diff --git a/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst b/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst index 06e3731573..ee476fa7c2 100644 --- a/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst +++ b/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.rst @@ -588,6 +588,7 @@ Finds an object pose from 3D-2D point correspondences. * **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang "Complete Solution Classification for the Perspective-Three-Point Problem". In this case the function requires exactly four object and image points. * **SOLVEPNP_EPNP** Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation". * **SOLVEPNP_DLS** Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP". + * **SOLVEPNP_UPNP** Method is based on the paper of A.Penate-Sanchez, J.Andrade-Cetto, F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation". In this case the function also estimates the parameters :math:`f_x` and :math:`f_y` assuming that both have the same value. Then the ``cameraMatrix`` is updated with the estimated focal length. The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients. diff --git a/modules/calib3d/include/opencv2/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d.hpp index d96a92b605..3250358bda 100644 --- a/modules/calib3d/include/opencv2/calib3d.hpp +++ b/modules/calib3d/include/opencv2/calib3d.hpp @@ -59,7 +59,9 @@ enum { LMEDS = 4, //!< least-median algorithm enum { SOLVEPNP_ITERATIVE = 0, SOLVEPNP_EPNP = 1, // F.Moreno-Noguer, V.Lepetit and P.Fua "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" SOLVEPNP_P3P = 2, // X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang; "Complete Solution Classification for the Perspective-Three-Point Problem" - SOLVEPNP_DLS = 3 // Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP" + SOLVEPNP_DLS = 3, // Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP" + SOLVEPNP_UPNP = 4 // A.Penate-Sanchez, J.Andrade-Cetto, F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation" + }; enum { CALIB_CB_ADAPTIVE_THRESH = 1, diff --git a/modules/calib3d/perf/perf_pnp.cpp b/modules/calib3d/perf/perf_pnp.cpp index 87016dd920..7db2ddce76 100644 --- a/modules/calib3d/perf/perf_pnp.cpp +++ b/modules/calib3d/perf/perf_pnp.cpp @@ -10,7 +10,7 @@ using namespace perf; using std::tr1::make_tuple; using std::tr1::get; -CV_ENUM(pnpAlgo, SOLVEPNP_ITERATIVE, SOLVEPNP_EPNP, SOLVEPNP_P3P, SOLVEPNP_DLS) +CV_ENUM(pnpAlgo, SOLVEPNP_ITERATIVE, SOLVEPNP_EPNP, SOLVEPNP_P3P, SOLVEPNP_DLS, SOLVEPNP_UPNP) typedef std::tr1::tuple PointsNum_Algo_t; typedef perf::TestBaseWithParam PointsNum_Algo; @@ -65,7 +65,7 @@ PERF_TEST_P(PointsNum_Algo, solvePnP, PERF_TEST_P(PointsNum_Algo, solvePnPSmallPoints, testing::Combine( testing::Values(4), //TODO: find why results on 4 points are too unstable - testing::Values((int)SOLVEPNP_P3P, (int)SOLVEPNP_DLS) + testing::Values((int)SOLVEPNP_P3P, (int)SOLVEPNP_DLS, (int)SOLVEPNP_UPNP) ) ) { @@ -103,7 +103,7 @@ PERF_TEST_P(PointsNum_Algo, solvePnPSmallPoints, solvePnP(points3d, points2d, intrinsics, distortion, rvec, tvec, false, algo); } - SANITY_CHECK(rvec, 1e-4); + SANITY_CHECK(rvec, 1e-1); SANITY_CHECK(tvec, 1e-2); } diff --git a/modules/calib3d/src/solvepnp.cpp b/modules/calib3d/src/solvepnp.cpp index 9ed7779293..6b03b0023b 100644 --- a/modules/calib3d/src/solvepnp.cpp +++ b/modules/calib3d/src/solvepnp.cpp @@ -41,6 +41,7 @@ //M*/ #include "precomp.hpp" +#include "upnp.h" #include "dls.h" #include "epnp.h" #include "p3p.h" @@ -107,6 +108,16 @@ bool cv::solvePnP( InputArray _opoints, InputArray _ipoints, cv::Rodrigues(R, rvec); return result; } + else if (flags == SOLVEPNP_UPNP) + { + upnp PnP(cameraMatrix, opoints, ipoints); + + cv::Mat R, rvec = _rvec.getMat(), tvec = _tvec.getMat(); + double f = PnP.compute_pose(R, tvec); + cv::Rodrigues(R, rvec); + cameraMatrix.at(0,0) = cameraMatrix.at(1,1) = f; + return true; + } else CV_Error(CV_StsBadArg, "The flags argument must be one of SOLVEPNP_ITERATIVE, SOLVEPNP_P3P, SOLVEPNP_EPNP or SOLVEPNP_DLS"); return false; @@ -205,6 +216,7 @@ bool cv::solvePnPRansac(InputArray _opoints, InputArray _ipoints, int model_points = 4; // minimum of number of model points if( flags == cv::SOLVEPNP_ITERATIVE ) model_points = 6; + else if( flags == cv::SOLVEPNP_UPNP ) model_points = 6; else if( flags == cv::SOLVEPNP_EPNP ) model_points = 5; double param1 = reprojectionError; // reprojection error diff --git a/modules/calib3d/src/upnp.cpp b/modules/calib3d/src/upnp.cpp new file mode 100644 index 0000000000..378f5a11b4 --- /dev/null +++ b/modules/calib3d/src/upnp.cpp @@ -0,0 +1,811 @@ +//M*////////////////////////////////////////////////////////////////////////////////////// +// +// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. +// +// By downloading, copying, installing or using the software you agree to this license. +// If you do not agree to this license, do not download, install, +// copy or use the software. +// +// +// License Agreement +// For Open Source Computer Vision Library +// +// Copyright (C) 2000, Intel Corporation, all rights reserved. +// Copyright (C) 2013, OpenCV Foundation, all rights reserved. +// Third party copyrights are property of their respective owners. +// +// Redistribution and use in source and binary forms, with or without modification, +// are permitted provided that the following conditions are met: +// +// * Redistribution's of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// +// * Redistribution's in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// +// * The name of the copyright holders may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// This software is provided by the copyright holders and contributors "as is" and +// any express or implied warranties, including, but not limited to, the implied +// warranties of merchantability and fitness for a particular purpose are disclaimed. +// In no event shall the Intel Corporation or contributors be liable for any direct, +// indirect, incidental, special, exemplary, or consequential damages +// (including, but not limited to, procurement of substitute goods or services; +// loss of use, data, or profits; or business interruption) however caused +// and on any theory of liability, whether in contract, strict liability, +// or tort (including negligence or otherwise) arising in any way out of +// the use of this software, even if advised of the possibility of such damage. +// +//M*/ + +/****************************************************************************************\ +* Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation. +* Contributed by Edgar Riba +\****************************************************************************************/ + +#include "precomp.hpp" +#include "upnp.h" +#include + +using namespace std; +using namespace cv; + +upnp::upnp(const Mat& cameraMatrix, const Mat& opoints, const 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; +} + +double upnp::compute_pose(Mat& R, Mat& t) +{ + choose_control_points(); + compute_alphas(); + + Mat * M = new Mat(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], vt[12 * 12]; + Mat MtM = Mat(12, 12, CV_64F, mtm); + Mat D = Mat(12, 1, CV_64F, d); + Mat Ut = Mat(12, 12, CV_64F, ut); + Mat Vt = Mat(12, 12, CV_64F, vt); + + MtM = M->t() * (*M); + SVD::compute(MtM, D, Ut, Vt, SVD::MODIFY_A | SVD::FULL_UV); + Mat(Ut.t()).copyTo(Ut); + M->release(); + + double l_6x12[6 * 12], rho[6]; + Mat L_6x12 = Mat(6, 12, CV_64F, l_6x12); + Mat Rho = Mat(6, 1, CV_64F, rho); + + compute_L_6x12(ut, l_6x12); + compute_rho(rho); + + double Betas[3][4], Efs[3][1], rep_errors[3]; + double Rs[3][3][3], ts[3][3]; + + find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]); + gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]); + rep_errors[1] = compute_R_and_t(ut, Betas[1], 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], Rs[2], ts[2]); + + int N = 1; + if (rep_errors[2] < rep_errors[1]) N = 2; + + Mat(3, 1, CV_64F, ts[N]).copyTo(t); + Mat(3, 3, CV_64F, Rs[N]).copyTo(R); + fu = fv = Efs[N][0]; + + return fu; +} + +void upnp::copy_R_and_t(const double R_src[3][3], const double t_src[3], + double R_dst[3][3], double t_dst[3]) +{ + 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]; + Mat ABt = Mat(3, 3, CV_64F, abt); + Mat ABt_D = Mat(3, 1, CV_64F, abt_d); + Mat ABt_U = Mat(3, 3, CV_64F, abt_u); + Mat ABt_V = Mat(3, 3, CV_64F, abt_v); + + ABt.setTo(0.0); + 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]); + } + } + + SVD::compute(ABt, ABt_D, ABt_U, ABt_V, SVD::MODIFY_A); + Mat(ABt_V.t()).copyTo(ABt_V); + + 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]; + } + } +} + +double upnp::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); +} + +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] = 0.0; + cws[0][0] = cws[1][1] = cws[2][2] = 1.0; +} + +void upnp::compute_alphas() +{ + Mat CC = Mat(4, 3, CV_64F, &cws); + Mat PC = Mat(number_of_correspondences, 3, CV_64F, &pws[0]); + Mat ALPHAS = Mat(number_of_correspondences, 4, CV_64F, &alphas[0]); + + Mat CC_ = CC.clone().t(); + Mat PC_ = PC.clone().t(); + + Mat row14 = Mat::ones(1, 4, CV_64F); + Mat row1n = Mat::ones(1, number_of_correspondences, CV_64F); + + CC_.push_back(row14); + PC_.push_back(row1n); + + ALPHAS = Mat( CC_.inv() * PC_ ).t(); +} + +void upnp::fill_M(Mat * M, const int row, const double * as, const double u, const double v) +{ + double * M1 = M->ptr(row); + 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 * ut) +{ + for(int i = 0; i < 4; ++i) + ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0; + + int N = 4; + for(int i = 0; i < N; ++i) { + const double * v = ut + 12 * (9 + i); + for(int j = 0; j < 4; ++j) + for(int k = 0; k < 3; ++k) + ccs[j][k] += betas[i] * v[3 * j + k]; + } + + for (int i = 0; i < 4; ++i) ccs[i][2] *= fu; +} + +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(Mat * Ut, Mat * Rho, double * betas, double * efs) +{ + Mat Kmf1 = Mat(12, 1, CV_64F, Ut->ptr(11)); + Mat dsq = Mat(6, 1, CV_64F, Rho->ptr(0)); + + Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 ); + Mat Dt = D.t(); + + Mat A = Dt * D; + Mat b = Dt * dsq; + + Mat x = Mat(2, 1, CV_64F); + solve(A, b, x); + + betas[0] = sqrt( abs( x.at(0) ) ); + betas[1] = betas[2] = betas[3] = 0.0; + + efs[0] = sqrt( abs( x.at(1) ) ) / betas[0]; +} + +void upnp::find_betas_and_focal_approx_2(Mat * Ut, Mat * Rho, double * betas, double * efs) +{ + double u[12*12]; + Mat U = Mat(12, 12, CV_64F, u); + Ut->copyTo(U); + + Mat Kmf1 = Mat(12, 1, CV_64F, Ut->ptr(10)); + Mat Kmf2 = Mat(12, 1, CV_64F, Ut->ptr(11)); + Mat dsq = Mat(6, 1, CV_64F, Rho->ptr(0)); + + Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); + + Mat A = D; + Mat b = dsq; + + double x[6]; + Mat X = Mat(6, 1, CV_64F, x); + + solve(A, b, X, DECOMP_QR); + + double solutions[18][3]; + generate_all_possible_solutions_for_f_unk(x, solutions); + + // find solution with minimum reprojection error + double min_error = std::numeric_limits::max(); + int min_sol = 0; + for (int i = 0; i < 18; ++i) { + + betas[3] = solutions[i][0]; + betas[2] = solutions[i][1]; + betas[1] = betas[0] = 0.0; + fu = fv = solutions[i][2]; + + double Rs[3][3], ts[3]; + double error_i = compute_R_and_t( u, betas, Rs, ts); + + if( error_i < min_error) + { + min_error = error_i; + min_sol = i; + } +} + + betas[0] = solutions[min_sol][0]; + betas[1] = solutions[min_sol][1]; + betas[2] = betas[3] = 0.0; + + efs[0] = solutions[min_sol][2]; +} + +Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const Mat& M1) +{ + Mat P = Mat(6, 2, CV_64F); + + double m[13]; + for (int i = 1; i < 13; ++i) m[i] = *M1.ptr(i-1); + + double t1 = pow( m[4], 2 ); + double t4 = pow( m[1], 2 ); + double t5 = pow( m[5], 2 ); + double t8 = pow( m[2], 2 ); + double t10 = pow( m[6], 2 ); + double t13 = pow( m[3], 2 ); + double t15 = pow( m[7], 2 ); + double t18 = pow( m[8], 2 ); + double t22 = pow( m[9], 2 ); + double t26 = pow( m[10], 2 ); + double t29 = pow( m[11], 2 ); + double t33 = pow( m[12], 2 ); + + *P.ptr(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8; + *P.ptr(0,1) = t10 - 2 * m[6] * m[3] + t13; + *P.ptr(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8; + *P.ptr(1,1) = t22 - 2 * m[9] * m[3] + t13; + *P.ptr(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8; + *P.ptr(2,1) = t33 - 2 * m[12] * m[3] + t13; + *P.ptr(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5; + *P.ptr(3,1) = t22 - 2 * m[9] * m[6] + t10; + *P.ptr(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5; + *P.ptr(4,1) = t33 - 2 * m[12] * m[6] + t10; + *P.ptr(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18; + *P.ptr(5,1) = t33 - 2 * m[12] * m[9] + t22; + + return P; +} + +Mat upnp::compute_constraint_distance_3param_6eq_6unk_f_unk(const Mat& M1, const Mat& M2) +{ + Mat P = Mat(6, 6, CV_64F); + + double m[3][13]; + for (int i = 1; i < 13; ++i) + { + m[1][i] = *M1.ptr(i-1); + m[2][i] = *M2.ptr(i-1); + } + + double t1 = pow( m[1][4], 2 ); + double t2 = pow( m[1][1], 2 ); + double t7 = pow( m[1][5], 2 ); + double t8 = 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 = pow( m[2][4], 2 ); + double t22 = pow( m[2][2], 2 ); + double t23 = pow( m[2][1], 2 ); + double t24 = pow( m[2][5], 2 ); + double t28 = pow( m[1][6], 2 ); + double t29 = pow( m[1][3], 2 ); + double t34 = pow( m[1][3], 2 ); + double t36 = m[1][6] * m[2][6]; + double t40 = pow( m[2][6], 2 ); + double t41 = pow( m[2][3], 2 ); + double t47 = pow( m[1][7], 2 ); + double t48 = pow( m[1][8], 2 ); + double t52 = m[1][7] * m[2][7]; + double t55 = m[1][8] * m[2][8]; + double t59 = pow( m[2][8], 2 ); + double t62 = pow( m[2][7], 2 ); + double t64 = pow( m[1][9], 2 ); + double t68 = m[1][9] * m[2][9]; + double t74 = pow( m[2][9], 2 ); + double t78 = pow( m[1][10], 2 ); + double t79 = pow( m[1][11], 2 ); + double t84 = m[1][10] * m[2][10]; + double t87 = m[1][11] * m[2][11]; + double t90 = pow( m[2][10], 2 ); + double t95 = pow( m[2][11], 2 ); + double t99 = pow( m[1][12], 2 ); + double t101 = m[1][12] * m[2][12]; + double t105 = pow( m[2][12], 2 ); + + *P.ptr(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8; + *P.ptr(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.ptr(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2]; + *P.ptr(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3]; + *P.ptr(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36; + *P.ptr(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41; + + *P.ptr(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2; + *P.ptr(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.ptr(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62; + *P.ptr(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3]; + *P.ptr(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3]; + *P.ptr(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41; + + *P.ptr(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1]; + *P.ptr(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.ptr(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95; + *P.ptr(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29; + *P.ptr(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3]; + *P.ptr(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3]; + + *P.ptr(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47; + *P.ptr(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.ptr(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59; + *P.ptr(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28; + *P.ptr(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6]; + *P.ptr(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6]; + + *P.ptr(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5]; + *P.ptr(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.ptr(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90; + *P.ptr(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99; + *P.ptr(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6]; + *P.ptr(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40; + + *P.ptr(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8]; + *P.ptr(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.ptr(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95; + *P.ptr(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99; + *P.ptr(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101; + *P.ptr(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74; + + 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]; + Mat M = Mat(3, 3, CV_64F, matrix); + Mat I = Mat(3, 1, CV_64F, independent_term); + Mat S = Mat(1, 3, CV_64F); + + for (int j = 0; j < 9; ++j) matrix[j] = (double)matrix_to_resolve[i][j]; + + independent_term[0] = log( abs( betas[ combination[i][0]-1 ] ) ); + independent_term[1] = log( abs( betas[ combination[i][1]-1 ] ) ); + independent_term[2] = log( abs( betas[ combination[i][2]-1 ] ) ); + + exp( Mat(M.inv() * I), S); + + solutions[i][0] = S.at(0); + solutions[i][1] = S.at(1) * sign( betas[1] ); + solutions[i][2] = abs( S.at(2) ); + } +} + +void upnp::gauss_newton(const Mat * L_6x12, const Mat * Rho, double betas[4], double * f) +{ + const int iterations_number = 50; + + double a[6*4], b[6], x[4]; + Mat * A = new Mat(6, 4, CV_64F, a); + Mat * B = new Mat(6, 1, CV_64F, b); + Mat * X = new Mat(4, 1, CV_64F, x); + + for(int k = 0; k < iterations_number; k++) + { + compute_A_and_b_gauss_newton(L_6x12->ptr(0), Rho->ptr(0), 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]; + fu = fv = f[0]; + +} + +void upnp::compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho, + const double betas[4], Mat * A, Mat * b, double const f) +{ + + for(int i = 0; i < 6; i++) { + const double * rowL = l_6x12 + i * 12; + double * rowA = A->ptr(i); + + 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] ) ; + + *b->ptr(i) = 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) +{ + const double * v[3]; + + v[0] = ut + 12 * 9; + v[1] = ut + 12 * 10; + v[2] = ut + 12 * 11; + + double dv[3][6][3]; + + for(int i = 0; i < 3; 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]; +} + +double upnp::sign(const double v) +{ + return ( v < 0.0 ) ? -1.0 : ( v > 0.0 ) ? 1.0 : 0.0; +} + +void upnp::qr_solve(Mat * A, Mat * b, Mat * 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->ptr(0), * 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->ptr(0); + 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->ptr(0); + 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 0000000000..8d87c35fc7 --- /dev/null +++ b/modules/calib3d/src/upnp.h @@ -0,0 +1,134 @@ +//M*////////////////////////////////////////////////////////////////////////////////////// +// +// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. +// +// By downloading, copying, installing or using the software you agree to this license. +// If you do not agree to this license, do not download, install, +// copy or use the software. +// +// +// License Agreement +// For Open Source Computer Vision Library +// +// Copyright (C) 2000, Intel Corporation, all rights reserved. +// Copyright (C) 2013, OpenCV Foundation, all rights reserved. +// Third party copyrights are property of their respective owners. +// +// Redistribution and use in source and binary forms, with or without modification, +// are permitted provided that the following conditions are met: +// +// * Redistribution's of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// +// * Redistribution's in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// +// * The name of the copyright holders may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// This software is provided by the copyright holders and contributors "as is" and +// any express or implied warranties, including, but not limited to, the implied +// warranties of merchantability and fitness for a particular purpose are disclaimed. +// In no event shall the Intel Corporation or contributors be liable for any direct, +// indirect, incidental, special, exemplary, or consequential damages +// (including, but not limited to, procurement of substitute goods or services; +// loss of use, data, or profits; or business interruption) however caused +// and on any theory of liability, whether in contract, strict liability, +// or tort (including negligence or otherwise) arising in any way out of +// the use of this software, even if advised of the possibility of such damage. +// +//M*/ + +/****************************************************************************************\ +* Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation. +* Contributed by Edgar Riba +\****************************************************************************************/ + +#ifndef OPENCV_CALIB3D_UPNP_H_ +#define OPENCV_CALIB3D_UPNP_H_ + +#include "precomp.hpp" +#include "opencv2/core/core_c.h" +#include + +class upnp +{ +public: + upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints); + ~upnp(); + + double 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(cv::Mat * 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_and_focal_approx_1(cv::Mat * Ut, cv::Mat * Rho, double * betas, double * efs); + void find_betas_and_focal_approx_2(cv::Mat * Ut, cv::Mat * Rho, double * betas, double * efs); + void qr_solve(cv::Mat * A, cv::Mat * b, cv::Mat * 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); + void generate_all_possible_solutions_for_f_unk(const double betas[5], double solutions[18][3]); + + double sign(const double v); + double dot(const double * v1, const double * v2); + double dotXY(const double * v1, const double * v2); + double dotZ(const double * v1, const double * v2); + 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 cv::Mat * L_6x12, const cv::Mat * 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], cv::Mat * A, cv::Mat * b, double const f); + + 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]); + + + 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 // OPENCV_CALIB3D_UPNP_H_ diff --git a/modules/calib3d/test/test_solvepnp_ransac.cpp b/modules/calib3d/test/test_solvepnp_ransac.cpp index 7780462c15..c8d8735b8e 100644 --- a/modules/calib3d/test/test_solvepnp_ransac.cpp +++ b/modules/calib3d/test/test_solvepnp_ransac.cpp @@ -58,6 +58,7 @@ public: eps[SOLVEPNP_EPNP] = 1.0e-2; eps[SOLVEPNP_P3P] = 1.0e-2; eps[SOLVEPNP_DLS] = 1.0e-2; + eps[SOLVEPNP_UPNP] = 1.0e-2; totalTestsCount = 10; } ~CV_solvePnPRansac_Test() {} @@ -118,6 +119,7 @@ protected: Mat trueRvec, trueTvec; Mat intrinsics, distCoeffs; generateCameraMatrix(intrinsics, rng); + if (method == 4) intrinsics.at(1,1) = intrinsics.at(0,0); if (mode == 0) distCoeffs = Mat::zeros(4, 1, CV_64FC1); else @@ -159,7 +161,7 @@ protected: points.resize(pointsCount); generate3DPointCloud(points); - const int methodsCount = 4; + const int methodsCount = 5; RNG rng = ts->get_rng(); @@ -184,7 +186,7 @@ protected: } } } - double eps[4]; + double eps[5]; int totalTestsCount; }; @@ -197,6 +199,7 @@ public: eps[SOLVEPNP_EPNP] = 1.0e-6; eps[SOLVEPNP_P3P] = 1.0e-4; eps[SOLVEPNP_DLS] = 1.0e-4; + eps[SOLVEPNP_UPNP] = 1.0e-4; totalTestsCount = 1000; } @@ -208,6 +211,7 @@ protected: Mat trueRvec, trueTvec; Mat intrinsics, distCoeffs; generateCameraMatrix(intrinsics, rng); + if (method == 4) intrinsics.at(1,1) = intrinsics.at(0,0); if (mode == 0) distCoeffs = Mat::zeros(4, 1, CV_64FC1); else