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 {
 
// Essential matrix estimator from corresponding normalized point pairs.
//
// This algorithm solves the 5-Point problem based on the following paper:
//
//    D. Nister, An efficient solution to the five-point relative pose problem,
//    IEEE-T-PAMI, 26(6), 2004.
//    http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.8769
class EssentialMatrixFivePointEstimator {
public:
    typedef Eigen::Vector2d X_t;
    typedef Eigen::Vector2d Y_t;
    typedef Eigen::Matrix3d M_t;
 
    // The minimum number of samples needed to estimate a model.
    static const int kMinNumSamples = 5;
 
    // Estimate up to 10 possible essential matrix solutions from a set of
    // corresponding points.
    //
    //  The number of corresponding points must be at least 5.
    //
    // @param points1  First set of corresponding points.
    // @param points2  Second set of corresponding points.
    //
    // @return         Up to 10 solutions as a vector of 3x3 essential matrices.
    static std::vector<M_t> Estimate(const std::vector<X_t>& points1,
                                     const std::vector<Y_t>& points2);
 
    // Calculate the residuals of a set of corresponding points and a given
    // essential matrix.
    //
    // Residuals are defined as the squared Sampson error.
    //
    // @param points1    First set of corresponding points.
    // @param points2    Second set of corresponding points.
    // @param E          3x3 essential matrix.
    // @param residuals  Output vector of residuals.
    static void Residuals(const std::vector<X_t>& points1,
                          const std::vector<Y_t>& points2,
                          const M_t& E,
                          std::vector<double>* residuals);
};
 
// Essential matrix estimator from corresponding normalized point pairs.
//
// This algorithm solves the 8-Point problem based on the following paper:
//
//    Hartley and Zisserman, Multiple View Geometry, algorithm 11.1, page 282.
class EssentialMatrixEightPointEstimator {
public:
    typedef Eigen::Vector2d X_t;
    typedef Eigen::Vector2d Y_t;
    typedef Eigen::Matrix3d M_t;
 
    // The minimum number of samples needed to estimate a model.
    static const int kMinNumSamples = 8;
 
    // Estimate essential matrix solutions from  set of corresponding points.
    //
    // The number of corresponding points must be at least 8.
    //
    // @param points1  First set of corresponding points.
    // @param points2  Second set of corresponding points.
    static std::vector<M_t> Estimate(const std::vector<X_t>& points1,
                                     const std::vector<Y_t>& points2);
 
    // Calculate the residuals of a set of corresponding points and a given
    // essential matrix.
    //
    // Residuals are defined as the squared Sampson error.
    //
    // @param points1    First set of corresponding points.
    // @param points2    Second set of corresponding points.
    // @param E          3x3 essential matrix.
    // @param residuals  Output vector of residuals.
    static void Residuals(const std::vector<X_t>& points1,
                          const std::vector<Y_t>& points2,
                          const M_t& E,
                          std::vector<double>* residuals);
};
 
}  // namespace colmap