upnp.h

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/****************************************************************************************\
* Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation.
* Contributed by Edgar Riba
\****************************************************************************************/

#pragma once

#include <mrpt/config.h>
#include <mrpt/otherlibs/do_opencv_includes.h>

#if MRPT_HAS_OPENCV
//#include <opencv2/core/core_c.h>
#include <iostream>

namespace mrpt::vision::pnp
{
/** \addtogroup pnp Perspective-n-Point pose estimation
 *  \ingroup mrpt_vision_grp
 *  @{
 */

/**
 * @class upnp
 * @author Chandra Mangipudi
 * @date 12/08/16
 * @file upnp.h
 * @brief Unified PnP - Eigen Wrapper for OpenCV function
 */
class upnp
{
   public:
    //! Constructor for UPnP class
    upnp(
        const cv::Mat& cameraMatrix, const cv::Mat& opoints,
        const cv::Mat& ipoints);

    //! Destructor for UPnP class
    ~upnp();

    /**
     * @brief Function to compute pose
     * @param[out] R Rotation Matrix
     * @param[out] t Translation Vector
     * @return
     */
    double compute_pose(cv::Mat& R, cv::Mat& t);

   private:
    /**
     * @brief Initialize camera variables using camera intrinsic matrix
     * @param[in] cameraMatrix Camera Intrinsic Matrix
     */
    template <typename T>
    void init_camera_parameters(const cv::Mat& cameraMatrix)
    {
        uc = cameraMatrix.at<T>(0, 2);
        vc = cameraMatrix.at<T>(1, 2);
        fu = 1;
        fv = 1;
    }

    /**
     * @brief Iniialize Object points and image points from OpenCV Matrix
     * @param[in] opoints Object Points
     * @param[in] ipoints Image Points
     */
    template <typename OpointType, typename IpointType>
    void init_points(const cv::Mat& opoints, const cv::Mat& ipoints)
    {
        for (int i = 0; i < number_of_correspondences; i++)
        {
            pws[3 * i] = opoints.at<OpointType>(i).x;
            pws[3 * i + 1] = opoints.at<OpointType>(i).y;
            pws[3 * i + 2] = opoints.at<OpointType>(i).z;

            us[2 * i] = ipoints.at<IpointType>(i).x;
            us[2 * i + 1] = ipoints.at<IpointType>(i).y;
        }
    }

    /**
     * @brief Compute the reprojection error using the estimated Rotation matrix
     * and Translation Vector
     * @param[in] R Rotation matrix
     * @param[in] t Trnaslation Vector
     * @return  Linear least squares error in pixels
     */
    double reprojection_error(const double R[3][3], const double t[3]);

    /**
     * @brief Function to select 4 control points
     */
    void choose_control_points();

    /**
     * @brief Function to comput @alphas
     */
    void compute_alphas();

    /**
     * @brief Function to compute Maucaulay matrix M
     * @param[out] M Maucaulay matrix
     * @param[in] row Internal member
     * @param[in] alphas Internal member
     * @param[in] u Image pixel x co-ordinate
     * @param[in] v Image pixel y co-ordinate
     */
    void fill_M(
        cv::Mat* M, const int row, const double* alphas, const double u,
        const double v);

    /**
     * @brief Compute the control points
     * @param[in] betas Internal member variable
     * @param[in] ut Internal member variable
     */
    void compute_ccs(const double* betas, const double* ut);

    /**
     * @brief Compute object points based on control points
     */
    void compute_pcs();

    /**
     * @brief Internal member function
     */
    void solve_for_sign();

    /**
     * @brief Function to approximately calculate betas and focal length
     * @param[in] Ut
     * @param[in] Rho
     * @param[out] betas
     * @param[out] efs
     */
    void find_betas_and_focal_approx_1(
        cv::Mat* Ut, cv::Mat* Rho, double* betas, double* efs);

    /**
     * @brief Function to calculate betas and focal length (more accurate)
     * @param[in] Ut
     * @param[in] Rho
     * @param[out] betas
     * @param[out] efs
     */
    void find_betas_and_focal_approx_2(
        cv::Mat* Ut, cv::Mat* Rho, double* betas, double* efs);

    /**
     * @brief Function to do a QR decomposition
     * @param[in] A Matrix to be decomposed
     * @param[out] b
     * @param[out] X
     */
    void qr_solve(cv::Mat* A, cv::Mat* b, cv::Mat* X);

    /**
     * @brief Internal function
     * @param[in] M1
     * @return Distance
     */
    cv::Mat compute_constraint_distance_2param_6eq_2unk_f_unk(
        const cv::Mat& M1);

    /**
     * @brief Internal function
     * @param[in] M1
     * @param[in] M2
     * @return Distance
     */
    cv::Mat compute_constraint_distance_3param_6eq_6unk_f_unk(
        const cv::Mat& M1, const cv::Mat& M2);

    /**
     * @brief Get all possible solutions
     * @param[in] betas
     * @param[out] solutions
     */
    void generate_all_possible_solutions_for_f_unk(
        const double betas[5], double solutions[18][3]);

    /**
     * @brief Return the sign of the scalar
     * @param[in] v
     * @return True if positive else Flase
     */
    double sign(const double v);

    /**
     * @brief Compute the dot product between two vectors
     * @param[in] v1
     * @param[in] v2
     * @return Dot product
     */
    double dot(const double* v1, const double* v2);

    /**
     * @brief Compute dot product in 2D with only x and y components
     * @param[in] v1
     * @param[in] v2
     * @return Dot product
     */
    double dotXY(const double* v1, const double* v2);

    /**
     * @brief Compute the dot product using only z component
     * @param[in] v1
     * @param[in] v2
     * @return Dot product
     */
    double dotZ(const double* v1, const double* v2);

    /**
     * @brief Compute the euclidean distance squared between two points in 3D
     * @param[in] p1
     * @param[in] p2
     * @return Distance squared
     */
    double dist2(const double* p1, const double* p2);

    /**
     * @brief Internal fucntion
     * @param[out] rho
     */
    void compute_rho(double* rho);

    /**
     * @brief Internal function
     * @param[in] ut
     * @param[out] l_6x12
     */
    void compute_L_6x12(const double* ut, double* l_6x12);

    /**
     * @brief Gauss Newton Iterative optimization
     * @param[in] L_6x12
     * @param[in] Rho
     * @param[in,out] current_betas
     * @param[out] efs
     */
    void gauss_newton(
        const cv::Mat* L_6x12, const cv::Mat* Rho, double current_betas[4],
        double* efs);

    /**
     * @brief Compute matrix A and vector b
     * @param[in] l_6x12
     * @param[in] rho
     * @param[in] cb
     * @param[out] A
     * @param[out] b
     * @param[in] f
     */
    void compute_A_and_b_gauss_newton(
        const double* l_6x12, const double* rho, const double cb[4], cv::Mat* A,
        cv::Mat* b, double const f);

    /**
     * @brief Function to compute the pose
     * @param[in] ut
     * @param[in] betas
     * @param[out] R Rotation Matrix
     * @param[out] t Translation VectorS
     * @return
     */
    double compute_R_and_t(
        const double* ut, const double* betas, double R[3][3], double t[3]);

    /**
     * @brief Helper function to function compute_R_and_t()
     * @param[out] R Rotaiton matrix
     * @param[out] t Translation vector
     */
    void estimate_R_and_t(double R[3][3], double t[3]);

    /**
     * @brief Function to copy the pose
     * @param[in] R_dst
     * @param[in] t_dst
     * @param[out] R_src
     * @param[out] t_src
     */
    void copy_R_and_t(
        const double R_dst[3][3], const double t_dst[3], double R_src[3][3],
        double t_src[3]);

    double uc;  //! Image center in x-direction
    double vc;  //! Image center in y-direction
    double fu;  //! Focal length in x-direction
    double fv;  //! Focal length in y-direction

    std::vector<double> pws;  //! Object points
    std::vector<double> us;  //! Image points
    std::vector<double> alphas, pcs;  //! Internal variable
    int number_of_correspondences;  //! Number of 2d/3d correspondences

    double cws[4][3], ccs[4][3];  //! Control point variables
    int max_nr;  //! Internal variable
    double *A1, *A2;  //! Internal variable
};

/** @}  */  // end of grouping
}  // namespace mrpt::vision::pnp
#endif  // Check for OPENCV_LIB