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// 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)
#ifndef COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_
#define COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_
#include <array>
#include <vector>
#include <Eigen/Core>
#include "util/alignment.h"
#include "util/types.h"
namespace colmap {
// Analytic solver for the P3P (Perspective-Three-Point) problem.
//
// The algorithm is based on the following paper:
//
// X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang. Complete Solution
// Classification for the Perspective-Three-Point Problem.
// http://www.mmrc.iss.ac.cn/~xgao/paper/ieee.pdf
class P3PEstimator {
public:
// The 2D image feature observations.
typedef Eigen::Vector2d X_t;
// The observed 3D features in the world frame.
typedef Eigen::Vector3d Y_t;
// The transformation from the world to the camera frame.
typedef Eigen::Matrix3x4d M_t;
// The minimum number of samples needed to estimate a model.
static const int kMinNumSamples = 3;
// Estimate the most probable solution of the P3P problem from a set of
// three 2D-3D point correspondences.
//
// @param points2D Normalized 2D image points as 3x2 matrix.
// @param points3D 3D world points as 3x3 matrix.
//
// @return Most probable pose as length-1 vector of a 3x4 matrix.
static std::vector<M_t> Estimate(const std::vector<X_t>& points2D,
const std::vector<Y_t>& points3D);
// Calculate the squared reprojection error given a set of 2D-3D point
// correspondences and a projection matrix.
//
// @param points2D Normalized 2D image points as Nx2 matrix.
// @param points3D 3D world points as Nx3 matrix.
// @param proj_matrix 3x4 projection matrix.
// @param residuals Output vector of residuals.
static void Residuals(const std::vector<X_t>& points2D,
const std::vector<Y_t>& points3D,
const M_t& proj_matrix, std::vector<double>* residuals);
};
// EPNP solver for the PNP (Perspective-N-Point) problem. The solver needs a
// minimum of 4 2D-3D correspondences.
//
// The algorithm is based on the following paper:
//
// Lepetit, Vincent, Francesc Moreno-Noguer, and Pascal Fua.
// "Epnp: An accurate o (n) solution to the pnp problem."
// International journal of computer vision 81.2 (2009): 155-166.
//
// The implementation is based on their original open-source release, but is
// ported to Eigen and contains several improvements over the original code.
class EPNPEstimator {
public:
// The 2D image feature observations.
typedef Eigen::Vector2d X_t;
// The observed 3D features in the world frame.
typedef Eigen::Vector3d Y_t;
// The transformation from the world to the camera frame.
typedef Eigen::Matrix3x4d M_t;
// The minimum number of samples needed to estimate a model.
static const int kMinNumSamples = 4;
// Estimate the most probable solution of the P3P problem from a set of
// three 2D-3D point correspondences.
//
// @param points2D Normalized 2D image points as 3x2 matrix.
// @param points3D 3D world points as 3x3 matrix.
//
// @return Most probable pose as length-1 vector of a 3x4 matrix.
static std::vector<M_t> Estimate(const std::vector<X_t>& points2D,
const std::vector<Y_t>& points3D);
// Calculate the squared reprojection error given a set of 2D-3D point
// correspondences and a projection matrix.
//
// @param points2D Normalized 2D image points as Nx2 matrix.
// @param points3D 3D world points as Nx3 matrix.
// @param proj_matrix 3x4 projection matrix.
// @param residuals Output vector of residuals.
static void Residuals(const std::vector<X_t>& points2D,
const std::vector<Y_t>& points3D,
const M_t& proj_matrix, std::vector<double>* residuals);
private:
bool ComputePose(const std::vector<Eigen::Vector2d>& points2D,
const std::vector<Eigen::Vector3d>& points3D,
Eigen::Matrix3x4d* proj_matrix);
void ChooseControlPoints();
bool ComputeBarycentricCoordinates();
Eigen::Matrix<double, Eigen::Dynamic, 12> ComputeM();
Eigen::Matrix<double, 6, 10> ComputeL6x10(
const Eigen::Matrix<double, 12, 12>& Ut);
Eigen::Matrix<double, 6, 1> ComputeRho();
void FindBetasApprox1(const Eigen::Matrix<double, 6, 10>& L_6x10,
const Eigen::Matrix<double, 6, 1>& rho,
Eigen::Vector4d* betas);
void FindBetasApprox2(const Eigen::Matrix<double, 6, 10>& L_6x10,
const Eigen::Matrix<double, 6, 1>& rho,
Eigen::Vector4d* betas);
void FindBetasApprox3(const Eigen::Matrix<double, 6, 10>& L_6x10,
const Eigen::Matrix<double, 6, 1>& rho,
Eigen::Vector4d* betas);
void RunGaussNewton(const Eigen::Matrix<double, 6, 10>& L_6x10,
const Eigen::Matrix<double, 6, 1>& rho,
Eigen::Vector4d* betas);
double ComputeRT(const Eigen::Matrix<double, 12, 12>& Ut,
const Eigen::Vector4d& betas, Eigen::Matrix3d* R,
Eigen::Vector3d* t);
void ComputeCcs(const Eigen::Vector4d& betas,
const Eigen::Matrix<double, 12, 12>& Ut);
void ComputePcs();
void SolveForSign();
void EstimateRT(Eigen::Matrix3d* R, Eigen::Vector3d* t);
double ComputeTotalReprojectionError(const Eigen::Matrix3d& R,
const Eigen::Vector3d& t);
const std::vector<Eigen::Vector2d>* points2D_ = nullptr;
const std::vector<Eigen::Vector3d>* points3D_ = nullptr;
std::vector<Eigen::Vector3d> pcs_;
std::vector<Eigen::Vector4d> alphas_;
std::array<Eigen::Vector3d, 4> cws_;
std::array<Eigen::Vector3d, 4> ccs_;
};
} // namespace colmap
#endif // COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_
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