视觉SLAM 十四讲——三角测量

主要内容

1. 求解

　　P153-154

2. 讨论

　　1）三角测量是由平移得到的，有平移才会有对极几何中的三角形

　　　　纯旋转无法使用三角测量

　　2） 三角测量的不确定性

　　　　平移较大时，在同样的相机分辨率下，三角化测量将更精确

3. 提高三角测量精度：

　　1） 提高特征点的提取精度，提高图像分辨率

　　　　缺点是增大计算成本

　　2） 增大平移量

　　　　缺点：图像的外观发生明显的变化，外观变化会使得特征提取与匹配变得困难（三角化的矛盾）

4. 代码中需注意的点

　　1）cv::triangulatePoints 函数的使用（输入参数，输出结果的形式，坐标系等）

　　2） 最终结果的验证方式：利用像素坐标计算的归一化坐标和三角化计算的三维左边，计算两种方式的残差信息。（这是后续3D-2D的核心思想——最小化重投影误差）

 

参考链接

 Opencv学习（9）——triangulatePoints()

 

代码

#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" // 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
);

// 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 )
{
    if ( argc != 3 )
    {
        cout<<"usage: triangulation 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 );

    //-- 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 );
    for ( int i=0; i<matches.size(); i++ )
    {
        Point2d pt1_cam = pixel2cam( keypoints_1[ matches[i].queryIdx ].pt, K );
        Point2d pt1_cam_3d(
            points[i].x/points[i].z, 
            points[i].y/points[i].z 
        );
        
        cout<<"point in the first camera frame: "<<pt1_cam<<endl;
        cout<<"point projected from 3D "<<pt1_cam_3d<<", d="<<points[i].z<<endl;
        
        // 第二个图
        Point2f pt2_cam = pixel2cam( keypoints_2[ matches[i].trainIdx ].pt, K );
        Mat pt2_trans = R*( Mat_<double>(3,1) << points[i].x, points[i].y, points[i].z ) + t;
        pt2_trans /= pt2_trans.at<double>(2,0);
        cout<<"point in the second camera frame: "<<pt2_cam<<endl;
        cout<<"point reprojected from second frame: "<<pt2_trans.t()<<endl;
        cout<<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();
    // 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] );
        }
    }
}

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<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 );
    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;
    cout<<"t is "<<endl<<t<<endl;
}

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 )
{
    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) );
    }
    
    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) 
    );
}

结果及分析

point in the first camera frame: [-0.151193, -0.0780827]
point projected from 3D [-0.151193, -0.0780893], d=9.31937
point in the second camera frame: [-0.179854, -0.0589785]
point reprojected from second frame: [-0.1798545644710269, -0.05897215312873306, 1]

　　输出结果为：

　　某一像素点：

　　　　在第一幅图中利用像素坐标计算归一化坐标信息， 和 利用三角测量计算出来的坐标归一化以后的残差信息

　　　　在第二幅图中利用像素坐标计算归一化坐标信息， 和 利用运动信息和三角测量出来的点的信息，得到第二个相机下的三维坐标，归一化，相减得到残差信息

　　残差的精度在0.000×。