十四讲课后7.7

同样借阅的灰色的石头的博客.

感谢灰色的石头博主的回复我的问题.让我对g2o一元边二元边和误差,雅克比有了了解.

一元边(ICP)的误差空间点之间的误差,优化的是pose,优化的类型只有一个.二元边的误差是重投影误差,即空间点经过位姿变换后,再投影到像素平面上,与观测到的位置之间的误差,优化的是空间点位置和位姿Pose,也就是边的链接节点类型有两个.

有了对一元边二元边和误差的理解,后面的重点是雅克比的怎么写.Xi是误差空间点的导数,Xj是误差到相机位姿的导数.需要求解相应的雅克比矩阵.可以参考P164.但与之对比的是ICP没有用到相机模型,仅考虑到3D点之间的变换,所以没有重投影误差.故Xj为

而没有下面这一项(对比).

Xi也就只是P对P'的导数,只剩下R了.

#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
//节点为优化变量，这里是g2o::VertexSE3Expmap类型的相机位姿(李代数形式)，由于只有一帧，所以整个图中只有一个位姿量，也就只有一个顶点，进而边就是一元边，只连接到一个顶点
//边是误差项，这里的误差是观测到的3d点坐标减去计算得到的3d点坐标，也即观测值减去计算值，
class EdgeProjectXYZRGBDPoseOnly : public g2o::BaseBinaryEdge<3, Eigen::Vector3d,g2o::VertexSBAPointXYZ, g2o::VertexSE3Expmap>//一个继承类
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
    //构造函数,需要构造一个Vector3d的point.
    EdgeProjectXYZRGBDPoseOnly( ) {}

    virtual void computeError()
    {
        //从顶点容器_vertices[]中将唯的一个顶点取出来，并将其类型转换成位姿节点指针(注意这里还是节点类型指针，虽然这个节点是位姿，
        // 但是还是节点类型)，用于后面_error中的计算值求取
        const g2o::VertexSE3Expmap* pose = static_cast<const g2o::VertexSE3Expmap*> ( _vertices[1] );
        const g2o::VertexSBAPointXYZ *point = dynamic_cast<const g2o::VertexSBAPointXYZ*>(_vertices[0]);
        // measurement is p, point is p'
        ////ICP中误差相就是只考虑3D点之间点的变换,和相机没有关系.
        _error = _measurement - pose->estimate().map( point->estimate() );
    }

    virtual void linearizeOplus()
    {

        g2o::VertexSE3Expmap* pose = static_cast<g2o::VertexSE3Expmap *>(_vertices[1]);
        g2o::VertexSBAPointXYZ* point = dynamic_cast<g2o::VertexSBAPointXYZ*>(_vertices[0]);


        g2o::SE3Quat T(pose->estimate());

        //_point就是p'的坐标,经过T变换,成为了p坐标 (P173)
        Eigen::Vector3d xyz_trans = T.map(point->estimate());
        double x = xyz_trans[0];
        double y = xyz_trans[1];
        double z = xyz_trans[2];
        //T.rotation是g2o中的函数.
        _jacobianOplusXi = -T.rotation().toRotationMatrix(); //四元数提出旋转向量,再转换成矩阵

        ////因为雅克比矩阵经计算知道，只跟变换后的坐标有关系，所以求出来直接定义就好了。P175页式7.60与P164页式7.44
        _jacobianOplusXj(0,0) = 0;
        _jacobianOplusXj(0,1) = -z;
        _jacobianOplusXj(0,2) = y;
        _jacobianOplusXj(0,3) = -1;
        _jacobianOplusXj(0,4) = 0;
        _jacobianOplusXj(0,5) = 0;

        _jacobianOplusXj(1,0) = z;
        _jacobianOplusXj(1,1) = 0;
        _jacobianOplusXj(1,2) = -x;
        _jacobianOplusXj(1,3) = 0;
        _jacobianOplusXj(1,4) = -1;
        _jacobianOplusXj(1,5) = 0;

        _jacobianOplusXj(2,0) = -y;
        _jacobianOplusXj(2,1) = x;
        _jacobianOplusXj(2,2) = 0;
        _jacobianOplusXj(2,3) = 0;
        _jacobianOplusXj(2,4) = 0;
        _jacobianOplusXj(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 depth
            continue;
        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;//.t是Mat类型中的逆
    cout<<"t_inv = "<<-R.t() *t<<endl;////???????

    cout<<"calling bundle adjustment"<<endl;

    bundleAdjustment( pts1, pts2, R, t );

    // verify p1 = R*p2 + t
    for ( 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 OpenCV3
    Ptr<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 )
            );
}
//SVD
void pose_estimation_3d3d (
        const vector<Point3f>& pts1,
        const vector<Point3f>& pts2,
        Mat& R, Mat& t
)
{
    Point3f p1, p2;     // center of mass
    int N = pts1.size();
    for ( int i=0; i<N; i++ )
    {
        p1 += pts1[i];
        p2 += pts2[i];
    }
    p1 = Point3f( Vec3f(p1) /  N);// 这里先将p1、p2转换成Vec3f类型，再除以N。 质心
    p2 = Point3f( Vec3f(p2) / N);
    vector<Point3f>     q1 ( N ), q2 ( N ); // remove the center
    //去质心运算
    for ( int i=0; i<N; i++ )
    {
        q1[i] = pts1[i] - p1;
        q2[i] = pts2[i] - p2;
    }

    // compute q1*q2^T(P174最下面)
    Eigen::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 W
    Eigen::JacobiSVD<Eigen::Matrix3d> svd ( W, Eigen::ComputeFullU|Eigen::ComputeFullV );
    Eigen::Matrix3d U = svd.matrixU();
    Eigen::Matrix3d V = svd.matrixV();
    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::Mat   就是将Eigen型的Rt转换成Mat型
    R = ( 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g2o
    typedef g2o::BlockSolver< g2o::BlockSolverTraits<6,3> > Block;  // pose维度为 6, landmark 维度为 3
    Block::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 );

    // vertex
    g2o::VertexSE3Expmap* pose = new g2o::VertexSE3Expmap(); // camera pose
    pose->setId(0);
//    pose->setEstimate( g2o::SE3Quat(
//            Eigen::Matrix3d::Identity(),
//            Eigen::Vector3d( 0,0,0 )
//    ) );
    Eigen::Matrix3d R_mat;
    R_mat<<
         R.at<double>(0,0),R.at<double>(0,1),R.at<double>(0,2),
                R.at<double>(1,0),R.at<double>(1,1),R.at<double>(1,2),
                        R.at<double>(2,0),R.at<double>(2,1),R.at<double>(2,2);
    pose->setEstimate(g2o::SE3Quat(R_mat,Eigen::Vector3d(t.at<double>(0,0),t.at<double>(0,1),t.at<double>(0,2))));
    optimizer.addVertex( pose );
    ///*这里要加上一个对Point的优化添加*///
    int pointIndex=1;
    for (auto &p:pts2){
        //for (const Point3f p:points_3d) 对比一下
        auto point=new g2o::VertexSBAPointXYZ();
        point->setId(pointIndex++);
        point->setMarginalized(true);
        point->setEstimate(Eigen::Vector3d(p.x,p.y,p.z));
        optimizer.addVertex(point);
    }

    // edges
    int index = 0;
    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) );
        EdgeProjectXYZRGBDPoseOnly* edge =new EdgeProjectXYZRGBDPoseOnly();///对应着构造函数.
        edge->setId( index );
        edge->setVertex( 0, dynamic_cast<g2o::VertexSBAPointXYZ*>(optimizer.vertex(index)));//point对应很多
        edge->setVertex(1, pose);
        edge->setMeasurement( Eigen::Vector3d(
                pts1[i].x, pts1[i].y, pts1[i].z) );
        //信息矩阵是啥东西...le4是啥
        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;

}