slambook2+ch7+pose_estimated_2d2d代码理解

算法流程

• 寻找关键点，计算描述子，寻找匹配点

• 利用对极几何计算本质矩阵，基础矩阵，单应矩阵

• 8点法求解本质矩阵（基础矩阵）

• 大于8点时可采用最小二乘法、随机采样一致性（RANSAC）

• 存在误匹配时倾向使用RANSAC

• 利用SVD(奇异值分解)求得旋转矩阵和平移矩阵

• 数值法、分析法分解单应矩阵求得R、t

• 验证本质矩阵，对极约束

• 相机内参数矩阵、焦距、光心已知

• 因为对极约束的尺度特性，真实的地图通常与计算出的相差一个非0常数倍

• 因为本质矩阵为平移矩阵叉乘旋转矩阵求得，当相机没有做平移运动时，对极几何无法应用

• 分析对极约束结果可知，算法精度不高

代码

//
// Created by wcm on 2020/6/6.
//
#include 
#include 
#include 
#include 
#include 

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
***********************************/

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
        );

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

int main( ){
    //--读取图像
    Mat img_1=imread("/home/automobile/wcm/slambook2/ch7/1.png", CV_LOAD_IMAGE_COLOR);
    Mat img_2=imread("/home/automobile/wcm/slambook2/ch7/2.png", CV_LOAD_IMAGE_COLOR);
    assert(img_1.data && img_2.data && "Cannot load images");

    //--寻找关键点，计算描述子，匹配关键点
    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
    //R=R21
    Mat R, t;
    pose_estimation_2d2d(keypoints_1, keypoints_2, matches, R, t);

    //--验证E=t^R*scale
    //首先声明一个3*3的空矩阵，然后根据t求取t的反对称矩阵t^
    //at(i,j)函数表示像素点的位置坐标
    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
    //首先给出相机内参数矩阵K，然后将像素坐标转换为归一化坐标
    //将坐标转换为矩阵，验证极限约束表达式是否为0
    //.t()表示转秩
    Mat K = (Mat_<double>(3,3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);//给相机内参数矩阵赋值
    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;
        cout << " epipolar constraint = " << d <<endl;
    }

    return 0;
}

    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();
    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，既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;
        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);

    //当描述子之间距离大于两倍最小距离时，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]);
        }
    }
}

    //像素坐标与相机坐标转换
    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 Freiburg2
    Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);

    //--把匹配点转换成vector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].queryIdx].pt);
    }

    //--计算基础矩阵
    //使用像素坐标计算基础矩阵
    //CV_FM_8POINT采用8点法求解基础矩阵
    Mat fundamental_matrix;
    fundamental_matrix = findFundamentalMat(points1, points2, CV_FM_8POINT);
    cout << " fundamental_matrix is " << endl << fundamental_matrix <<endl;

    //--计算本质矩阵
    //使用归一化坐标计算本质矩阵，需要知道相机的光心，焦距
    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
    //--但是本例中场景不是平面，单应矩阵意义不大
    Mat homography_matrix;
    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
    //SVD奇异值分解
    //此函数仅在OpenCV3中提供
    recoverPose(essential_matrix, points1, points2, R, t, focal_length, principal_point);
    cout << "R is " << endl << R << endl;
    cout << "t is " << endl << t <<endl;

}

运行结果

[ INFO:0] Initialize OpenCL runtime...
 --Max dist : 95.000000 
 --Min dist : 7.000000 
 一共找到了 81 组匹配点 
 fundamental_matrix is 
[1.455900569774558e-07, 4.172375256092383e-07, -0.000247367342610671;
 1.984383403826e-06, 1.639671857682763e-05, -0.004365075631543996;
 -0.0004620281656059453, -0.003641645418601539, 1]
essential_Matrix is 
[0.3016723863865509, 0.6285032399186232, 0.02435146277233041;
 -0.6010017169873993, 0.3163461564700642, -0.1572219925828741;
 -0.1542190765679919, -0.05131484904355308, -0.03116100395886274]
homography_matrix is 
[-0.7483500806577918, -0.06258427032975751, 325.3185890263245;
 -0.238998269067723, -0.01160828848589558, 102.8107936795173;
 -0.002274322034400319, -0.0002520331084630441, 1]
R is 
[-0.8986890561148634, 0.433848611244593, -0.06429123533199321;
 -0.4137934068328298, -0.8873149959911232, -0.2035856437741956;
 -0.1453719260416433, -0.1563569007444517, 0.9769439711204183]
t is 
[-0.1636120714646943;
 0.1673516687283813;
 -0.9722265728958749]
 t^R = 
[-0.4266291802213185, -0.8888378058883485, -0.03443816891625309;
 0.8499447791730966, -0.4473810248845647, 0.2223454742140221;
 0.2180987096591085, 0.07257015546852119, 0.04406831441578762]
 epipolar constraint = [-0.0753274369265802]
 epipolar constraint = [-0.0197752973799656]
 epipolar constraint = [-0.1046929147455941]
 epipolar constraint = [0.0005126175133886024]
 epipolar constraint = [-0.1213941807408835]
 epipolar constraint = [0.02403999634887131]
 epipolar constraint = [-0.1671191278662195]
 epipolar constraint = [-0.1654927648396349]
 epipolar constraint = [0.08008318133752024]
 epipolar constraint = [0.07987401303791081]
 epipolar constraint = [0.02004886716519435]
 epipolar constraint = [-0.1295686192381137]
 epipolar constraint = [0.04728527035355962]
 epipolar constraint = [0.07956578239334794]
 epipolar constraint = [-0.02010893812539163]
 epipolar constraint = [0.02535571662279874]
 epipolar constraint = [-0.0725455187807351]
 epipolar constraint = [-0.0648802293330764]
 epipolar constraint = [-0.1432906102530886]
 epipolar constraint = [0.0795074765672304]
 epipolar constraint = [0.04698029361071185]
 epipolar constraint = [0.02043948672883346]
 epipolar constraint = [0.07887714352210105]
 epipolar constraint = [0.02409017705086632]
 epipolar constraint = [-0.118665570392088]
 epipolar constraint = [4.975159681777641e-05]
 epipolar constraint = [-0.02070309538864171]
 epipolar constraint = [0.09482041447460186]
 epipolar constraint = [0.08182358399842843]
 epipolar constraint = [0.02426878878025789]
 epipolar constraint = [0.02338380562908568]
 epipolar constraint = [0.04598268064876031]
 epipolar constraint = [0.02001780253126184]
 epipolar constraint = [-0.0003069505996259048]
 epipolar constraint = [-0.1220772359154428]
 epipolar constraint = [0.08325145780153809]
 epipolar constraint = [0.08236049675707369]
 epipolar constraint = [0.07869747038600788]
 epipolar constraint = [-0.07990720858727506]
 epipolar constraint = [0.04564596841157867]
 epipolar constraint = [0.02513498140701478]
 epipolar constraint = [0.02337542451177792]
 epipolar constraint = [-0.07295260521777472]
 epipolar constraint = [-0.1466903373879551]
 epipolar constraint = [-0.1395273996603885]
 epipolar constraint = [-0.01947703069502896]
 epipolar constraint = [-0.001141843294882525]
 epipolar constraint = [-0.002456622453787444]
 epipolar constraint = [-0.0732793545158362]
 epipolar constraint = [0.01973318595401235]
 epipolar constraint = [-0.08083851314227503]
 epipolar constraint = [0.02354058695529868]
 epipolar constraint = [-0.01980839500064362]
 epipolar constraint = [0.0456828129048461]
 epipolar constraint = [-0.06631671784511953]
 epipolar constraint = [-0.001834739444027178]
 epipolar constraint = [-0.07437755472915204]
 epipolar constraint = [-0.0001807371694217824]
 epipolar constraint = [0.04540427905859452]
 epipolar constraint = [-0.02005764036946135]
 epipolar constraint = [-0.08144013822751789]
 epipolar constraint = [0.02050452810374639]
 epipolar constraint = [0.1232878056105139]
 epipolar constraint = [-0.06540835801465628]
 epipolar constraint = [0.04340646585659767]
 epipolar constraint = [-0.01932535269732853]
 epipolar constraint = [-0.05191972230379729]
 epipolar constraint = [0.1275598467816627]
 epipolar constraint = [0.02231074084289995]
 epipolar constraint = [0.129278607563628]
 epipolar constraint = [0.1266038441333597]
 epipolar constraint = [-0.02094436566004827]
 epipolar constraint = [0.0418862919457927]
 epipolar constraint = [0.02177178826535921]
 epipolar constraint = [-0.08173698020641162]
 epipolar constraint = [0.04301362181850519]
 epipolar constraint = [-0.06698270016010799]
 epipolar constraint = [0.02743731289131052]
 epipolar constraint = [0.000436628349686885]
 epipolar constraint = [0.04659252356669603]
 epipolar constraint = [0.1120717034333355]

Process finished with exit code 0