slambook2+ch7+triangulation+代码理解

算法流程

1. 找寻特征点
2. 匹配特征点
3. 采用对极几何的方法求取相机位姿的旋转矩阵和平移矩阵
4. 根据特征点、相机位姿求解空间三维点
5. 对不同深度的特征点用不同颜色圈出

代码部分

//
// Created by wcm on 2020/6/9.
//

#include 
#include 
// #include "extra.h" // used in opencv2
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);

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

void triangulation(
        const vector<KeyPoint> &keypoint_1,
        const vector<KeyPoint> &keypoint_2,
        const std::vector<DMatch> &matches,
        const Mat &R, const Mat &t,
        vector<Point3d> &points
);

// 作图用
//cv::Scalar函数用来设置图片的颜色，前三个参数为RGB，第四个参数为透明度
//输入参数depth为三角测量求得的像素点的深度，深度不同，画出的颜色也不同
inline cv::Scalar get_color(float depth) {
    float up_th = 50, low_th = 10, th_range = up_th - low_th;
    if (depth > up_th) depth = up_th;
    if (depth < low_th) depth = low_th;
    return cv::Scalar(255 * depth / th_range, 0, 255 * (1 - depth / th_range));
}

// 像素坐标转相机归一化坐标
Point2f pixel2cam(const Point2d &p, const Mat &K);

int main(int argc, char **argv) {

    //-- 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);

    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;
    pose_estimation_2d2d(keypoints_1, keypoints_2, matches, R, t);

    //-- 三角化
    vector<Point3d> points;
    triangulation(keypoints_1, keypoints_2, matches, R, t, points);

    //-- 验证三角化点与特征点的重投影关系
    Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
    Mat img1_plot = img_1.clone();
    Mat img2_plot = img_2.clone();
    for (int i = 0; i < matches.size(); i++) {
        // 第一个图
        //cv::circle()画圈函数，在关键点周围画圈，
        //cv::DMatch(queryIdx("new image"), trainIdx("old image"),
        // imgIdx("identify the the practicular image from the training image ",
        // diatance("indicate the quality of match") ))
        float depth1 = points[i].z;
        cout << "depth: " << depth1 << endl;
        Point2d pt1_cam = pixel2cam(keypoints_1[matches[i].queryIdx].pt, K);
        cv::circle(img1_plot, keypoints_1[matches[i].queryIdx].pt, 2, get_color(depth1), 2);

        // 第二个图
        Mat pt2_trans = R * (Mat_<double>(3, 1) << points[i].x, points[i].y, points[i].z) + t;
        float depth2 = pt2_trans.at<double>(2, 0);
        cv::circle(img2_plot, keypoints_2[matches[i].trainIdx].pt, 2, get_color(depth2), 2);
    }
    cv::imshow("img 1", img1_plot);
    cv::imshow("img 2", img2_plot);
    cv::waitKey();

    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();
    // use this if you are in OpenCV2
    // Ptr detector = FeatureDetector::create ( "ORB" );
    // Ptr 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]);
        }
    }
}

void pose_estimation_2d2d(
        const std::vector<KeyPoint> &keypoints_1,
        const std::vector<KeyPoint> &keypoints_2,
        const 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);

    //-- 把匹配点转换为vector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);
    }

    //-- 计算本质矩阵
    Point2d principal_point(325.1, 249.7);        //相机主点, TUM dataset标定值
    int focal_length = 521;            //相机焦距, TUM dataset标定值
    Mat essential_matrix;
    essential_matrix = findEssentialMat(points1, points2, focal_length, principal_point);

    //-- 从本质矩阵中恢复旋转和平移信息.
    recoverPose(essential_matrix, points1, points2, R, t, focal_length, principal_point);
}

void triangulation(
        const vector<KeyPoint> &keypoint_1,
        const vector<KeyPoint> &keypoint_2,
        const std::vector<DMatch> &matches,
        const Mat &R, const Mat &t,
        vector<Point3d> &points) {

    //T1、T2为两个相机的位姿矩阵
    Mat T1 = (Mat_<float>(3, 4) <<
                                1, 0, 0, 0,
            0, 1, 0, 0,
            0, 0, 1, 0);
    Mat T2 = (Mat_<float>(3, 4) <<
                                R.at<double>(0, 0), R.at<double>(0, 1), R.at<double>(0, 2), t.at<double>(0, 0),
            R.at<double>(1, 0), R.at<double>(1, 1), R.at<double>(1, 2), t.at<double>(1, 0),
            R.at<double>(2, 0), R.at<double>(2, 1), R.at<double>(2, 2), t.at<double>(2, 0)
    );

    Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
    vector<Point2f> pts_1, pts_2;
    for (DMatch m:matches) {
        // 将像素坐标转换至相机坐标
        pts_1.push_back(pixel2cam(keypoint_1[m.queryIdx].pt, K));
        pts_2.push_back(pixel2cam(keypoint_2[m.trainIdx].pt, K));
    }

    //cv::triangulaPoints(projMatr1("3*4 projection matrix of cam1"),
    // projMatr2("3*4 projection matrix of cam2"),
    // projPoints1("2*N array of corresponding points in first image"),
    // projPoints2("2*N array of corresponding points in second image"),
    // points4D("4*N array of reconstruction in homogeneous coordinates"))
    Mat pts_4d;
    cv::triangulatePoints(T1, T2, pts_1, pts_2, pts_4d);

    // 转换成非齐次坐标
    for (int i = 0; i < pts_4d.cols; i++) {
        Mat x = pts_4d.col(i);
        x /= x.at<float>(3, 0); // 归一化
        Point3d p(
                x.at<float>(0, 0),
                x.at<float>(1, 0),
                x.at<float>(2, 0)
        );
        points.push_back(p);
    }
}

Point2f pixel2cam(const Point2d &p, const Mat &K) {
    return Point2f
            (
                    (p.x - K.at<double>(0, 2)) / K.at<double>(0, 0),
                    (p.y - K.at<double>(1, 2)) / K.at<double>(1, 1)
            );
}

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
depth: 66.0186
depth: 21.0728
depth: 20.3952
depth: 16.9029
depth: 19.8927
depth: 37.7193
depth: 22.5936
depth: 20.9212
depth: 16.1058
depth: 16.9235
depth: 21.188
depth: 22.2664
depth: 17.1165
depth: 17.4836
depth: 21.982
depth: 34.889
depth: 77.3512
depth: 80.3103
depth: 20.7005
depth: 17.1341
depth: 17.7618
depth: 20.41
depth: 17.1729
depth: 37.5745
depth: 20.7774
depth: 17.3433
depth: 21.9547
depth: 14.74
depth: 16.6306
depth: 34.7793
depth: 34.5093
depth: 17.7108
depth: 19.9396
depth: 17.077
depth: 20.9776
depth: 16.3867
depth: 16.5827
depth: 16.2495
depth: 65.2504
depth: 17.1249
depth: 35.5666
depth: 35.8194
depth: 68.6612
depth: 21.0837
depth: 22.3647
depth: 21.2923
depth: 17.3458
depth: 20.1207
depth: 27.1816
depth: 19.8897
depth: 24.2379
depth: 37.1623
depth: 20.4894
depth: 18.3041
depth: 25.206
depth: 18.6171
depth: 23.9337
depth: 17.8096
depth: 18.5897
depth: 20.0973
depth: 24.9094
depth: 22.4146
depth: 12.884
depth: 22.8616
depth: 16.1684
depth: 20.0982
depth: 30.8074
depth: 11.9117
depth: 19.4316
depth: 11.6402
depth: 11.3385
depth: 20.5574
depth: 17.5733
depth: 23.1775
depth: 23.7922
depth: 21.7831
depth: 24.9361
depth: 20.0201
depth: 17.1896
depth: 20.7021
depth: 13.3843