ICP 3D3D

SVD方法

非线性方法

实践

使用两幅图的RGB-D图像，通过特征匹配获取两组3D点，最后利用ICP计算他们的位姿变换。

pose_estimation_3d3d

#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <Eigen/SVD>
#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/solvers/eigen/linear_solver_eigen.h>
#include <g2o/types/sba/types_six_dof_expmap.h>
#include <chrono>using namespace std;
using namespace cv;void find_feature_matches (const Mat& img_1, const Mat& img_2,std::vector<KeyPoint>& keypoints_1,std::vector<KeyPoint>& keypoints_2,std::vector< DMatch >& matches );// 像素坐标转相机归一化坐标
Point2d pixel2cam ( const Point2d& p, const Mat& K );void pose_estimation_3d3d (const vector<Point3f>& pts1,const vector<Point3f>& pts2,Mat& R, Mat& t
);void bundleAdjustment(const vector<Point3f>& points_3d,const vector<Point3f>& points_2d,Mat& R, Mat& t
);// g2o edge
class EdgeProjectXYZRGBDPoseOnly : public g2o::BaseUnaryEdge<3, Eigen::Vector3d, g2o::VertexSE3Expmap>
{
public:EIGEN_MAKE_ALIGNED_OPERATOR_NEW;EdgeProjectXYZRGBDPoseOnly( const Eigen::Vector3d& point ) : _point(point) {}virtual void computeError(){const g2o::VertexSE3Expmap* pose = static_cast<const g2o::VertexSE3Expmap*> ( _vertices[0] );// measurement is p, point is p'_error = _measurement - pose->estimate().map( _point );}virtual void linearizeOplus(){g2o::VertexSE3Expmap* pose = static_cast<g2o::VertexSE3Expmap *>(_vertices[0]);g2o::SE3Quat T(pose->estimate());Eigen::Vector3d xyz_trans = T.map(_point);double x = xyz_trans[0];double y = xyz_trans[1];double z = xyz_trans[2];_jacobianOplusXi(0,0) = 0;_jacobianOplusXi(0,1) = -z;_jacobianOplusXi(0,2) = y;_jacobianOplusXi(0,3) = -1;_jacobianOplusXi(0,4) = 0;_jacobianOplusXi(0,5) = 0;_jacobianOplusXi(1,0) = z;_jacobianOplusXi(1,1) = 0;_jacobianOplusXi(1,2) = -x;_jacobianOplusXi(1,3) = 0;_jacobianOplusXi(1,4) = -1;_jacobianOplusXi(1,5) = 0;_jacobianOplusXi(2,0) = -y;_jacobianOplusXi(2,1) = x;_jacobianOplusXi(2,2) = 0;_jacobianOplusXi(2,3) = 0;_jacobianOplusXi(2,4) = 0;_jacobianOplusXi(2,5) = -1;}bool read ( istream& in ) {}bool write ( ostream& out ) const {}
protected:Eigen::Vector3d _point;
};int main ( int argc, char** argv )
{if ( argc != 5 ){cout<<"usage: pose_estimation_3d3d img1 img2 depth1 depth2"<<endl;return 1;}//-- 读取图像Mat img_1 = imread ( argv[1], CV_LOAD_IMAGE_COLOR );Mat img_2 = imread ( argv[2], CV_LOAD_IMAGE_COLOR );vector<KeyPoint> keypoints_1, keypoints_2;vector<DMatch> matches;find_feature_matches ( img_1, img_2, keypoints_1, keypoints_2, matches );cout<<"一共找到了"<<matches.size() <<"组匹配点"<<endl;// 建立3D点Mat depth1 = imread ( argv[3], CV_LOAD_IMAGE_UNCHANGED );       // 深度图为16位无符号数，单通道图像Mat depth2 = imread ( argv[4], CV_LOAD_IMAGE_UNCHANGED );       // 深度图为16位无符号数，单通道图像Mat K = ( Mat_<double> ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1 );vector<Point3f> pts1, pts2;for ( DMatch m:matches ){ushort d1 = depth1.ptr<unsigned short> ( int ( keypoints_1[m.queryIdx].pt.y ) ) [ int ( keypoints_1[m.queryIdx].pt.x ) ];ushort d2 = depth2.ptr<unsigned short> ( int ( keypoints_2[m.trainIdx].pt.y ) ) [ int ( keypoints_2[m.trainIdx].pt.x ) ];if ( d1==0 || d2==0 )   // bad depthcontinue;Point2d p1 = pixel2cam ( keypoints_1[m.queryIdx].pt, K );Point2d p2 = pixel2cam ( keypoints_2[m.trainIdx].pt, K );float dd1 = float ( d1 ) /5000.0;float dd2 = float ( d2 ) /5000.0;pts1.push_back ( Point3f ( p1.x*dd1, p1.y*dd1, dd1 ) );pts2.push_back ( Point3f ( p2.x*dd2, p2.y*dd2, dd2 ) );}cout<<"3d-3d pairs: "<<pts1.size() <<endl;Mat R, t;pose_estimation_3d3d ( pts1, pts2, R, t );cout<<"ICP via SVD results: "<<endl;cout<<"R = "<<R<<endl;cout<<"t = "<<t<<endl;cout<<"R_inv = "<<R.t() <<endl;cout<<"t_inv = "<<-R.t() *t<<endl;cout<<"calling bundle adjustment"<<endl;bundleAdjustment( pts1, pts2, R, t );// verify p1 = R*p2 + tfor ( int i=0; i<5; i++ ){cout<<"p1 = "<<pts1[i]<<endl;cout<<"p2 = "<<pts2[i]<<endl;cout<<"(R*p2+t) = "<<R * (Mat_<double>(3,1)<<pts2[i].x, pts2[i].y, pts2[i].z) + t<<endl;cout<<endl;}
}void find_feature_matches ( const Mat& img_1, const Mat& img_2,std::vector<KeyPoint>& keypoints_1,std::vector<KeyPoint>& keypoints_2,std::vector< DMatch >& matches )
{//-- 初始化Mat descriptors_1, descriptors_2;// used in OpenCV3Ptr<FeatureDetector> detector = ORB::create();Ptr<DescriptorExtractor> descriptor = ORB::create();// use this if you are in OpenCV2// Ptr<FeatureDetector> detector = FeatureDetector::create ( "ORB" );// Ptr<DescriptorExtractor> descriptor = DescriptorExtractor::create ( "ORB" );Ptr<DescriptorMatcher> matcher  = DescriptorMatcher::create("BruteForce-Hamming");//-- 第一步:检测 Oriented FAST 角点位置detector->detect ( img_1,keypoints_1 );detector->detect ( img_2,keypoints_2 );//-- 第二步:根据角点位置计算 BRIEF 描述子descriptor->compute ( img_1, keypoints_1, descriptors_1 );descriptor->compute ( img_2, keypoints_2, descriptors_2 );//-- 第三步:对两幅图像中的BRIEF描述子进行匹配，使用 Hamming 距离vector<DMatch> match;// BFMatcher matcher ( NORM_HAMMING );matcher->match ( descriptors_1, descriptors_2, match );//-- 第四步:匹配点对筛选double min_dist=10000, max_dist=0;//找出所有匹配之间的最小距离和最大距离, 即是最相似的和最不相似的两组点之间的距离for ( int i = 0; i < descriptors_1.rows; i++ ){double dist = match[i].distance;if ( dist < min_dist ) min_dist = dist;if ( dist > max_dist ) max_dist = dist;}printf ( "-- Max dist : %f \n", max_dist );printf ( "-- Min dist : %f \n", min_dist );//当描述子之间的距离大于两倍的最小距离时,即认为匹配有误.但有时候最小距离会非常小,设置一个经验值30作为下限.for ( int i = 0; i < descriptors_1.rows; i++ ){if ( match[i].distance <= max ( 2*min_dist, 30.0 ) ){matches.push_back ( match[i] );}}
}Point2d pixel2cam ( const Point2d& p, const Mat& K )
{return Point2d(( p.x - K.at<double> ( 0,2 ) ) / K.at<double> ( 0,0 ),( p.y - K.at<double> ( 1,2 ) ) / K.at<double> ( 1,1 ));
}void pose_estimation_3d3d (const vector<Point3f>& pts1,const vector<Point3f>& pts2,Mat& R, Mat& t
)
{Point3f p1, p2;     // center of massint N = pts1.size();for ( int i=0; i<N; i++ ){p1 += pts1[i];p2 += pts2[i];}p1 = Point3f( Vec3f(p1) /  N);p2 = Point3f( Vec3f(p2) / N);vector<Point3f>     q1 ( N ), q2 ( N ); // remove the centerfor ( int i=0; i<N; i++ ){q1[i] = pts1[i] - p1;q2[i] = pts2[i] - p2;}// compute q1*q2^TEigen::Matrix3d W = Eigen::Matrix3d::Zero();for ( int i=0; i<N; i++ ){W += Eigen::Vector3d ( q1[i].x, q1[i].y, q1[i].z ) * Eigen::Vector3d ( q2[i].x, q2[i].y, q2[i].z ).transpose();}cout<<"W="<<W<<endl;// SVD on WEigen::JacobiSVD<Eigen::Matrix3d> svd ( W, Eigen::ComputeFullU|Eigen::ComputeFullV );Eigen::Matrix3d U = svd.matrixU();Eigen::Matrix3d V = svd.matrixV();if (U.determinant() * V.determinant() < 0){for (int x = 0; x < 3; ++x){U(x, 2) *= -1;}}cout<<"U="<<U<<endl;cout<<"V="<<V<<endl;Eigen::Matrix3d R_ = U* ( V.transpose() );Eigen::Vector3d t_ = Eigen::Vector3d ( p1.x, p1.y, p1.z ) - R_ * Eigen::Vector3d ( p2.x, p2.y, p2.z );// convert to cv::MatR = ( Mat_<double> ( 3,3 ) <<R_ ( 0,0 ), R_ ( 0,1 ), R_ ( 0,2 ),R_ ( 1,0 ), R_ ( 1,1 ), R_ ( 1,2 ),R_ ( 2,0 ), R_ ( 2,1 ), R_ ( 2,2 ));t = ( Mat_<double> ( 3,1 ) << t_ ( 0,0 ), t_ ( 1,0 ), t_ ( 2,0 ) );
}void bundleAdjustment (const vector< Point3f >& pts1,const vector< Point3f >& pts2,Mat& R, Mat& t )
{// 初始化g2otypedef g2o::BlockSolver< g2o::BlockSolverTraits<6,3> > Block;  // pose维度为 6, landmark 维度为 3Block::LinearSolverType* linearSolver = new g2o::LinearSolverEigen<Block::PoseMatrixType>(); // 线性方程求解器Block* solver_ptr = new Block( linearSolver );      // 矩阵块求解器g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton( solver_ptr );g2o::SparseOptimizer optimizer;optimizer.setAlgorithm( solver );// vertexg2o::VertexSE3Expmap* pose = new g2o::VertexSE3Expmap(); // camera posepose->setId(0);pose->setEstimate( g2o::SE3Quat(Eigen::Matrix3d::Identity(),Eigen::Vector3d( 0,0,0 )) );optimizer.addVertex( pose );// edgesint index = 1;vector<EdgeProjectXYZRGBDPoseOnly*> edges;for ( size_t i=0; i<pts1.size(); i++ ){EdgeProjectXYZRGBDPoseOnly* edge = new EdgeProjectXYZRGBDPoseOnly(Eigen::Vector3d(pts2[i].x, pts2[i].y, pts2[i].z) );edge->setId( index );edge->setVertex( 0, dynamic_cast<g2o::VertexSE3Expmap*> (pose) );edge->setMeasurement( Eigen::Vector3d(pts1[i].x, pts1[i].y, pts1[i].z) );edge->setInformation( Eigen::Matrix3d::Identity()*1e4 );optimizer.addEdge(edge);index++;edges.push_back(edge);}chrono::steady_clock::time_point t1 = chrono::steady_clock::now();optimizer.setVerbose( true );optimizer.initializeOptimization();optimizer.optimize(10);chrono::steady_clock::time_point t2 = chrono::steady_clock::now();chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2-t1);cout<<"optimization costs time: "<<time_used.count()<<" seconds."<<endl;cout<<endl<<"after optimization:"<<endl;cout<<"T="<<endl<<Eigen::Isometry3d( pose->estimate() ).matrix()<<endl;}

./build/pose_estimation_3d3d 1.png 2.png 1_depth.png 2_depth.png

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ICP 3D3D

SVD方法

非线性方法

实践

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