SLAM14讲 第七章 2D-2D 对极几何

根据匹配点估计相机运动

单目2D-2D 对极几何与三角测量

正确的匹配点：同一个空间点在两个成像平面上的投影

 

 

#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/calib3d/calib3d.hpp>
// #include "extra.h" // use this if in OpenCV2 
using namespace std;
using namespace cv;

/****************************************************
 * 本程序演示了如何使用2D-2D的特征匹配估计相机运动
 * **************************************************/

//前一节的orb特征提取和匹配封装成find_feature_matches函数
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 );

void pose_estimation_2d2d (
    std::vector<KeyPoint> keypoints_1,
    std::vector<KeyPoint> keypoints_2,
    std::vector< DMatch > matches,
    Mat& essential_matrix,
    Mat& R, Mat& t );

// 像素坐标转相机归一化坐标
Point2d pixel2cam ( const Point2d& p, const Mat& K );

int main ( int argc, char** argv )
{
    if ( argc != 3 )
    {
        cout<<"usage: pose_estimation_2d2d img1 img2"<<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;

    //-- 估计两张图像间运动
    Mat R,t,essential_matrix;
    pose_estimation_2d2d ( keypoints_1, keypoints_2, matches, essential_matrix, R, t );

    //-- 验证E=t^R*scale
    Mat t_x = ( Mat_<double> ( 3,3 ) <<
                0,                      -t.at<double> ( 2,0 ),     t.at<double> ( 1,0 ),
                t.at<double> ( 2,0 ),      0,                      -t.at<double> ( 0,0 ),
                -t.at<double> ( 1,0 ),     t.at<double> ( 0,0 ),      0 );

    cout<<"t^R="<<endl<<t_x*R<<endl;

    //-- 验证对极约束x2Tt^Rx1是否=0
    Mat K = ( Mat_<double> ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1 );
    for ( DMatch m: matches )
    {
        Point2d pt1 = pixel2cam ( keypoints_1[ m.queryIdx ].pt, K );
        Mat y1 = ( Mat_<double> ( 3,1 ) << pt1.x, pt1.y, 1 );
        Point2d pt2 = pixel2cam ( keypoints_2[ m.trainIdx ].pt, K );
        Mat y2 = ( Mat_<double> ( 3,1 ) << pt2.x, pt2.y, 1 );
        Mat d1 = y2.t() * t_x * R * y1;
        Mat d2 = y2.t() * essential_matrix * y1;
        cout << "epipolar constraint = " << d1 << endl;
        cout << "用E计算 = " << d2 << endl;
    }

    return 0;
}

//前一节的orb特征提取和匹配封装成find_feature_matches函数
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] );
        }
    }
}

// 像素坐标p转相机归一化坐标x
Point2d pixel2cam ( const Point2d& p, const Mat& K )
{
    return Point2d
           (
                //Mat获取元素M.at<double>(i,j)
               ( p.x - K.at<double> ( 0,2 ) ) / K.at<double> ( 0,0 ),
               ( p.y - K.at<double> ( 1,2 ) ) / K.at<double> ( 1,1 )
           );
}

//位姿估计
void pose_estimation_2d2d ( std::vector<KeyPoint> keypoints_1,
                            std::vector<KeyPoint> keypoints_2,
                            std::vector< DMatch > matches,
                            Mat& essential_matrix,
                            Mat& R, Mat& t )
{
    // 相机内参,TUM Freiburg2
    Mat K = ( Mat_<double> ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1 );

    //-- 把匹配点转换为vector<Point2f>的形式
    vector<Point2f> points1;
    vector<Point2f> points2;

    for ( int i = 0; i < ( int ) matches.size(); i++ )//遍历所有的匹配点
    {
        //vector类中的push_back函数：在vector尾部加入一个数据
        //std::vector< DMatch > matches
        //queryIdx : 查询点的索引（当前要寻找匹配结果的点在它所在图片上的索引）.
        //trainIdx : 被查询到的点的索引（存储库中的点的在存储库上的索引）
        //std::vector<KeyPoint> keypoints_1——pt存储point2f格式的坐标
        points1.push_back ( keypoints_1[matches[i].queryIdx].pt );
        points2.push_back ( keypoints_2[matches[i].trainIdx].pt );
    }

    //-- 计算基础矩阵F
    Mat fundamental_matrix;
    //CV_FM_7POINT, CV_FM_8POINT, CV_FM_LMEDS, CV_FM_RANSAC
    fundamental_matrix = findFundamentalMat ( points1, points2, CV_FM_8POINT );//八点法
    cout<<"fundamental_matrix is "<<endl<< fundamental_matrix<<endl;

    //-- 计算本质矩阵E
    //F和E之间只差相机参数
    Point2d principal_point ( 325.1, 249.7 );    //相机光心, TUM dataset标定值，double
    double focal_length = 521;            //相机焦距, TUM dataset标定值
    //Mat essential_matrix;
    essential_matrix = findEssentialMat ( points1, points2, focal_length, principal_point );
    cout<<"essential_matrix is "<<endl<< essential_matrix<<endl;

    //-- 计算单应矩阵H
    Mat homography_matrix;
    //ransacReprojThreshold——将点对视为内点的最大允许重投影错误阈值（仅用于RANSAC和RHO方法），1-10
    homography_matrix = findHomography ( points1, points2, RANSAC, 3 );
    cout<<"homography_matrix is "<<endl<<homography_matrix<<endl;

    //-- 从本质矩阵中恢复旋转和平移信息.E-->R,t 图1到图2的变换
    recoverPose ( essential_matrix, points1, points2, R, t, focal_length, principal_point );
    cout<<"R is "<<endl<<R<<endl;
    cout<<"t is "<<endl<<t<<endl;
    
}