projection.h

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// ----------------------------------------------------------------------------
// -                        CloudViewer: www.cloudViewer.org                  -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2024 www.cloudViewer.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
 
#pragma once
 
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <limits>
#include <vector>
 
#include "base/camera.h"
 
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