通过两张图片实现2D-2D对极几何位姿估计

需要安装opencv3并且编译了features模块

代码中的1.png

代码中的2.png

// 来自高翔SLAM十四讲
#include<iostream>
#include<opencv2/core/core.hpp>
#include<opencv2/features2d/features2d.hpp>
#include<opencv2/highgui/highgui.hpp>
#include<opencv2/calib3d/calib3d.hpp>

using namespace std;
using namespace cv;

/*
    2D-2D的特征匹配估计相机运动
*/


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& 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(){
    // 读取图像
    Mat img_1 = imread("1.png", CV_LOAD_IMAGE_COLOR);
    Mat img_2 = imread("2.png", 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;

    // 估计两张图像之间的运动
    Mat R,t;
    pose_estimation_2d2d(keypoints_1, keypoints_2, matches, 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);
    // 这个t^R就是essential矩阵（本质矩阵），但是相差一个倍数
    cout<<"t^R = "<<endl<<t_x * R<<endl;

    // 验证对极约束
    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 d = y2.t() * t_x * R * y1;
        // 验证对极约束，理论上这个d应该是近似为0的
        cout<<"epipolar constraint = "<<d<<endl;
    }
    return 0;
}

// 找到匹配的特征点
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;
    Ptr<FeatureDetector>detector = ORB::create();
    Ptr<DescriptorExtractor>descriptor = ORB::create();
    Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");   // 暴力匹配

    // 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，使用汉明距离
    vector<DMatch> match;
    matcher->match(descriptors_1, descriptors_2, match);

    // 第四步：对匹配点对进行筛选
    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;
        min_dist = min_dist<dist?min_dist:dist;
        max_dist = max_dist>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
    // 设置30为阈值
    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_2d2d(std::vector<KeyPoint>keypoints_1,
                                                std::vector<KeyPoint>keypoints_2,
                                                std::vector<DMatch>matches,
                                                Mat&R ,Mat& t){
    // 相机内参,TUM Feriburg2
    Mat K = (Mat_<double>(3,3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);

    // 把匹配点转化为vector<Point2f>的形式
    vector<Point2f>points1;
    vector<Point2f>points2;

    for(int i=0; i<(int)matches.size(); i++){
        points1.push_back(keypoints_1[matches[i].queryIdx].pt);
        points2.push_back(keypoints_2[matches[i].trainIdx].pt);
    }

    // 计算基础矩阵:使用的8点法，但是书上说8点法是用来计算本质矩阵的呀，这两个有什么关系吗
    // 答：对于计算来说没有什么区别，本质矩阵就是基础矩阵乘以一个相机内参
    // 多于8个点就用最小二乘去解
    Mat fundamental_matrix;
    fundamental_matrix = findFundamentalMat(points1, points2, CV_FM_8POINT);    // Eigen库计算会更快一些
    cout<<"fundamental_matrix is "<<endl<<fundamental_matrix<<endl;

    // 计算本质矩阵：是由对极约束定义的：对极约束是等式为零的约束
    Point2d principal_point(325.1, 249.7);  // 相机光心,TUM dataset标定值
    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:通常描述处于共同平面上的一些点在两张图像之间的变换关系
    Mat homography_matrix;
    homography_matrix = findHomography(points1, points2, RANSAC, 3);
    cout<<"homography_matrix is "<<endl<<homography_matrix<<endl;

    // 从不本质矩阵中恢复旋转和平移信息
    // 这里的R,t组成的变换矩阵，满足的对极约束是:x2 = R * x1 + t,是第一个图到第二个图的坐标变换矩阵x2 = T21 * x1
    recoverPose(essential_matrix, points1, points2, R, t, focal_length, principal_point);
    cout<<"R is "<<endl<<R<<endl;
    cout<<"t is "<<endl<<t<<endl;
}