Code tutorial
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/*
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* PnPProblem.cpp
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*
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* Created on: Mar 28, 2014
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* Author: Edgar Riba
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*/
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#include <iostream>
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#include <sstream>
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#include "PnPProblem.h"
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#include "Mesh.h"
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#include <opencv2/calib3d/calib3d.hpp>
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/* Functions for Möller–Trumbore intersection algorithm
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* */
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cv::Point3f CROSS(cv::Point3f v1, cv::Point3f v2)
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{
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cv::Point3f tmp_p;
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tmp_p.x = v1.y*v2.z - v1.z*v2.y;
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tmp_p.y = v1.z*v2.x - v1.x*v2.z;
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tmp_p.z = v1.x*v2.y - v1.y*v2.x;
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return tmp_p;
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}
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double DOT(cv::Point3f v1, cv::Point3f v2)
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{
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return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
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}
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cv::Point3f SUB(cv::Point3f v1, cv::Point3f v2)
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{
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cv::Point3f tmp_p;
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tmp_p.x = v1.x - v2.x;
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tmp_p.y = v1.y - v2.y;
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tmp_p.z = v1.z - v2.z;
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return tmp_p;
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}
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/* End functions for Möller–Trumbore intersection algorithm
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* */
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// Function to get the nearest 3D point to the Ray origin
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cv::Point3f get_nearest_3D_point(std::vector<cv::Point3f> &points_list, cv::Point3f origin)
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{
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cv::Point3f p1 = points_list[0];
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cv::Point3f p2 = points_list[1];
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double d1 = std::sqrt( std::pow(p1.x-origin.x, 2) + std::pow(p1.y-origin.y, 2) + std::pow(p1.z-origin.z, 2) );
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double d2 = std::sqrt( std::pow(p2.x-origin.x, 2) + std::pow(p2.y-origin.y, 2) + std::pow(p2.z-origin.z, 2) );
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if(d1 < d2)
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{
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return p1;
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}
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else
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{
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return p2;
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}
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}
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// Custom constructor given the intrinsic camera parameters
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PnPProblem::PnPProblem(const double params[])
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{
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_A_matrix = cv::Mat::zeros(3, 3, CV_64FC1); // intrinsic camera parameters
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_A_matrix.at<double>(0, 0) = params[0]; // [ fx 0 cx ]
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_A_matrix.at<double>(1, 1) = params[1]; // [ 0 fy cy ]
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_A_matrix.at<double>(0, 2) = params[2]; // [ 0 0 1 ]
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_A_matrix.at<double>(1, 2) = params[3];
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_A_matrix.at<double>(2, 2) = 1;
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_R_matrix = cv::Mat::zeros(3, 3, CV_64FC1); // rotation matrix
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_t_matrix = cv::Mat::zeros(3, 1, CV_64FC1); // translation matrix
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_P_matrix = cv::Mat::zeros(3, 4, CV_64FC1); // rotation-translation matrix
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}
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PnPProblem::~PnPProblem()
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{
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// TODO Auto-generated destructor stub
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}
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void PnPProblem::set_P_matrix( const cv::Mat &R_matrix, const cv::Mat &t_matrix)
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{
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// Rotation-Translation Matrix Definition
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_P_matrix.at<double>(0,0) = R_matrix.at<double>(0,0);
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_P_matrix.at<double>(0,1) = R_matrix.at<double>(0,1);
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_P_matrix.at<double>(0,2) = R_matrix.at<double>(0,2);
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_P_matrix.at<double>(1,0) = R_matrix.at<double>(1,0);
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_P_matrix.at<double>(1,1) = R_matrix.at<double>(1,1);
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_P_matrix.at<double>(1,2) = R_matrix.at<double>(1,2);
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_P_matrix.at<double>(2,0) = R_matrix.at<double>(2,0);
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_P_matrix.at<double>(2,1) = R_matrix.at<double>(2,1);
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_P_matrix.at<double>(0,3) = t_matrix.at<double>(0);
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_P_matrix.at<double>(1,3) = t_matrix.at<double>(1);
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_P_matrix.at<double>(2,3) = t_matrix.at<double>(2);
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}
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// Estimate the pose given a list of 2D/3D correspondences and the method to use
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bool PnPProblem::estimatePose( const std::vector<cv::Point3f> &list_points3d,
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const std::vector<cv::Point2f> &list_points2d,
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int flags)
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{
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cv::Mat distCoeffs = cv::Mat::zeros(4, 1, CV_64FC1);
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cv::Mat rvec = cv::Mat::zeros(3, 1, CV_64FC1);
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cv::Mat tvec = cv::Mat::zeros(3, 1, CV_64FC1);
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bool useExtrinsicGuess = false;
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// Pose estimation
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bool correspondence = cv::solvePnP( list_points3d, list_points2d, _A_matrix, distCoeffs, rvec, tvec,
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useExtrinsicGuess, flags);
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// Transforms Rotation Vector to Matrix
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Rodrigues(rvec,_R_matrix);
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_t_matrix = tvec;
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// Set projection matrix
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this->set_P_matrix(_R_matrix, _t_matrix);
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return correspondence;
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}
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// Estimate the pose given a list of 2D/3D correspondences with RANSAC and the method to use
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void PnPProblem::estimatePoseRANSAC( const std::vector<cv::Point3f> &list_points3d, // list with model 3D coordinates
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const std::vector<cv::Point2f> &list_points2d, // list with scene 2D coordinates
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int flags, cv::Mat &inliers, int iterationsCount, // PnP method; inliers container
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float reprojectionError, float confidence ) // Ransac parameters
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{
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cv::Mat distCoeffs = cv::Mat::zeros(4, 1, CV_64FC1); // vector of distortion coefficients
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cv::Mat rvec = cv::Mat::zeros(3, 1, CV_64FC1); // output rotation vector
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cv::Mat tvec = cv::Mat::zeros(3, 1, CV_64FC1); // output translation vector
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bool useExtrinsicGuess = false; // if true the function uses the provided rvec and tvec values as
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// initial approximations of the rotation and translation vectors
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cv::solvePnPRansac( list_points3d, list_points2d, _A_matrix, distCoeffs, rvec, tvec,
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useExtrinsicGuess, iterationsCount, reprojectionError, confidence,
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inliers, flags );
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Rodrigues(rvec,_R_matrix); // converts Rotation Vector to Matrix
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_t_matrix = tvec; // set translation matrix
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this->set_P_matrix(_R_matrix, _t_matrix); // set rotation-translation matrix
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}
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// Given the mesh, backproject the 3D points to 2D to verify the pose estimation
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std::vector<cv::Point2f> PnPProblem::verify_points(Mesh *mesh)
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{
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std::vector<cv::Point2f> verified_points_2d;
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for( int i = 0; i < mesh->getNumVertices(); i++)
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{
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cv::Point3f point3d = mesh->getVertex(i);
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cv::Point2f point2d = this->backproject3DPoint(point3d);
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verified_points_2d.push_back(point2d);
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}
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return verified_points_2d;
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}
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// Backproject a 3D point to 2D using the estimated pose parameters
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cv::Point2f PnPProblem::backproject3DPoint(const cv::Point3f &point3d)
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{
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// 3D point vector [x y z 1]'
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cv::Mat point3d_vec = cv::Mat(4, 1, CV_64FC1);
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point3d_vec.at<double>(0) = point3d.x;
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point3d_vec.at<double>(1) = point3d.y;
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point3d_vec.at<double>(2) = point3d.z;
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point3d_vec.at<double>(3) = 1;
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// 2D point vector [u v 1]'
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cv::Mat point2d_vec = cv::Mat(4, 1, CV_64FC1);
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point2d_vec = _A_matrix * _P_matrix * point3d_vec;
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// Normalization of [u v]'
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cv::Point2f point2d;
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point2d.x = point2d_vec.at<double>(0) / point2d_vec.at<double>(2);
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point2d.y = point2d_vec.at<double>(1) / point2d_vec.at<double>(2);
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return point2d;
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}
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// Back project a 2D point to 3D and returns if it's on the object surface
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bool PnPProblem::backproject2DPoint(const Mesh *mesh, const cv::Point2f &point2d, cv::Point3f &point3d)
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{
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// Triangles list of the object mesh
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std::vector<std::vector<int> > triangles_list = mesh->getTrianglesList();
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double lambda = 8;
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double u = point2d.x;
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double v = point2d.y;
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// Point in vector form
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cv::Mat point2d_vec = cv::Mat::ones(3, 1, CV_64F); // 3x1
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point2d_vec.at<double>(0) = u * lambda;
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point2d_vec.at<double>(1) = v * lambda;
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point2d_vec.at<double>(2) = lambda;
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// Point in camera coordinates
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cv::Mat X_c = _A_matrix.inv() * point2d_vec ; // 3x1
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// Point in world coordinates
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cv::Mat X_w = _R_matrix.inv() * ( X_c - _t_matrix ); // 3x1
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// Center of projection
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cv::Mat C_op = cv::Mat(_R_matrix.inv()).mul(-1) * _t_matrix; // 3x1
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// Ray direction vector
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cv::Mat ray = X_w - C_op; // 3x1
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ray = ray / cv::norm(ray); // 3x1
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// Set up Ray
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Ray R((cv::Point3f)C_op, (cv::Point3f)ray);
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// A vector to store the intersections found
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std::vector<cv::Point3f> intersections_list;
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// Loop for all the triangles and check the intersection
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for (unsigned int i = 0; i < triangles_list.size(); i++)
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{
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cv::Point3f V0 = mesh->getVertex(triangles_list[i][0]);
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cv::Point3f V1 = mesh->getVertex(triangles_list[i][1]);
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cv::Point3f V2 = mesh->getVertex(triangles_list[i][2]);
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Triangle T(i, V0, V1, V2);
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double out;
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if(this->intersect_MollerTrumbore(R, T, &out))
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{
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cv::Point3f tmp_pt = R.getP0() + out*R.getP1(); // P = O + t*D
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intersections_list.push_back(tmp_pt);
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}
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}
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// If there are intersection, find the nearest one
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if (!intersections_list.empty())
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{
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point3d = get_nearest_3D_point(intersections_list, R.getP0());
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return true;
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}
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else
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{
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return false;
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}
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}
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// Möller–Trumbore intersection algorithm
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bool PnPProblem::intersect_MollerTrumbore(Ray &Ray, Triangle &Triangle, double *out)
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{
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const double EPSILON = 0.000001;
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cv::Point3f e1, e2;
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cv::Point3f P, Q, T;
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double det, inv_det, u, v;
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double t;
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cv::Point3f V1 = Triangle.getV0(); // Triangle vertices
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cv::Point3f V2 = Triangle.getV1();
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cv::Point3f V3 = Triangle.getV2();
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cv::Point3f O = Ray.getP0(); // Ray origin
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cv::Point3f D = Ray.getP1(); // Ray direction
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//Find vectors for two edges sharing V1
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e1 = SUB(V2, V1);
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e2 = SUB(V3, V1);
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// Begin calculation determinant - also used to calculate U parameter
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P = CROSS(D, e2);
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// If determinant is near zero, ray lie in plane of triangle
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det = DOT(e1, P);
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//NOT CULLING
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if(det > -EPSILON && det < EPSILON) return false;
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inv_det = 1.f / det;
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//calculate distance from V1 to ray origin
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T = SUB(O, V1);
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//Calculate u parameter and test bound
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u = DOT(T, P) * inv_det;
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//The intersection lies outside of the triangle
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if(u < 0.f || u > 1.f) return false;
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//Prepare to test v parameter
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Q = CROSS(T, e1);
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//Calculate V parameter and test bound
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v = DOT(D, Q) * inv_det;
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//The intersection lies outside of the triangle
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if(v < 0.f || u + v > 1.f) return false;
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t = DOT(e2, Q) * inv_det;
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if(t > EPSILON) { //ray intersection
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*out = t;
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return true;
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}
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// No hit, no win
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return false;
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}
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