| // This file is part of OpenCV project. | |
| // It is subject to the license terms in the LICENSE file found in the top-level directory | |
| // of this distribution and at http://opencv.org/license.html | |
| // This file is based on file issued with the following license: | |
| /* | |
| BSD 3-Clause License | |
| Copyright (c) 2020, George Terzakis | |
| All rights reserved. | |
| Redistribution and use in source and binary forms, with or without | |
| modification, are permitted provided that the following conditions are met: | |
| 1. Redistributions of source code must retain the above copyright notice, this | |
| list of conditions and the following disclaimer. | |
| 2. Redistributions 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. | |
| 3. Neither the name of the copyright holder nor the names of its | |
| contributors may 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 COPYRIGHT HOLDER 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. | |
| */ | |
| namespace cv { | |
| namespace sqpnp { | |
| class PoseSolver { | |
| public: | |
| /** | |
| * @brief PoseSolver constructor | |
| */ | |
| PoseSolver(); | |
| /** | |
| * @brief Finds the possible poses of a camera given a set of 3D points | |
| * and their corresponding 2D image projections. The poses are | |
| * sorted by lowest squared error (which corresponds to lowest | |
| * reprojection error). | |
| * @param objectPoints Array or vector of 3 or more 3D points defined in object coordinates. | |
| * 1xN/Nx1 3-channel (float or double) where N is the number of points. | |
| * @param imagePoints Array or vector of corresponding 2D points, 1xN/Nx1 2-channel. | |
| * @param rvec The output rotation solutions (up to 18 3x1 rotation vectors) | |
| * @param tvec The output translation solutions (up to 18 3x1 vectors) | |
| */ | |
| void solve(InputArray objectPoints, InputArray imagePoints, OutputArrayOfArrays rvec, | |
| OutputArrayOfArrays tvec); | |
| private: | |
| struct SQPSolution | |
| { | |
| cv::Matx<double, 9, 1> r_hat; | |
| cv::Matx<double, 3, 1> t; | |
| double sq_error; | |
| SQPSolution() : sq_error(0) {} | |
| }; | |
| /* | |
| * @brief Computes the 9x9 PSD Omega matrix and supporting matrices. | |
| * @param objectPoints Array or vector of 3 or more 3D points defined in object coordinates. | |
| * 1xN/Nx1 3-channel (float or double) where N is the number of points. | |
| * @param imagePoints Array or vector of corresponding 2D points, 1xN/Nx1 2-channel. | |
| */ | |
| void computeOmega(InputArray objectPoints, InputArray imagePoints); | |
| /* | |
| * @brief Computes the 9x9 PSD Omega matrix and supporting matrices. | |
| * @param objectPoints The 3D points in object coordinates. | |
| */ | |
| void solveInternal(InputArray objectPoints); | |
| /* | |
| * @brief Produces the distance from being orthogonal for a given 3x3 matrix | |
| * in row-major order. | |
| * @param e The vector to test representing a 3x3 matrix in row-major order. | |
| * @return The distance the matrix is from being orthogonal. | |
| */ | |
| static double orthogonalityError(const cv::Matx<double, 9, 1>& e); | |
| /* | |
| * @brief Processes a solution and sorts it by error. | |
| * @param solution The solution to evaluate. | |
| * @param objectPoints The 3D points in object coordinates. | |
| * @param min_error The current minimum error. | |
| */ | |
| void checkSolution(SQPSolution& solution, InputArray objectPoints, double& min_error); | |
| /* | |
| * @brief Computes the determinant of a matrix stored in row-major order. | |
| * @param e Vector representing a 3x3 matrix stored in row-major order. | |
| * @return The determinant of the matrix. | |
| */ | |
| static double det3x3(const cv::Matx<double, 9, 1>& e); | |
| /* | |
| * @brief Tests the cheirality on the mean object point for a given solution. | |
| * @param solution The solution to evaluate. | |
| */ | |
| inline bool positiveDepth(const SQPSolution& solution) const; | |
| /* | |
| * @brief Tests the cheirality on all object points for a given solution. | |
| * @param solution The solution to evaluate. | |
| * @param objectPoints The 3D points in object coordinates. | |
| */ | |
| inline bool positiveMajorityDepths(const SQPSolution& solution, InputArray objectPoints) const; | |
| /* | |
| * @brief Determines the nearest rotation matrix to a given rotation matrix using SVD. | |
| * Input and output are 9x1 vector representing a matrix stored in row-major | |
| * order. | |
| * @param e The input 3x3 matrix stored in a vector in row-major order. | |
| * @param r The nearest rotation matrix to the input e (again in row-major order). | |
| */ | |
| static void nearestRotationMatrixSVD(const cv::Matx<double, 9, 1>& e, | |
| cv::Matx<double, 9, 1>& r); | |
| /* | |
| * @brief Determines the nearest rotation matrix to a given rotation matrix using the FOAM algorithm. | |
| * Input and output are 9x1 vector representing a matrix stored in row-major | |
| * order. | |
| * @param e The input 3x3 matrix stored in a vector in row-major order. | |
| * @param r The nearest rotation matrix to the input e (again in row-major order). | |
| */ | |
| static void nearestRotationMatrixFOAM(const cv::Matx<double, 9, 1>& e, | |
| cv::Matx<double, 9, 1>& r); | |
| /* | |
| * @brief Runs the sequential quadratic programming on orthogonal matrices. | |
| * @param r0 The start point of the solver. | |
| */ | |
| SQPSolution runSQP(const cv::Matx<double, 9, 1>& r0); | |
| /* | |
| * @brief Steps down the gradient for the given matrix r to solve the SQP system. | |
| * @param r The current matrix step. | |
| * @param delta The next step down the gradient. | |
| */ | |
| void solveSQPSystem(const cv::Matx<double, 9, 1>& r, cv::Matx<double, 9, 1>& delta); | |
| /* | |
| * @brief Analytically computes the inverse of a symmetric 3x3 matrix using the | |
| * lower triangle. | |
| * @param Q The matrix to invert. | |
| * @param Qinv The inverse of Q. | |
| * @param threshold The threshold to determine if Q is singular and non-invertible. | |
| */ | |
| bool analyticalInverse3x3Symm(const cv::Matx<double, 3, 3>& Q, | |
| cv::Matx<double, 3, 3>& Qinv, | |
| const double& threshold = 1e-8); | |
| /* | |
| * @brief Computes the 3D null space and 6D normal space of the constraint Jacobian | |
| * at a 9D vector r (representing a rank-3 matrix). Note that K is lower | |
| * triangular so upper triangle is undefined. | |
| * @param r 9D vector representing a rank-3 matrix. | |
| * @param H 6D row space of the constraint Jacobian at r. | |
| * @param N 3D null space of the constraint Jacobian at r. | |
| * @param K The constraint Jacobian at r. | |
| * @param norm_threshold Threshold for column vector norm of Pn (the projection onto the null space | |
| * of the constraint Jacobian). | |
| */ | |
| void computeRowAndNullspace(const cv::Matx<double, 9, 1>& r, | |
| cv::Matx<double, 9, 6>& H, | |
| cv::Matx<double, 9, 3>& N, | |
| cv::Matx<double, 6, 6>& K, | |
| const double& norm_threshold = 0.1); | |
| static const double RANK_TOLERANCE; | |
| static const double SQP_SQUARED_TOLERANCE; | |
| static const double SQP_DET_THRESHOLD; | |
| static const double ORTHOGONALITY_SQUARED_ERROR_THRESHOLD; | |
| static const double EQUAL_VECTORS_SQUARED_DIFF; | |
| static const double EQUAL_SQUARED_ERRORS_DIFF; | |
| static const double POINT_VARIANCE_THRESHOLD; | |
| static const int SQP_MAX_ITERATION; | |
| static const double SQRT3; | |
| cv::Matx<double, 9, 9> omega_; | |
| cv::Vec<double, 9> s_; | |
| cv::Matx<double, 9, 9> u_; | |
| cv::Matx<double, 3, 9> p_; | |
| cv::Vec3d point_mean_; | |
| int num_null_vectors_; | |
| SQPSolution solutions_[18]; | |
| int num_solutions_; | |
| }; | |
| } | |
| } | |