opoints.at(0,i).x, opoints.at(0,i).y, opoints.at(0,i).z, undistortedPoints.at(0,i).x* cameraMatrix.at (0, 0) + cameraMatrix.at (0, 2), + undistortedPoints.at(0,i).y* cameraMatrix.at (1, 1) + cameraMatrix.at (1, 2)); + } + double R_est[3][3], t_est[3]; + double error = PnP.compute_pose(R_est, t_est); + + _tvec.create(3,1,CV_64F); + _rvec.create(3,1,CV_64F); + Mat(3, 1, CV_64FC1, t_est).copyTo(_tvec.getMat()); + Rodrigues(Mat(3, 3, CV_64FC1, R_est), _rvec.getMat()); + return error; +} +} + +epnp::epnp(void) +{ + maximum_number_of_correspondences = 0; + number_of_correspondences = 0; + + pws = 0; + us = 0; + alphas = 0; + pcs = 0; +} + +epnp::~epnp() +{ + delete [] pws; + delete [] us; + delete [] alphas; + delete [] pcs; +} + +void epnp::set_internal_parameters(double uc, double vc, double fu, double fv) +{ + this->uc = uc; + this->vc = vc; + this->fu = fu; + this->fv = fv; +} + +void epnp::set_maximum_number_of_correspondences(int n) +{ + if (maximum_number_of_correspondences < n) { + if (pws != 0) delete [] pws; + if (us != 0) delete [] us; + if (alphas != 0) delete [] alphas; + if (pcs != 0) delete [] pcs; + + maximum_number_of_correspondences = n; + pws = new double[3 * maximum_number_of_correspondences]; + us = new double[2 * maximum_number_of_correspondences]; + alphas = new double[4 * maximum_number_of_correspondences]; + pcs = new double[3 * maximum_number_of_correspondences]; + } +} + +void epnp::reset_correspondences(void) +{ + number_of_correspondences = 0; +} + +void epnp::add_correspondence(double X, double Y, double Z, double u, double v) +{ + pws[3 * number_of_correspondences ] = X; + pws[3 * number_of_correspondences + 1] = Y; + pws[3 * number_of_correspondences + 2] = Z; + + us[2 * number_of_correspondences ] = u; + us[2 * number_of_correspondences + 1] = v; + + number_of_correspondences++; +} + +void epnp::choose_control_points(void) +{ + // Take C0 as the reference points centroid: + cws[0][0] = cws[0][1] = cws[0][2] = 0; + for(int i = 0; i < number_of_correspondences; i++) + for(int j = 0; j < 3; j++) + cws[0][j] += pws[3 * i + j]; + + for(int j = 0; j < 3; j++) + cws[0][j] /= number_of_correspondences; + + + // Take C1, C2, and C3 from PCA on the reference points: + CvMat * PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F); + + double pw0tpw0[3 * 3], dc[3], uct[3 * 3]; + CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0); + CvMat DC = cvMat(3, 1, CV_64F, dc); + CvMat UCt = cvMat(3, 3, CV_64F, uct); + + for(int i = 0; i < number_of_correspondences; i++) + for(int j = 0; j < 3; j++) + PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j]; + + cvMulTransposed(PW0, &PW0tPW0, 1); + cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T); + + cvReleaseMat(&PW0); + + for(int i = 1; i < 4; i++) { + double k = sqrt(dc[i - 1] / number_of_correspondences); + for(int j = 0; j < 3; j++) + cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j]; + } +} + +void epnp::compute_barycentric_coordinates(void) +{ + double cc[3 * 3], cc_inv[3 * 3]; + CvMat CC = cvMat(3, 3, CV_64F, cc); + CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv); + + for(int i = 0; i < 3; i++) + for(int j = 1; j < 4; j++) + cc[3 * i + j - 1] = cws[j][i] - cws[0][i]; + + cvInvert(&CC, &CC_inv, CV_SVD); + double * ci = cc_inv; + for(int i = 0; i < number_of_correspondences; i++) { + double * pi = pws + 3 * i; + double * a = alphas + 4 * i; + + for(int j = 0; j < 3; j++) + a[1 + j] = + ci[3 * j ] * (pi[0] - cws[0][0]) + + ci[3 * j + 1] * (pi[1] - cws[0][1]) + + ci[3 * j + 2] * (pi[2] - cws[0][2]); + a[0] = 1.0f - a[1] - a[2] - a[3]; + } +} + +void epnp::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 epnp::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++) { + const double * v = ut + 12 * (11 - i); + for(int j = 0; j < 4; j++) + for(int k = 0; k < 3; k++) + ccs[j][k] += betas[i] * v[3 * j + k]; + } +} + +void epnp::compute_pcs(void) +{ + for(int i = 0; i < number_of_correspondences; i++) { + double * a = alphas + 4 * i; + double * pc = pcs + 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]; + } +} + +double epnp::compute_pose(double R[3][3], double t[3]) +{ + choose_control_points(); + compute_barycentric_coordinates(); + + 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 + 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); + cvReleaseMat(&M); + + double l_6x10[6 * 10], rho[6]; + CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10); + CvMat Rho = cvMat(6, 1, CV_64F, rho); + + compute_L_6x10(ut, l_6x10); + compute_rho(rho); + + double Betas[4][4], rep_errors[4]; + double Rs[4][3][3], ts[4][3]; + + find_betas_approx_1(&L_6x10, &Rho, Betas[1]); + gauss_newton(&L_6x10, &Rho, Betas[1]); + rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]); + + find_betas_approx_2(&L_6x10, &Rho, Betas[2]); + gauss_newton(&L_6x10, &Rho, Betas[2]); + rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]); + + find_betas_approx_3(&L_6x10, &Rho, Betas[3]); + gauss_newton(&L_6x10, &Rho, Betas[3]); + rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]); + + int N = 1; + if (rep_errors[2] < rep_errors[1]) N = 2; + if (rep_errors[3] < rep_errors[N]) N = 3; + + copy_R_and_t(Rs[N], ts[N], R, t); + + return rep_errors[N]; +} + +void epnp::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]; + } +} + +double epnp::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 epnp::dot(const double * v1, const double * v2) +{ + return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2]; +} + +double epnp::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 epnp::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 epnp::print_pose(const double R[3][3], const double t[3]) +{ + cout << R[0][0] << " " << R[0][1] << " " << R[0][2] << " " << t[0] << endl; + cout << R[1][0] << " " << R[1][1] << " " << R[1][2] << " " << t[1] << endl; + cout << R[2][0] << " " << R[2][1] << " " << R[2][2] << " " << t[2] << endl; +} + +void epnp::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]; + } + } +} + +double epnp::compute_R_and_t(const double * ut, const double * betas, + double R[3][3], double t[3]) +{ + compute_ccs(betas, ut); + compute_pcs(); + + solve_for_sign(); + + estimate_R_and_t(R, t); + + return reprojection_error(R, t); +} + +// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] +// betas_approx_1 = [B11 B12 B13 B14] + +void epnp::find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho, + double * betas) +{ + double l_6x4[6 * 4], b4[4]; + CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4); + CvMat B4 = cvMat(4, 1, CV_64F, b4); + + for(int i = 0; i < 6; i++) { + cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0)); + cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1)); + cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3)); + cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6)); + } + + cvSolve(&L_6x4, Rho, &B4, CV_SVD); + + if (b4[0] < 0) { + betas[0] = sqrt(-b4[0]); + betas[1] = -b4[1] / betas[0]; + betas[2] = -b4[2] / betas[0]; + betas[3] = -b4[3] / betas[0]; + } else { + betas[0] = sqrt(b4[0]); + betas[1] = b4[1] / betas[0]; + betas[2] = b4[2] / betas[0]; + betas[3] = b4[3] / betas[0]; + } +} + +// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] +// betas_approx_2 = [B11 B12 B22 ] + +void epnp::find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho, + double * betas) +{ + double l_6x3[6 * 3], b3[3]; + CvMat L_6x3 = cvMat(6, 3, CV_64F, l_6x3); + CvMat B3 = cvMat(3, 1, CV_64F, b3); + + for(int i = 0; i < 6; i++) { + cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0)); + cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1)); + cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2)); + } + + cvSolve(&L_6x3, Rho, &B3, CV_SVD); + + if (b3[0] < 0) { + betas[0] = sqrt(-b3[0]); + betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0; + } else { + betas[0] = sqrt(b3[0]); + betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0; + } + + if (b3[1] < 0) betas[0] = -betas[0]; + + betas[2] = 0.0; + betas[3] = 0.0; +} + +// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] +// betas_approx_3 = [B11 B12 B22 B13 B23 ] + +void epnp::find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho, + double * betas) +{ + double l_6x5[6 * 5], b5[5]; + CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5); + CvMat B5 = cvMat(5, 1, CV_64F, b5); + + for(int i = 0; i < 6; i++) { + cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0)); + cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1)); + cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2)); + cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3)); + cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4)); + } + + cvSolve(&L_6x5, Rho, &B5, CV_SVD); + + if (b5[0] < 0) { + betas[0] = sqrt(-b5[0]); + betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0; + } else { + betas[0] = sqrt(b5[0]); + betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0; + } + if (b5[1] < 0) betas[0] = -betas[0]; + betas[2] = b5[3] / betas[0]; + betas[3] = 0.0; +} + +void epnp::compute_L_6x10(const double * ut, double * l_6x10) +{ + const double * v[4]; + + v[0] = ut + 12 * 11; + v[1] = ut + 12 * 10; + v[2] = ut + 12 * 9; + v[3] = ut + 12 * 8; + + double dv[4][6][3]; + + for(int i = 0; i < 4; 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_6x10 + 10 * i; + + row[0] = dot(dv[0][i], dv[0][i]); + row[1] = 2.0f * dot(dv[0][i], dv[1][i]); + row[2] = dot(dv[1][i], dv[1][i]); + row[3] = 2.0f * dot(dv[0][i], dv[2][i]); + row[4] = 2.0f * dot(dv[1][i], dv[2][i]); + row[5] = dot(dv[2][i], dv[2][i]); + row[6] = 2.0f * dot(dv[0][i], dv[3][i]); + row[7] = 2.0f * dot(dv[1][i], dv[3][i]); + row[8] = 2.0f * dot(dv[2][i], dv[3][i]); + row[9] = dot(dv[3][i], dv[3][i]); + } +} + +void epnp::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]); +} + +void epnp::compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho, + double betas[4], CvMat * A, CvMat * b) +{ + for(int i = 0; i < 6; i++) { + const double * rowL = l_6x10 + i * 10; + double * rowA = A->data.db + i * 4; + + rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[3] * betas[2] + rowL[6] * betas[3]; + rowA[1] = rowL[1] * betas[0] + 2 * rowL[2] * betas[1] + rowL[4] * betas[2] + rowL[7] * betas[3]; + rowA[2] = rowL[3] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + rowL[8] * betas[3]; + rowA[3] = rowL[6] * betas[0] + rowL[7] * betas[1] + rowL[8] * betas[2] + 2 * rowL[9] * betas[3]; + + cvmSet(b, i, 0, rho[i] - + ( + rowL[0] * betas[0] * betas[0] + + rowL[1] * betas[0] * betas[1] + + rowL[2] * betas[1] * betas[1] + + rowL[3] * betas[0] * betas[2] + + rowL[4] * betas[1] * betas[2] + + rowL[5] * betas[2] * betas[2] + + rowL[6] * betas[0] * betas[3] + + rowL[7] * betas[1] * betas[3] + + rowL[8] * betas[2] * betas[3] + + rowL[9] * betas[3] * betas[3] + )); + } +} + +void epnp::gauss_newton(const CvMat * L_6x10, const CvMat * Rho, + double betas[4]) +{ + const int iterations_number = 5; + + 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_6x10->data.db, Rho->data.db, + betas, &A, &B); + qr_solve(&A, &B, &X); + + for(int i = 0; i < 4; i++) + betas[i] += x[i]; + } +} + +void epnp::qr_solve(CvMat * A, CvMat * b, CvMat * X) +{ + static int max_nr = 0; + static double * A1, * A2; + + 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 * ppAik = ppAkk, eta = fabs(*ppAik); + for(int i = k + 1; i < nr; i++) { + double elt = fabs(*ppAik); + if (eta < elt) eta = elt; + ppAik += nc; + } + + if (eta == 0) { + A1[k] = A2[k] = 0.0; + cerr << "God damnit, A is singular, this shouldn't happen." << endl; + return; + } else { + double * ppAik = ppAkk, sum = 0.0, inv_eta = 1. / eta; + for(int i = k; i < nr; i++) { + *ppAik *= inv_eta; + sum += *ppAik * *ppAik; + ppAik += nc; + } + double sigma = sqrt(sum); + 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]; + } +} + + + +void epnp::relative_error(double & rot_err, double & transl_err, + const double Rtrue[3][3], const double ttrue[3], + const double Rest[3][3], const double test[3]) +{ + double qtrue[4], qest[4]; + + mat_to_quat(Rtrue, qtrue); + mat_to_quat(Rest, qest); + + double rot_err1 = sqrt((qtrue[0] - qest[0]) * (qtrue[0] - qest[0]) + + (qtrue[1] - qest[1]) * (qtrue[1] - qest[1]) + + (qtrue[2] - qest[2]) * (qtrue[2] - qest[2]) + + (qtrue[3] - qest[3]) * (qtrue[3] - qest[3]) ) / + sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]); + + double rot_err2 = sqrt((qtrue[0] + qest[0]) * (qtrue[0] + qest[0]) + + (qtrue[1] + qest[1]) * (qtrue[1] + qest[1]) + + (qtrue[2] + qest[2]) * (qtrue[2] + qest[2]) + + (qtrue[3] + qest[3]) * (qtrue[3] + qest[3]) ) / + sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]); + + rot_err = min(rot_err1, rot_err2); + + transl_err = + sqrt((ttrue[0] - test[0]) * (ttrue[0] - test[0]) + + (ttrue[1] - test[1]) * (ttrue[1] - test[1]) + + (ttrue[2] - test[2]) * (ttrue[2] - test[2])) / + sqrt(ttrue[0] * ttrue[0] + ttrue[1] * ttrue[1] + ttrue[2] * ttrue[2]); +} + +void epnp::mat_to_quat(const double R[3][3], double q[4]) +{ + double tr = R[0][0] + R[1][1] + R[2][2]; + double n4; + + if (tr > 0.0f) { + q[0] = R[1][2] - R[2][1]; + q[1] = R[2][0] - R[0][2]; + q[2] = R[0][1] - R[1][0]; + q[3] = tr + 1.0f; + n4 = q[3]; + } else if ( (R[0][0] > R[1][1]) && (R[0][0] > R[2][2]) ) { + q[0] = 1.0f + R[0][0] - R[1][1] - R[2][2]; + q[1] = R[1][0] + R[0][1]; + q[2] = R[2][0] + R[0][2]; + q[3] = R[1][2] - R[2][1]; + n4 = q[0]; + } else if (R[1][1] > R[2][2]) { + q[0] = R[1][0] + R[0][1]; + q[1] = 1.0f + R[1][1] - R[0][0] - R[2][2]; + q[2] = R[2][1] + R[1][2]; + q[3] = R[2][0] - R[0][2]; + n4 = q[1]; + } else { + q[0] = R[2][0] + R[0][2]; + q[1] = R[2][1] + R[1][2]; + q[2] = 1.0f + R[2][2] - R[0][0] - R[1][1]; + q[3] = R[0][1] - R[1][0]; + n4 = q[2]; + } + double scale = 0.5f / double(sqrt(n4)); + + q[0] *= scale; + q[1] *= scale; + q[2] *= scale; + q[3] *= scale; +} diff --git a/modules/calib3d/src/epnp.h b/modules/calib3d/src/epnp.h new file mode 100644 index 0000000..a7c8cfe --- /dev/null +++ b/modules/calib3d/src/epnp.h @@ -0,0 +1,73 @@ +#ifndef epnp_h +#define epnp_h + +#include "precomp.hpp" + +class epnp { + public: + epnp(void); + ~epnp(); + + void set_internal_parameters(const double uc, const double vc, + const double fu, const double fv); + + void set_maximum_number_of_correspondences(const int n); + void reset_correspondences(void); + void add_correspondence(const double X, const double Y, const double Z, + const double u, const double v); + + double compute_pose(double R[3][3], double T[3]); + + void relative_error(double & rot_err, double & transl_err, + const double Rtrue[3][3], const double ttrue[3], + const double Rest[3][3], const double test[3]); + + void print_pose(const double R[3][3], const double t[3]); + double reprojection_error(const double R[3][3], const double t[3]); + + private: + void choose_control_points(void); + void compute_barycentric_coordinates(void); + 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 * ut); + void compute_pcs(void); + + void solve_for_sign(void); + + void find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho, double * betas); + void find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho, double * betas); + void find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho, double * betas); + void qr_solve(CvMat * A, CvMat * b, CvMat * X); + + double dot(const double * v1, const double * v2); + double dist2(const double * p1, const double * p2); + + void compute_rho(double * rho); + void compute_L_6x10(const double * ut, double * l_6x10); + + void gauss_newton(const CvMat * L_6x10, const CvMat * Rho, double current_betas[4]); + void compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho, + double cb[4], CvMat * A, CvMat * b); + + 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]); + + 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]); + + void mat_to_quat(const double R[3][3], double q[4]); + + + double uc, vc, fu, fv; + + double * pws, * us, * alphas, * pcs; + int maximum_number_of_correspondences; + int number_of_correspondences; + + double cws[4][3], ccs[4][3]; + double cws_determinant; +}; + +#endif -- 2.7.4