essential_matrix.h

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// ----------------------------------------------------------------------------
// -                        CloudViewer: www.cloudViewer.org                  -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2024 www.cloudViewer.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
 
#pragma once
 
#include <ceres/ceres.h>
 
#include <Eigen/Core>
#include <vector>
 
#include "util/alignment.h"
#include "util/types.h"
 
namespace colmap {
 
// Decompose an essential matrix into the possible rotations and translations.
//
// The first pose is assumed to be P = [I | 0] and the set of four other
// possible second poses are defined as: {[R1 | t], [R2 | t],
//                                        [R1 | -t], [R2 | -t]}
//
// @param E          3x3 essential matrix.
// @param R1         First possible 3x3 rotation matrix.
// @param R2         Second possible 3x3 rotation matrix.
// @param t          3x1 possible translation vector (also -t possible).
void DecomposeEssentialMatrix(const Eigen::Matrix3d& E,
                              Eigen::Matrix3d* R1,
                              Eigen::Matrix3d* R2,
                              Eigen::Vector3d* t);
 
// Recover the most probable pose from the given essential matrix.
//
// The pose of the first image is assumed to be P = [I | 0].
//
// @param E            3x3 essential matrix.
// @param points1      First set of corresponding points.
// @param points2      Second set of corresponding points.
// @param inlier_mask  Only points with `true` in the inlier mask are
//                     considered in the cheirality test. Size of the
//                     inlier mask must match the number of points N.
// @param R            Most probable 3x3 rotation matrix.
// @param t            Most probable 3x1 translation vector.
// @param points3D     Triangulated 3D points infront of camera.
void PoseFromEssentialMatrix(const Eigen::Matrix3d& E,
                             const std::vector<Eigen::Vector2d>& points1,
                             const std::vector<Eigen::Vector2d>& points2,
                             Eigen::Matrix3d* R,
                             Eigen::Vector3d* t,
                             std::vector<Eigen::Vector3d>* points3D);
 
// Compose essential matrix from relative camera poses.
//
// Assumes that first camera pose has projection matrix P = [I | 0], and
// pose of second camera is given as transformation from world to camera system.
//
// @param R             3x3 rotation matrix.
// @param t             3x1 translation vector.
//
// @return              3x3 essential matrix.
Eigen::Matrix3d EssentialMatrixFromPose(const Eigen::Matrix3d& R,
                                        const Eigen::Vector3d& t);
 
// Compose essential matrix from two absolute camera poses.
//
// @param proj_matrix1     3x4 projection matrix.
// @param proj_matrix2     3x4 projection matrix.
//
// @return                 3x3 essential matrix.
Eigen::Matrix3d EssentialMatrixFromAbsolutePoses(
        const Eigen::Matrix3x4d& proj_matrix1,
        const Eigen::Matrix3x4d& proj_matrix2);
 
// Find optimal image points, such that:
//
//     optimal_point1^t * E * optimal_point2 = 0
//
// as described in:
//
//   Lindstrom, P., "Triangulation made easy",
//   Computer Vision and Pattern Recognition (CVPR),
//   2010 IEEE Conference on , vol., no., pp.1554,1561, 13-18 June 2010
//
// @param E                Essential or fundamental matrix.
// @param point1           Corresponding 2D point in first image.
// @param point2           Corresponding 2D point in second image.
// @param optimal_point1   Estimated optimal image point in the first image.
// @param optimal_point2   Estimated optimal image point in the second image.
void FindOptimalImageObservations(const Eigen::Matrix3d& E,
                                  const Eigen::Vector2d& point1,
                                  const Eigen::Vector2d& point2,
                                  Eigen::Vector2d* optimal_point1,
                                  Eigen::Vector2d* optimal_point2);
 
// Compute the location of the epipole in homogeneous coordinates.
//
// @param E           3x3 essential matrix.
// @param left_image  If true, epipole in left image is computed,
//                    else in right image.
//
// @return            Epipole in homogeneous coordinates.
Eigen::Vector3d EpipoleFromEssentialMatrix(const Eigen::Matrix3d& E,
                                           const bool left_image);
 
// Invert the essential matrix, i.e. if the essential matrix E describes the
// transformation from camera A to B, the inverted essential matrix E' describes
// the transformation from camera B to A.
//
// @param E      3x3 essential matrix.
//
// @return       Inverted essential matrix.
Eigen::Matrix3d InvertEssentialMatrix(const Eigen::Matrix3d& matrix);
 
// Refine essential matrix.
//
// Decomposes the essential matrix into rotation and translation components
// and refines the relative pose using the function `RefineRelativePose`.
//
// @param E                3x3 essential matrix.
// @param points1          First set of corresponding points.
// @param points2          Second set of corresponding points.
// @param inlier_mask      Inlier mask for corresponding points.
// @param options          Solver options.
//
// @return                 Flag indicating if solution is usable.
bool RefineEssentialMatrix(const ceres::Solver::Options& options,
                           const std::vector<Eigen::Vector2d>& points1,
                           const std::vector<Eigen::Vector2d>& points2,
                           const std::vector<char>& inlier_mask,
                           Eigen::Matrix3d* E);
 
}  // namespace colmap