| // Copyright (c) 2022, ETH Zurich and UNC Chapel Hill. | |
| // All rights reserved. | |
| // | |
| // Redistribution and use in source and binary forms, with or without | |
| // modification, are permitted provided that the following conditions are met: | |
| // | |
| // * Redistributions of source code must retain the above copyright | |
| // notice, this list of conditions and the following disclaimer. | |
| // | |
| // * 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. | |
| // | |
| // * Neither the name of ETH Zurich and UNC Chapel Hill 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 HOLDERS 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. | |
| // | |
| // Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de) | |
| namespace colmap { | |
| // Compose projection matrix from rotation and translation components. | |
| // | |
| // The projection matrix transforms 3D world to image points. | |
| // | |
| // @param qvec Unit Quaternion rotation coefficients (w, x, y, z). | |
| // @param tvec 3x1 translation vector. | |
| // | |
| // @return 3x4 projection matrix. | |
| Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Vector4d& qvec, | |
| const Eigen::Vector3d& tvec); | |
| // Compose projection matrix from rotation matrix and translation components). | |
| // | |
| // The projection matrix transforms 3D world to image points. | |
| // | |
| // @param R 3x3 rotation matrix. | |
| // @param t 3x1 translation vector. | |
| // | |
| // @return 3x4 projection matrix. | |
| Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Matrix3d& R, | |
| const Eigen::Vector3d& T); | |
| // Invert projection matrix, defined as: | |
| // | |
| // P = [R | t] with R \in SO(3) and t \in R^3 | |
| // | |
| // and the inverse projection matrix as: | |
| // | |
| // P' = [R^T | -R^T t] | |
| // | |
| // @param proj_matrix 3x4 projection matrix. | |
| // | |
| // @return 3x4 inverse projection matrix. | |
| Eigen::Matrix3x4d InvertProjectionMatrix(const Eigen::Matrix3x4d& proj_matrix); | |
| // Compute the closes rotation matrix with the closest Frobenius norm by setting | |
| // the singular values of the given matrix to 1. | |
| Eigen::Matrix3d ComputeClosestRotationMatrix(const Eigen::Matrix3d& matrix); | |
| // Decompose projection matrix into intrinsic camera matrix, rotation matrix and | |
| // translation vector. Returns false if decomposition fails. This implementation | |
| // is inspired by the OpenCV implementation with some additional checks. | |
| bool DecomposeProjectionMatrix(const Eigen::Matrix3x4d& proj_matrix, | |
| Eigen::Matrix3d* K, Eigen::Matrix3d* R, | |
| Eigen::Vector3d* T); | |
| // Project 3D point to image. | |
| // | |
| // @param points3D 3D world point as 3x1 vector. | |
| // @param proj_matrix 3x4 projection matrix. | |
| // @param camera Camera used to project to image plane. | |
| // | |
| // @return Projected image point. | |
| Eigen::Vector2d ProjectPointToImage(const Eigen::Vector3d& point3D, | |
| const Eigen::Matrix3x4d& proj_matrix, | |
| const Camera& camera); | |
| // Calculate the reprojection error. | |
| // | |
| // The reprojection error is the Euclidean distance between the observation | |
| // in the image and the projection of the 3D point into the image. If the | |
| // 3D point is behind the camera, then this function returns DBL_MAX. | |
| double CalculateSquaredReprojectionError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Vector4d& qvec, | |
| const Eigen::Vector3d& tvec, | |
| const Camera& camera); | |
| double CalculateSquaredReprojectionError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Matrix3x4d& proj_matrix, | |
| const Camera& camera); | |
| // Calculate the angular error. | |
| // | |
| // The angular error is the angle between the observed viewing ray and the | |
| // actual viewing ray from the camera center to the 3D point. | |
| double CalculateAngularError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Vector4d& qvec, | |
| const Eigen::Vector3d& tvec, const Camera& camera); | |
| double CalculateAngularError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Matrix3x4d& proj_matrix, | |
| const Camera& camera); | |
| // Calculate angulate error using normalized image points. | |
| // | |
| // The angular error is the angle between the observed viewing ray and the | |
| // actual viewing ray from the camera center to the 3D point. | |
| double CalculateNormalizedAngularError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Vector4d& qvec, | |
| const Eigen::Vector3d& tvec); | |
| double CalculateNormalizedAngularError(const Eigen::Vector2d& point2D, | |
| const Eigen::Vector3d& point3D, | |
| const Eigen::Matrix3x4d& proj_matrix); | |
| // Calculate depth of 3D point with respect to camera. | |
| // | |
| // The depth is defined as the Euclidean distance of a 3D point from the | |
| // camera and is positive if the 3D point is in front and negative if | |
| // behind of the camera. | |
| // | |
| // @param proj_matrix 3x4 projection matrix. | |
| // @param point3D 3D point as 3x1 vector. | |
| // | |
| // @return Depth of 3D point. | |
| double CalculateDepth(const Eigen::Matrix3x4d& proj_matrix, | |
| const Eigen::Vector3d& point3D); | |
| // Check if 3D point passes cheirality constraint, | |
| // i.e. it lies in front of the camera and not in the image plane. | |
| // | |
| // @param proj_matrix 3x4 projection matrix. | |
| // @param point3D 3D point as 3x1 vector. | |
| // | |
| // @return True if point lies in front of camera. | |
| bool HasPointPositiveDepth(const Eigen::Matrix3x4d& proj_matrix, | |
| const Eigen::Vector3d& point3D); | |
| } // namespace colmap | |