视觉slam14讲ch7

已知文件夹pose_estimation_2d2d下面两幅图像1.png 2.png

单目相机2d-2d：对极几何验证

#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;


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 );

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;
    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 );

    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 );    //像素坐标转相机归一化坐标
        Mat y1 = ( Mat_<double> ( 3,1 ) << pt1.x, pt1.y, 1 );           //y1 = [x1,y1,1]T 相当于 x1 = [u1,v1,1]T
        Point2d pt2 = pixel2cam ( keypoints_2[ m.trainIdx ].pt, K );
        Mat y2 = ( Mat_<double> ( 3,1 ) << pt2.x, pt2.y, 1 );           //y2 = [x2,y2,1]T
        Mat d = y2.t() * t_x * R * y1;                          //验证y2T * t_x * y1是否近似于0满足对极几何,相当于x2T * t_x * x1
        cout << "epipolar constraint = " << d << endl;
    }
    return 0;
}

//ORB特征匹配函数
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();
    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] );
        }
    }
}

// 像素坐标转相机归一化坐标
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 )
           );
}

//2d-2d单目对极几何计算
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
    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
    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
    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.
    recoverPose ( essential_matrix, points1, points2, R, t, focal_length, principal_point );
    cout<<"R is "<<endl<<R<<endl;
}

 在vscode终端输入以下指令

gmm@WP:~/slambook/ch7/pose_estimation_2d2d$ build/pose_estimation_2d2d 1.png 2.png

 得到结果

-- Max dist : 95.000000 
-- Min dist : 7.000000 
一共找到了81组匹配点
fundamental_matrix is 
[5.435453065936294e-06, 0.0001366043242989641, -0.02140890086948122;
 -0.0001321142229824704, 2.339475702778057e-05, -0.006332906454396256;
 0.02107630352202776, -0.00366683395295285, 1]
essential_matrix is 
[0.01724015832721706, 0.328054335794133, 0.0473747783144249;
 -0.3243229585962962, 0.03292958445202408, -0.6262554366073018;
 -0.005885857752320116, 0.6253830041920333, 0.0153167864909267]
homography_matrix is 
[0.91317517918067, -0.1092435315821776, 29.95860009981271;
 0.02223560352310949, 0.9826008005061946, 6.50891083956826;
 -0.0001001560381023939, 0.0001037779436396116, 1]
R is 
[0.9985534106102478, -0.05339308467584758, 0.006345444621108698;
 0.05321959721496264, 0.9982715997131746, 0.02492965459802003;
 -0.007665548311697523, -0.02455588961730239, 0.9996690690694516]
t^R=
[-0.02438126572381045, -0.4639388908753606, -0.06699805400667856;
 0.4586619266358499, -0.04656946493536188, 0.8856589319599302;
 0.008323859859529846, -0.8844251262060034, -0.0216612071874423]
epipolar constraint = [0.004334754136721797]
epipolar constraint = [-0.0002809243685121809]
epipolar constraint = [-0.001438247945977744]
epipolar constraint = [0.0003269033947393973]
epipolar constraint = [-0.0003553231638489529]
epipolar constraint = [0.001284545296795364]
epipolar constraint = [0.0007111119070243033]
epipolar constraint = [0.0005809963024551446]
epipolar constraint = [-0.0004569505410570683]
epipolar constraint = [-0.0001985091674428126]
epipolar constraint = [0.0009954466629851014]
epipolar constraint = [0.004183444398105557]
epipolar constraint = [0.0003301500278483499]
epipolar constraint = [0.000433468422895756]
epipolar constraint = [0.002166463717508241]
epipolar constraint = [0.0008612142972820036]
epipolar constraint = [0.006260134367574832]
epipolar constraint = [0.007343864270669354]
epipolar constraint = [0.0006997299583792263]
epipolar constraint = [-0.0002735148772005716]
epipolar constraint = [-5.272337012321437e-07]
epipolar constraint = [0.0007372565015377822]
epipolar constraint = [-0.0006697357792934122]
epipolar constraint = [0.003123484301720714]
epipolar constraint = [-0.001231690598807428]
epipolar constraint = [0.0002668695748940936]
epipolar constraint = [0.004005543462373876]
epipolar constraint = [0.0003056705066544624]
epipolar constraint = [-0.003108414268527718]
epipolar constraint = [-1.915351944714594e-06]
epipolar constraint = [0.0006933459945522302]
epipolar constraint = [-1.20842520190817e-05]
epipolar constraint = [0.001931054288970224]
epipolar constraint = [-0.001327411567348349]
epipolar constraint = [-0.001158918062891631]
epipolar constraint = [-0.001858904428330923]
epipolar constraint = [0.0001556314587936695]
epipolar constraint = [-0.002373723544446836]
epipolar constraint = [0.004805889122330598]
epipolar constraint = [-0.0009747832347852675]
epipolar constraint = [0.0006571155616519331]
epipolar constraint = [0.002337204394122716]
epipolar constraint = [0.004765516758509947]
epipolar constraint = [-0.001750870050808317]
epipolar constraint = [0.001092859392827487]
epipolar constraint = [0.0006769492505509164]
epipolar constraint = [0.0003307429644405918]
epipolar constraint = [0.001876564994448115]
epipolar constraint = [0.001832354276950641]
epipolar constraint = [7.744615696386736e-07]
epipolar constraint = [-0.0007964236477854686]
epipolar constraint = [0.0001236409258935089]
epipolar constraint = [1.386843227244028e-06]
epipolar constraint = [0.0001450355326295741]
epipolar constraint = [0.00109731208246224]
epipolar constraint = [-0.002227053499071974]
epipolar constraint = [0.002240603253167585]
epipolar constraint = [0.0002359213388878484]
epipolar constraint = [0.003035338951631217]
epipolar constraint = [0.002650788007581513]
epipolar constraint = [-0.0002311129052587763]
epipolar constraint = [0.003158726652554816]
epipolar constraint = [0.00318443380492206]
epipolar constraint = [-0.0003030993775385848]
epipolar constraint = [-0.004151424678597325]
epipolar constraint = [0.000962908812924268]
epipolar constraint = [0.00166825104315349]
epipolar constraint = [-0.001953002815440141]
epipolar constraint = [-0.0024677215713114]
epipolar constraint = [0.0008218799177506786]
epipolar constraint = [1.369310688559278e-06]
epipolar constraint = [-0.001891259735584946]
epipolar constraint = [-0.0001304333417016107]
epipolar constraint = [0.0002565573533065552]
epipolar constraint = [0.006010380518284446]
epipolar constraint = [-0.0004837802950156331]
epipolar constraint = [0.00547529124350349]
epipolar constraint = [0.001722398975726524]
epipolar constraint = [-0.0004945848903547823]
epipolar constraint = [-0.004259380631293275]
epipolar constraint = [-0.0007738612238716719]

从程序结果可以看出，对极几何约束的精度约在10^-3量级。