自学SLAM（9）《第五讲：特征点法视觉里程计》作业

Chris·Bosh2023-12-27 4:09

文章目录

  • 1.ORB特征点
    • [1.1 ORB提取](#1.1 ORB提取)
    • [1.2 ORB描述](#1.2 ORB描述)
    • [1.3 暴力匹配](#1.3 暴力匹配)
    • [1.4 最后，请结合实验，回答下⾯⼏个问题](#1.4 最后，请结合实验，回答下⾯⼏个问题)
  • [2.从 E 恢复 R，t](#2.从 E 恢复 R，t)
  • [3.用 G-N 实现 Bundle Adjustment](#3.用 G-N 实现 Bundle Adjustment)
  • [4.* 用 ICP 实现轨迹对齐](#4.* 用 ICP 实现轨迹对齐)

1.ORB特征点

1.1 ORB提取

ORB(Oriented FAST and BRIEF) 特征是 SLAM 中⼀种很常⽤的特征，由于其⼆进制特性，使得它可以⾮常快速地提取与计算 [1]。下⾯，你将按照本题的指导，⾃⾏书写 ORB 的提取、描述⼦的计算以及匹配的代码。代码框架参照computeORB.cpp ⽂件，图像见 1.png ⽂件和 2.png。

1.2 ORB描述

1.3 暴力匹配


提⽰：

  1. 你需要按位计算两个描述⼦之间的汉明距离。
  2. OpenCV 的 DMatch 结构， queryIdx 为第⼀图的特征 ID， trainIdx 为第⼆个图的特征 ID。
  3. 作为验证，匹配之后输出图像应如图 2 所⽰。

1.4 最后，请结合实验，回答下⾯⼏个问题

最后，请结合实验，回答下⾯⼏个问题：

  1. 为什么说 ORB 是⼀种⼆进制特征？
  2. 为什么在匹配时使⽤ 50 作为阈值，取更⼤或更⼩值会怎么样？
  3. 暴⼒匹配在你的机器上表现如何？你能想到什么减少计算量的匹配⽅法吗？

我直接把1.1，1.2，1.3的代码和结果放到一起

computeORB.cpp：

cpp 复制代码 
#include <opencv2/opencv.hpp>

#include <string>

using namespace std;

// global variables
string first_file = "../1.png";
string second_file = "../2.png";

const double pi = 3.1415926;    // pi


// TODO implement this function
/**
 * compute the angle for ORB descriptor
 * @param [in] image input image
 * @param [in|out] detected keypoints
 */
void computeAngle(const cv::Mat &image, vector<cv::KeyPoint> &keypoints);

// TODO implement this function
/**
 * compute ORB descriptor
 * @param [in] image the input image
 * @param [in] keypoints detected keypoints
 * @param [out] desc descriptor
 */
typedef vector<bool> DescType;  // type of descriptor, 256 bools
void computeORBDesc(const cv::Mat &image, vector<cv::KeyPoint> &keypoints, vector<DescType> &desc);

// TODO implement this function
/**
 * brute-force match two sets of descriptors
 * @param desc1 the first descriptor
 * @param desc2 the second descriptor
 * @param matches matches of two images
 */
void bfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches);

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

    // load image
    cv::Mat first_image = cv::imread(first_file, 0);    // load grayscale image
    cv::Mat second_image = cv::imread(second_file, 0);  // load grayscale image

    // plot the image
    cv::imshow("first image", first_image);
    cv::imshow("second image", second_image);
    cv::waitKey(0);

    // detect FAST keypoints using threshold=40
    vector<cv::KeyPoint> keypoints;
    cv::FAST(first_image, keypoints, 40);
    cout << "keypoints: " << keypoints.size() << endl;

    // compute angle for each keypoint
    computeAngle(first_image, keypoints);

    // compute ORB descriptors
    vector<DescType> descriptors;
    computeORBDesc(first_image, keypoints, descriptors);

    // plot the keypoints
    cv::Mat image_show;
    cv::drawKeypoints(first_image, keypoints, image_show, cv::Scalar::all(-1),
                      cv::DrawMatchesFlags::DRAW_RICH_KEYPOINTS);
    cv::imshow("features", image_show);
    cv::imwrite("feat1.png", image_show);
    cv::waitKey(0);

    // we can also match descriptors between images
    // same for the second
    vector<cv::KeyPoint> keypoints2;
    cv::FAST(second_image, keypoints2, 40);
    cout << "keypoints: " << keypoints2.size() << endl;

    // compute angle for each keypoint
    computeAngle(second_image, keypoints2);

    // compute ORB descriptors
    vector<DescType> descriptors2;
    computeORBDesc(second_image, keypoints2, descriptors2);

    // find matches
    vector<cv::DMatch> matches;
    bfMatch(descriptors, descriptors2, matches);
    cout << "matches: " << matches.size() << endl;

    // plot the matches
    cv::drawMatches(first_image, keypoints, second_image, keypoints2, matches, image_show);
    cv::imshow("matches", image_show);
    cv::imwrite("matches.png", image_show);
    cv::waitKey(0);

    cout << "done." << endl;
    return 0;
}

// -------------------------------------------------------------------------------------------------- //

// compute the angle
void computeAngle(const cv::Mat &image, vector<cv::KeyPoint> &keypoints) {
    int half_patch_size = 8;
    for (auto &kp : keypoints) {
	// START YOUR CODE HERE (~7 lines)
         //judge if keypoint is on edge
        int x=cvRound(kp.pt.x);
        int y=cvRound(kp.pt.y);
        if( x-half_patch_size<0||x+half_patch_size>image.cols||
            y-half_patch_size<0||y+half_patch_size>image.rows)
            continue;  //结束当前循环，进入到下一次循环
        double m01=0,m10=0;   //定义变量的时候，要初始化，不然这里第一张图片所有kp.angle=0
        for(int i=-half_patch_size;i<half_patch_size;i++){    //-8<i<8,-8<j<8
            for(int j=-half_patch_size;j<half_patch_size;j++){
                m01 += j*image.at<uchar>(y+j,x+i);              //真实坐标(j,i)+(y,x)
                m10 += i*image.at<uchar>(y+j,x+i);              //获得单个像素值image.at<uchar>(y,x)
            }
        }
        kp.angle = atan(m01/m10)*180/pi;
        cout<<"m10 = "<<m01<<"   "<<"m01 = "<<m10<<"  "<<"kp.angle = "<<kp.angle<<endl;
        // END YOUR CODE HERE
    }
    return;
}

// -------------------------------------------------------------------------------------------------- //
// ORB pattern
int ORB_pattern[256 * 4] = {
        8, -3, 9, 5/*mean (0), correlation (0)*/,
        4, 2, 7, -12/*mean (1.12461e-05), correlation (0.0437584)*/,
        -11, 9, -8, 2/*mean (3.37382e-05), correlation (0.0617409)*/,
        7, -12, 12, -13/*mean (5.62303e-05), correlation (0.0636977)*/,
        2, -13, 2, 12/*mean (0.000134953), correlation (0.085099)*/,
        1, -7, 1, 6/*mean (0.000528565), correlation (0.0857175)*/,
        -2, -10, -2, -4/*mean (0.0188821), correlation (0.0985774)*/,
        -13, -13, -11, -8/*mean (0.0363135), correlation (0.0899616)*/,
        -13, -3, -12, -9/*mean (0.121806), correlation (0.099849)*/,
        10, 4, 11, 9/*mean (0.122065), correlation (0.093285)*/,
        -13, -8, -8, -9/*mean (0.162787), correlation (0.0942748)*/,
        -11, 7, -9, 12/*mean (0.21561), correlation (0.0974438)*/,
        7, 7, 12, 6/*mean (0.160583), correlation (0.130064)*/,
        -4, -5, -3, 0/*mean (0.228171), correlation (0.132998)*/,
        -13, 2, -12, -3/*mean (0.00997526), correlation (0.145926)*/,
        -9, 0, -7, 5/*mean (0.198234), correlation (0.143636)*/,
        12, -6, 12, -1/*mean (0.0676226), correlation (0.16689)*/,
        -3, 6, -2, 12/*mean (0.166847), correlation (0.171682)*/,
        -6, -13, -4, -8/*mean (0.101215), correlation (0.179716)*/,
        11, -13, 12, -8/*mean (0.200641), correlation (0.192279)*/,
        4, 7, 5, 1/*mean (0.205106), correlation (0.186848)*/,
        5, -3, 10, -3/*mean (0.234908), correlation (0.192319)*/,
        3, -7, 6, 12/*mean (0.0709964), correlation (0.210872)*/,
        -8, -7, -6, -2/*mean (0.0939834), correlation (0.212589)*/,
        -2, 11, -1, -10/*mean (0.127778), correlation (0.20866)*/,
        -13, 12, -8, 10/*mean (0.14783), correlation (0.206356)*/,
        -7, 3, -5, -3/*mean (0.182141), correlation (0.198942)*/,
        -4, 2, -3, 7/*mean (0.188237), correlation (0.21384)*/,
        -10, -12, -6, 11/*mean (0.14865), correlation (0.23571)*/,
        5, -12, 6, -7/*mean (0.222312), correlation (0.23324)*/,
        5, -6, 7, -1/*mean (0.229082), correlation (0.23389)*/,
        1, 0, 4, -5/*mean (0.241577), correlation (0.215286)*/,
        9, 11, 11, -13/*mean (0.00338507), correlation (0.251373)*/,
        4, 7, 4, 12/*mean (0.131005), correlation (0.257622)*/,
        2, -1, 4, 4/*mean (0.152755), correlation (0.255205)*/,
        -4, -12, -2, 7/*mean (0.182771), correlation (0.244867)*/,
        -8, -5, -7, -10/*mean (0.186898), correlation (0.23901)*/,
        4, 11, 9, 12/*mean (0.226226), correlation (0.258255)*/,
        0, -8, 1, -13/*mean (0.0897886), correlation (0.274827)*/,
        -13, -2, -8, 2/*mean (0.148774), correlation (0.28065)*/,
        -3, -2, -2, 3/*mean (0.153048), correlation (0.283063)*/,
        -6, 9, -4, -9/*mean (0.169523), correlation (0.278248)*/,
        8, 12, 10, 7/*mean (0.225337), correlation (0.282851)*/,
        0, 9, 1, 3/*mean (0.226687), correlation (0.278734)*/,
        7, -5, 11, -10/*mean (0.00693882), correlation (0.305161)*/,
        -13, -6, -11, 0/*mean (0.0227283), correlation (0.300181)*/,
        10, 7, 12, 1/*mean (0.125517), correlation (0.31089)*/,
        -6, -3, -6, 12/*mean (0.131748), correlation (0.312779)*/,
        10, -9, 12, -4/*mean (0.144827), correlation (0.292797)*/,
        -13, 8, -8, -12/*mean (0.149202), correlation (0.308918)*/,
        -13, 0, -8, -4/*mean (0.160909), correlation (0.310013)*/,
        3, 3, 7, 8/*mean (0.177755), correlation (0.309394)*/,
        5, 7, 10, -7/*mean (0.212337), correlation (0.310315)*/,
        -1, 7, 1, -12/*mean (0.214429), correlation (0.311933)*/,
        3, -10, 5, 6/*mean (0.235807), correlation (0.313104)*/,
        2, -4, 3, -10/*mean (0.00494827), correlation (0.344948)*/,
        -13, 0, -13, 5/*mean (0.0549145), correlation (0.344675)*/,
        -13, -7, -12, 12/*mean (0.103385), correlation (0.342715)*/,
        -13, 3, -11, 8/*mean (0.134222), correlation (0.322922)*/,
        -7, 12, -4, 7/*mean (0.153284), correlation (0.337061)*/,
        6, -10, 12, 8/*mean (0.154881), correlation (0.329257)*/,
        -9, -1, -7, -6/*mean (0.200967), correlation (0.33312)*/,
        -2, -5, 0, 12/*mean (0.201518), correlation (0.340635)*/,
        -12, 5, -7, 5/*mean (0.207805), correlation (0.335631)*/,
        3, -10, 8, -13/*mean (0.224438), correlation (0.34504)*/,
        -7, -7, -4, 5/*mean (0.239361), correlation (0.338053)*/,
        -3, -2, -1, -7/*mean (0.240744), correlation (0.344322)*/,
        2, 9, 5, -11/*mean (0.242949), correlation (0.34145)*/,
        -11, -13, -5, -13/*mean (0.244028), correlation (0.336861)*/,
        -1, 6, 0, -1/*mean (0.247571), correlation (0.343684)*/,
        5, -3, 5, 2/*mean (0.000697256), correlation (0.357265)*/,
        -4, -13, -4, 12/*mean (0.00213675), correlation (0.373827)*/,
        -9, -6, -9, 6/*mean (0.0126856), correlation (0.373938)*/,
        -12, -10, -8, -4/*mean (0.0152497), correlation (0.364237)*/,
        10, 2, 12, -3/*mean (0.0299933), correlation (0.345292)*/,
        7, 12, 12, 12/*mean (0.0307242), correlation (0.366299)*/,
        -7, -13, -6, 5/*mean (0.0534975), correlation (0.368357)*/,
        -4, 9, -3, 4/*mean (0.099865), correlation (0.372276)*/,
        7, -1, 12, 2/*mean (0.117083), correlation (0.364529)*/,
        -7, 6, -5, 1/*mean (0.126125), correlation (0.369606)*/,
        -13, 11, -12, 5/*mean (0.130364), correlation (0.358502)*/,
        -3, 7, -2, -6/*mean (0.131691), correlation (0.375531)*/,
        7, -8, 12, -7/*mean (0.160166), correlation (0.379508)*/,
        -13, -7, -11, -12/*mean (0.167848), correlation (0.353343)*/,
        1, -3, 12, 12/*mean (0.183378), correlation (0.371916)*/,
        2, -6, 3, 0/*mean (0.228711), correlation (0.371761)*/,
        -4, 3, -2, -13/*mean (0.247211), correlation (0.364063)*/,
        -1, -13, 1, 9/*mean (0.249325), correlation (0.378139)*/,
        7, 1, 8, -6/*mean (0.000652272), correlation (0.411682)*/,
        1, -1, 3, 12/*mean (0.00248538), correlation (0.392988)*/,
        9, 1, 12, 6/*mean (0.0206815), correlation (0.386106)*/,
        -1, -9, -1, 3/*mean (0.0364485), correlation (0.410752)*/,
        -13, -13, -10, 5/*mean (0.0376068), correlation (0.398374)*/,
        7, 7, 10, 12/*mean (0.0424202), correlation (0.405663)*/,
        12, -5, 12, 9/*mean (0.0942645), correlation (0.410422)*/,
        6, 3, 7, 11/*mean (0.1074), correlation (0.413224)*/,
        5, -13, 6, 10/*mean (0.109256), correlation (0.408646)*/,
        2, -12, 2, 3/*mean (0.131691), correlation (0.416076)*/,
        3, 8, 4, -6/*mean (0.165081), correlation (0.417569)*/,
        2, 6, 12, -13/*mean (0.171874), correlation (0.408471)*/,
        9, -12, 10, 3/*mean (0.175146), correlation (0.41296)*/,
        -8, 4, -7, 9/*mean (0.183682), correlation (0.402956)*/,
        -11, 12, -4, -6/*mean (0.184672), correlation (0.416125)*/,
        1, 12, 2, -8/*mean (0.191487), correlation (0.386696)*/,
        6, -9, 7, -4/*mean (0.192668), correlation (0.394771)*/,
        2, 3, 3, -2/*mean (0.200157), correlation (0.408303)*/,
        6, 3, 11, 0/*mean (0.204588), correlation (0.411762)*/,
        3, -3, 8, -8/*mean (0.205904), correlation (0.416294)*/,
        7, 8, 9, 3/*mean (0.213237), correlation (0.409306)*/,
        -11, -5, -6, -4/*mean (0.243444), correlation (0.395069)*/,
        -10, 11, -5, 10/*mean (0.247672), correlation (0.413392)*/,
        -5, -8, -3, 12/*mean (0.24774), correlation (0.411416)*/,
        -10, 5, -9, 0/*mean (0.00213675), correlation (0.454003)*/,
        8, -1, 12, -6/*mean (0.0293635), correlation (0.455368)*/,
        4, -6, 6, -11/*mean (0.0404971), correlation (0.457393)*/,
        -10, 12, -8, 7/*mean (0.0481107), correlation (0.448364)*/,
        4, -2, 6, 7/*mean (0.050641), correlation (0.455019)*/,
        -2, 0, -2, 12/*mean (0.0525978), correlation (0.44338)*/,
        -5, -8, -5, 2/*mean (0.0629667), correlation (0.457096)*/,
        7, -6, 10, 12/*mean (0.0653846), correlation (0.445623)*/,
        -9, -13, -8, -8/*mean (0.0858749), correlation (0.449789)*/,
        -5, -13, -5, -2/*mean (0.122402), correlation (0.450201)*/,
        8, -8, 9, -13/*mean (0.125416), correlation (0.453224)*/,
        -9, -11, -9, 0/*mean (0.130128), correlation (0.458724)*/,
        1, -8, 1, -2/*mean (0.132467), correlation (0.440133)*/,
        7, -4, 9, 1/*mean (0.132692), correlation (0.454)*/,
        -2, 1, -1, -4/*mean (0.135695), correlation (0.455739)*/,
        11, -6, 12, -11/*mean (0.142904), correlation (0.446114)*/,
        -12, -9, -6, 4/*mean (0.146165), correlation (0.451473)*/,
        3, 7, 7, 12/*mean (0.147627), correlation (0.456643)*/,
        5, 5, 10, 8/*mean (0.152901), correlation (0.455036)*/,
        0, -4, 2, 8/*mean (0.167083), correlation (0.459315)*/,
        -9, 12, -5, -13/*mean (0.173234), correlation (0.454706)*/,
        0, 7, 2, 12/*mean (0.18312), correlation (0.433855)*/,
        -1, 2, 1, 7/*mean (0.185504), correlation (0.443838)*/,
        5, 11, 7, -9/*mean (0.185706), correlation (0.451123)*/,
        3, 5, 6, -8/*mean (0.188968), correlation (0.455808)*/,
        -13, -4, -8, 9/*mean (0.191667), correlation (0.459128)*/,
        -5, 9, -3, -3/*mean (0.193196), correlation (0.458364)*/,
        -4, -7, -3, -12/*mean (0.196536), correlation (0.455782)*/,
        6, 5, 8, 0/*mean (0.1972), correlation (0.450481)*/,
        -7, 6, -6, 12/*mean (0.199438), correlation (0.458156)*/,
        -13, 6, -5, -2/*mean (0.211224), correlation (0.449548)*/,
        1, -10, 3, 10/*mean (0.211718), correlation (0.440606)*/,
        4, 1, 8, -4/*mean (0.213034), correlation (0.443177)*/,
        -2, -2, 2, -13/*mean (0.234334), correlation (0.455304)*/,
        2, -12, 12, 12/*mean (0.235684), correlation (0.443436)*/,
        -2, -13, 0, -6/*mean (0.237674), correlation (0.452525)*/,
        4, 1, 9, 3/*mean (0.23962), correlation (0.444824)*/,
        -6, -10, -3, -5/*mean (0.248459), correlation (0.439621)*/,
        -3, -13, -1, 1/*mean (0.249505), correlation (0.456666)*/,
        7, 5, 12, -11/*mean (0.00119208), correlation (0.495466)*/,
        4, -2, 5, -7/*mean (0.00372245), correlation (0.484214)*/,
        -13, 9, -9, -5/*mean (0.00741116), correlation (0.499854)*/,
        7, 1, 8, 6/*mean (0.0208952), correlation (0.499773)*/,
        7, -8, 7, 6/*mean (0.0220085), correlation (0.501609)*/,
        -7, -4, -7, 1/*mean (0.0233806), correlation (0.496568)*/,
        -8, 11, -7, -8/*mean (0.0236505), correlation (0.489719)*/,
        -13, 6, -12, -8/*mean (0.0268781), correlation (0.503487)*/,
        2, 4, 3, 9/*mean (0.0323324), correlation (0.501938)*/,
        10, -5, 12, 3/*mean (0.0399235), correlation (0.494029)*/,
        -6, -5, -6, 7/*mean (0.0420153), correlation (0.486579)*/,
        8, -3, 9, -8/*mean (0.0548021), correlation (0.484237)*/,
        2, -12, 2, 8/*mean (0.0616622), correlation (0.496642)*/,
        -11, -2, -10, 3/*mean (0.0627755), correlation (0.498563)*/,
        -12, -13, -7, -9/*mean (0.0829622), correlation (0.495491)*/,
        -11, 0, -10, -5/*mean (0.0843342), correlation (0.487146)*/,
        5, -3, 11, 8/*mean (0.0929937), correlation (0.502315)*/,
        -2, -13, -1, 12/*mean (0.113327), correlation (0.48941)*/,
        -1, -8, 0, 9/*mean (0.132119), correlation (0.467268)*/,
        -13, -11, -12, -5/*mean (0.136269), correlation (0.498771)*/,
        -10, -2, -10, 11/*mean (0.142173), correlation (0.498714)*/,
        -3, 9, -2, -13/*mean (0.144141), correlation (0.491973)*/,
        2, -3, 3, 2/*mean (0.14892), correlation (0.500782)*/,
        -9, -13, -4, 0/*mean (0.150371), correlation (0.498211)*/,
        -4, 6, -3, -10/*mean (0.152159), correlation (0.495547)*/,
        -4, 12, -2, -7/*mean (0.156152), correlation (0.496925)*/,
        -6, -11, -4, 9/*mean (0.15749), correlation (0.499222)*/,
        6, -3, 6, 11/*mean (0.159211), correlation (0.503821)*/,
        -13, 11, -5, 5/*mean (0.162427), correlation (0.501907)*/,
        11, 11, 12, 6/*mean (0.16652), correlation (0.497632)*/,
        7, -5, 12, -2/*mean (0.169141), correlation (0.484474)*/,
        -1, 12, 0, 7/*mean (0.169456), correlation (0.495339)*/,
        -4, -8, -3, -2/*mean (0.171457), correlation (0.487251)*/,
        -7, 1, -6, 7/*mean (0.175), correlation (0.500024)*/,
        -13, -12, -8, -13/*mean (0.175866), correlation (0.497523)*/,
        -7, -2, -6, -8/*mean (0.178273), correlation (0.501854)*/,
        -8, 5, -6, -9/*mean (0.181107), correlation (0.494888)*/,
        -5, -1, -4, 5/*mean (0.190227), correlation (0.482557)*/,
        -13, 7, -8, 10/*mean (0.196739), correlation (0.496503)*/,
        1, 5, 5, -13/*mean (0.19973), correlation (0.499759)*/,
        1, 0, 10, -13/*mean (0.204465), correlation (0.49873)*/,
        9, 12, 10, -1/*mean (0.209334), correlation (0.49063)*/,
        5, -8, 10, -9/*mean (0.211134), correlation (0.503011)*/,
        -1, 11, 1, -13/*mean (0.212), correlation (0.499414)*/,
        -9, -3, -6, 2/*mean (0.212168), correlation (0.480739)*/,
        -1, -10, 1, 12/*mean (0.212731), correlation (0.502523)*/,
        -13, 1, -8, -10/*mean (0.21327), correlation (0.489786)*/,
        8, -11, 10, -6/*mean (0.214159), correlation (0.488246)*/,
        2, -13, 3, -6/*mean (0.216993), correlation (0.50287)*/,
        7, -13, 12, -9/*mean (0.223639), correlation (0.470502)*/,
        -10, -10, -5, -7/*mean (0.224089), correlation (0.500852)*/,
        -10, -8, -8, -13/*mean (0.228666), correlation (0.502629)*/,
        4, -6, 8, 5/*mean (0.22906), correlation (0.498305)*/,
        3, 12, 8, -13/*mean (0.233378), correlation (0.503825)*/,
        -4, 2, -3, -3/*mean (0.234323), correlation (0.476692)*/,
        5, -13, 10, -12/*mean (0.236392), correlation (0.475462)*/,
        4, -13, 5, -1/*mean (0.236842), correlation (0.504132)*/,
        -9, 9, -4, 3/*mean (0.236977), correlation (0.497739)*/,
        0, 3, 3, -9/*mean (0.24314), correlation (0.499398)*/,
        -12, 1, -6, 1/*mean (0.243297), correlation (0.489447)*/,
        3, 2, 4, -8/*mean (0.00155196), correlation (0.553496)*/,
        -10, -10, -10, 9/*mean (0.00239541), correlation (0.54297)*/,
        8, -13, 12, 12/*mean (0.0034413), correlation (0.544361)*/,
        -8, -12, -6, -5/*mean (0.003565), correlation (0.551225)*/,
        2, 2, 3, 7/*mean (0.00835583), correlation (0.55285)*/,
        10, 6, 11, -8/*mean (0.00885065), correlation (0.540913)*/,
        6, 8, 8, -12/*mean (0.0101552), correlation (0.551085)*/,
        -7, 10, -6, 5/*mean (0.0102227), correlation (0.533635)*/,
        -3, -9, -3, 9/*mean (0.0110211), correlation (0.543121)*/,
        -1, -13, -1, 5/*mean (0.0113473), correlation (0.550173)*/,
        -3, -7, -3, 4/*mean (0.0140913), correlation (0.554774)*/,
        -8, -2, -8, 3/*mean (0.017049), correlation (0.55461)*/,
        4, 2, 12, 12/*mean (0.01778), correlation (0.546921)*/,
        2, -5, 3, 11/*mean (0.0224022), correlation (0.549667)*/,
        6, -9, 11, -13/*mean (0.029161), correlation (0.546295)*/,
        3, -1, 7, 12/*mean (0.0303081), correlation (0.548599)*/,
        11, -1, 12, 4/*mean (0.0355151), correlation (0.523943)*/,
        -3, 0, -3, 6/*mean (0.0417904), correlation (0.543395)*/,
        4, -11, 4, 12/*mean (0.0487292), correlation (0.542818)*/,
        2, -4, 2, 1/*mean (0.0575124), correlation (0.554888)*/,
        -10, -6, -8, 1/*mean (0.0594242), correlation (0.544026)*/,
        -13, 7, -11, 1/*mean (0.0597391), correlation (0.550524)*/,
        -13, 12, -11, -13/*mean (0.0608974), correlation (0.55383)*/,
        6, 0, 11, -13/*mean (0.065126), correlation (0.552006)*/,
        0, -1, 1, 4/*mean (0.074224), correlation (0.546372)*/,
        -13, 3, -9, -2/*mean (0.0808592), correlation (0.554875)*/,
        -9, 8, -6, -3/*mean (0.0883378), correlation (0.551178)*/,
        -13, -6, -8, -2/*mean (0.0901035), correlation (0.548446)*/,
        5, -9, 8, 10/*mean (0.0949843), correlation (0.554694)*/,
        2, 7, 3, -9/*mean (0.0994152), correlation (0.550979)*/,
        -1, -6, -1, -1/*mean (0.10045), correlation (0.552714)*/,
        9, 5, 11, -2/*mean (0.100686), correlation (0.552594)*/,
        11, -3, 12, -8/*mean (0.101091), correlation (0.532394)*/,
        3, 0, 3, 5/*mean (0.101147), correlation (0.525576)*/,
        -1, 4, 0, 10/*mean (0.105263), correlation (0.531498)*/,
        3, -6, 4, 5/*mean (0.110785), correlation (0.540491)*/,
        -13, 0, -10, 5/*mean (0.112798), correlation (0.536582)*/,
        5, 8, 12, 11/*mean (0.114181), correlation (0.555793)*/,
        8, 9, 9, -6/*mean (0.117431), correlation (0.553763)*/,
        7, -4, 8, -12/*mean (0.118522), correlation (0.553452)*/,
        -10, 4, -10, 9/*mean (0.12094), correlation (0.554785)*/,
        7, 3, 12, 4/*mean (0.122582), correlation (0.555825)*/,
        9, -7, 10, -2/*mean (0.124978), correlation (0.549846)*/,
        7, 0, 12, -2/*mean (0.127002), correlation (0.537452)*/,
        -1, -6, 0, -11/*mean (0.127148), correlation (0.547401)*/
};

// compute the descriptor
void computeORBDesc(const cv::Mat &image, vector<cv::KeyPoint> &keypoints, vector<DescType> &desc) {
    for (auto &kp: keypoints) {
        DescType d(256, false);
        for (int i = 0; i < 256; i++) {
            // START YOUR CODE HERE (~7 lines)
            auto cos_ = float(cos(kp.angle*pi/180)); //将角度转换成弧度再进行cos、sin的计算
            auto sin_ = float(sin(kp.angle*pi/180));
            //注意pattern中的数如何取
            cv::Point2f p_r(cos_*ORB_pattern[4*i]-sin_*ORB_pattern[4*i+1],
                    sin_*ORB_pattern[4*i]+cos_*ORB_pattern[4*i+1]);
            cv::Point2f q_r(cos_*ORB_pattern[4*i+2]-sin_*ORB_pattern[4*i+3],
                    sin_*ORB_pattern[4*i+2]+cos_*ORB_pattern[4*i+3]);
 
            cv::Point2f p(kp.pt+p_r); //获取p'与q'的真实坐标，才能获得其像素值
            cv::Point2f q(kp.pt+q_r);
 
            // if kp goes outside, set d.clear()
            if(p.x<0||p.y<0||p.x>image.cols||p.y>image.rows||
            q.x<0||q.y<0||q.x>image.cols||q.y>image.rows){
                d.clear();
                break;
            }
            //像素值比较
             d[i]=image.at<uchar>(p)>image.at<uchar>(q)?0:1; 
	    // END YOUR CODE HERE
        }
        desc.push_back(d);
    }

    int bad = 0;
    for (auto &d: desc) {
        if (d.empty()) bad++;
    }
    cout << "bad/total: " << bad << "/" << desc.size() << endl;
    return;
}

// brute-force matching
void bfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches) {
    int d_max = 50;

    // START YOUR CODE HERE (~12 lines)
    // find matches between desc1 and desc2. 
    for(int i=0;i<desc1.size();i++){
        if(desc1[i].empty())
            continue;
        int d_min=256 ,index=-1; //必须定义在这里，每次循环重新初始化
        for(int j=0;j<desc2.size();j++){ //这个for循环，取出最小的d_min
            if(desc2[j].empty())
                continue;
            int d=0; //必须定义在这里，每次循环重新初始化
            for(int k=0;k<256;k++){
                d += desc1[i][k]^desc2[j][k]; //异或：不同为1;
            }
            if(d<d_min){
                d_min=d;
                index=j;
            }
        }
        if(d_min<=d_max){
            cv::DMatch match(i,index,d_min);
            matches.push_back(match);
        }
    }
    // END YOUR CODE HERE

    for (auto &m: matches) {
        cout << m.queryIdx << ", " << m.trainIdx << ", " << m.distance << endl;
    }
    return;
}

CMakeLists.txt：

c 复制代码 
cmake_minimum_required( VERSION 2.8 )
project(stereoVision)
set( CMAKE_CXX_FLAGS "-std=c++11 -O3")
 
include_directories("/usr/include/eigen3")
find_package(Pangolin REQUIRED)
include_directories( ${Pangolin_INCLUDE_DIRS} )
 
find_package(OpenCV 3.0 QUIET) #find_package(<Name>)命令首先会在模块路径中寻找 Find<name>.cmake
if(NOT OpenCV_FOUND)
    find_package(OpenCV 2.4.3 QUIET)
    if(NOT OpenCV_FOUND)
        message(FATAL_ERROR "OpenCV > 2.4.3 not found.")
    endif()
endif()

include_directories(${OpenCV_INCLUDE_DIRS})

add_executable(computeORB computeORB.cpp)
target_link_libraries(computeORB ${OpenCV_LIBS})

然后就是五件套

mkdir build

cd build

cmake ...

make

./computeORB

然后是简答题：

1.为什么说 ORB 是⼀种⼆进制特征？

ORB使用改进的BRIEF特征描述，而BRIEF是一种二进制的描述子，其描述向量由许多个0和1组成。也就是说ORB采用二进制的描述子用来描述每个特征点的特征信息。
2.为什么在匹配时使⽤ 50 作为阈值，取更⼤或更⼩值会怎么样？ 当阈值为50的时候，可以检测出的特征对有95个匹配的特征对。但存在一些误匹配的点对。

当阈值为30的时候，可以检测到的特征点对很少，当然我还检测了20的时候，到20就一对特征点对也检测不出来了。

当阈值设置为90时,可以检测到非常多的个点对,误匹配很多

3.暴⼒匹配在你的机器上表现如何？你能想到什么减少计算量的匹配⽅法吗？

运行时间如图所示，使用快速近似最近邻的方法（FLANN）。

2.从 E 恢复 R，t

首先说一下运行中碰到的问题吧：
第一个问题：

如果碰到这个情况，那就是我们的E2Rt文件中找不到#include <sophus/so3.hpp>，只需要改为#include <sophus/so3.h>就可以了。
第二个问题：

如果是这种情况，我们就需要把E2Rt文件中62、63行的（文件中所有的）so3d改为so3即可。

E2Rt.cpp

cpp 复制代码 
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/Geometry>

using namespace Eigen;

#include <sophus/so3.h>

#include <iostream>

using namespace std;

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

    // 给定Essential矩阵
    Matrix3d E;
    E << -0.0203618550523477, -0.4007110038118445, -0.03324074249824097,
            0.3939270778216369, -0.03506401846698079, 0.5857110303721015,
            -0.006788487241438284, -0.5815434272915686, -0.01438258684486258;

    // 待计算的R,t
    Matrix3d R;
    Vector3d t;

    // SVD and fix sigular values
    // START YOUR CODE HERE
      JacobiSVD<MatrixXd> svd(E,ComputeThinU | ComputeThinV);
    Matrix3d U=svd.matrixU();
    Matrix3d V=svd.matrixV();
    VectorXd sigma_value=svd.singularValues();
    Matrix3d SIGMA=U.inverse()*E*V.transpose().inverse();
    Vector3d sigma_value2={(sigma_value[0]+sigma_value[1])/2,(sigma_value[0]+sigma_value[1])/2,0};
    Matrix3d SIGMA2=sigma_value2.asDiagonal();
    cout<<"SIGMA=\n"<<SIGMA<<endl;
    cout<<"sigma_value=\n"<<sigma_value<<endl;
    cout<<"SIGMA2=\n"<<SIGMA<<endl;
    cout<<"sigma_value2=\n"<<sigma_value<<endl;
    // END YOUR CODE HERE

    // set t1, t2, R1, R2 
    // START YOUR CODE HERE
    Matrix3d t_wedge1;
    Matrix3d t_wedge2;

    Matrix3d R1;
    Matrix3d R2;
     Matrix3d RZ1=AngleAxisd(M_PI/2,Vector3d(0,0,1)).toRotationMatrix();
    Matrix3d RZ2=AngleAxisd(-M_PI/2,Vector3d(0,0,1)).toRotationMatrix();
    t_wedge1=U*RZ1*SIGMA2*U.transpose();
    t_wedge2=U*RZ2*SIGMA2*U.transpose();
    R1=U*RZ1.transpose()*V.transpose();
    R2=U*RZ2.transpose()*V.transpose();
    // END YOUR CODE HERE

    cout << "R1 = " << R1 << endl;
    cout << "R2 = " << R2 << endl;
    cout << "t1 = " << Sophus::SO3::vee(t_wedge1) << endl;
    cout << "t2 = " << Sophus::SO3::vee(t_wedge2) << endl;

    // check t^R=E up to scale
    Matrix3d tR = t_wedge1 * R1;
    cout << "t^R = " << tR << endl;

    return 0;
}

CMakeLists.txt：

cpp 复制代码 
cmake_minimum_required(VERSION 3.0)
project(E2RT)
set(CMAKE_CXX_STANDARD 11)
set(CMAKE_BUILD_TYPE "Release")

#添加头文件
include_directories( "/usr/include/eigen3")
find_package(Sophus REQUIRED)
include_directories(${Sophus_INCLUDE_DIRS})

add_executable(E2Rt E2Rt.cpp)
#链接OpenCV库
target_link_libraries(E2Rt ${Sophus_LIBRARIES})

运行结果如下：

3.用 G-N 实现 Bundle Adjustment

这里如果cmake ...

make有问题的话，和上一题的解决方法是一样的。

GN-BA.cpp

cpp 复制代码 
#include <Eigen/Core>
#include <Eigen/Dense>

using namespace Eigen;

#include <vector>
#include <fstream>
#include <iostream>
#include <iomanip>

#include "sophus/se3.h"

using namespace std;

typedef vector<Vector3d, Eigen::aligned_allocator<Vector3d>> VecVector3d;
typedef vector<Vector2d, Eigen::aligned_allocator<Vector3d>> VecVector2d;
typedef Matrix<double, 6, 1> Vector6d;

string p3d_file = "../p3d.txt";
string p2d_file = "../p2d.txt";

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

    VecVector2d p2d;
    VecVector3d p3d;
    Matrix3d K;
    double fx = 520.9, fy = 521.0, cx = 325.1, cy = 249.7;
    K << fx, 0, cx, 0, fy, cy, 0, 0, 1;

    // load points in to p3d and p2d 
    // START YOUR CODE HERE
    ifstream p3d_fin(p3d_file);
    ifstream p2d_fin(p2d_file);
    Vector3d p3d_input;
    Vector2d p2d_input;
    if (!p3d_fin) {
        cerr << "p3d_fin " << p3d_file << " not found." << endl;
    }
    while (!p3d_fin.eof()) {
        p3d_fin >> p3d_input(0) >> p3d_input(1) >> p3d_input(2);
        p3d.push_back(p3d_input);
    }
    p3d_fin.close();

    if (!p2d_fin) {
        cerr << "p2d_fin " << p2d_file << " not found." << endl;
    }
    while (!p2d_fin.eof()) {
        p2d_fin >> p2d_input(0) >> p2d_input(1);
        p2d.push_back(p2d_input);
    }
    p2d_fin.close();
    // END YOUR CODE HERE
    assert(p3d.size() == p2d.size());

    int iterations = 100;
    double cost = 0, lastCost = 0;
    int nPoints = p3d.size();
    cout << "points: " << nPoints << endl;

    Sophus::SE3 T_esti; // estimated pose

    for (int iter = 0; iter < iterations; iter++) {

        Matrix<double, 6, 6> H = Matrix<double, 6, 6>::Zero();
        Vector6d b = Vector6d::Zero();

        cost = 0;
        // compute cost
        for (int i = 0; i < nPoints; i++) {
            // compute cost for p3d[I] and p2d[I]
            // START YOUR CODE HERE 
            Eigen::Vector3d pc = T_esti * p3d[i];
            Eigen::Vector2d proj(fx * pc[0] / pc[2] + cx, fy * pc[1] / pc[2] + cy);
            Eigen::Vector2d e = p2d[i] - proj;

            cost += e.squaredNorm()/2;
	    // END YOUR CODE HERE

	    // compute jacobian
            Matrix<double, 2, 6> J;
            // START YOUR CODE HERE
            double inv_z = 1.0 / pc[2];
            double inv_z2 = inv_z * inv_z;
            J << -fx * inv_z,
                    0,
                    fx * pc[0] * inv_z2,
                    fx * pc[0] * pc[1] * inv_z2,
                    -fx - fx * pc[0] * pc[0] * inv_z2,
                    fx * pc[1] * inv_z,
                    0,
                    -fy * inv_z,
                    fy * pc[1] * inv_z2,
                    fy + fy * pc[1] * pc[1] * inv_z2,
                    -fy * pc[0] * pc[1] * inv_z2,
                    -fy * pc[0] * inv_z;
	    // END YOUR CODE HERE

            H += J.transpose() * J;
            b += -J.transpose() * e;
        }

	// solve dx 
        Vector6d dx;

        // START YOUR CODE HERE 
        dx = H.ldlt().solve(b);
        // END YOUR CODE HERE

        if (isnan(dx[0])) {
            cout << "result is nan!" << endl;
            break;
        }

        if (iter > 0 && cost >= lastCost) {
            // cost increase, update is not good
            cout << "cost: " << cost << ", last cost: " << lastCost << endl;
            break;
        }

        // update your estimation
        // START YOUR CODE HERE 
        T_esti = Sophus::SE3::exp(dx) * T_esti;
        // END YOUR CODE HERE
        
        lastCost = cost;

        cout << "iteration " << iter << " cost=" << cout.precision(12) << cost << endl;
    }

    cout << "estimated pose: \n" << T_esti.matrix() << endl;
    return 0;
}

CMakeLists.txt:

cpp 复制代码 
cmake_minimum_required(VERSION 3.0)

project(E2RT)
set(CMAKE_CXX_STANDARD 11)
set(CMAKE_BUILD_TYPE "Release")

#添加头文件
include_directories( "/usr/include/eigen3")
find_package(Sophus REQUIRED)
include_directories(${Sophus_INCLUDE_DIRS})


add_executable(gn_ba GN-BA.cpp)

#链接OpenCV库
target_link_libraries(gn_ba ${Sophus_LIBRARIES})

运行结果：

1.如何定义重投影误差？

像素位置与空间点的位置关系如下：

写成矩阵形式为S~i~u~i~=KTP~i~

由于相机位姿未知及观测点的噪声，该等式存在一个误差。把误差求和，构建最小二乘问题，然后寻找最好的相机位姿，使它最小化：

将该问题的误差项，是将3D点的投影与观测位置做差，称之为重投影误差。

2.该误差关于⾃变量的雅可⽐矩阵是什么？

3.解出更新量之后，如何更新⾄之前的估计上？

左乘或右乘微小扰动exp(dx)

代码中为左乘

4.* 用 ICP 实现轨迹对齐

icp.cpp

cpp 复制代码 
#include <sophus/se3.h>
#include <string>
#include <iostream>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <opencv2/core/core.hpp>
#include <pangolin/pangolin.h>
#include <unistd.h>

using namespace std;
using namespace Eigen;
using namespace cv;

string trajectory_file = "../compare.txt";

void pose_estimation_3d3d(const vector<Point3f> &pts1,const vector<Point3f> &pts2, Eigen::Matrix3d &R_, Eigen::Vector3d &t_);
void DrawTrajectory(vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_e,
        vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_g,
        const string& ID);

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

    vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_e;
    vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_g;
    vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_gt;
    vector<Point3f> pts_e,pts_g;
    ifstream fin(trajectory_file);
    if(!fin){
        cerr<<"can't find file at "<<trajectory_file<<endl;
        return 1;
    }
    while(!fin.eof()){
        double t1,tx1,ty1,tz1,qx1,qy1,qz1,qw1;
        double t2,tx2,ty2,tz2,qx2,qy2,qz2,qw2;
        fin>>t1>>tx1>>ty1>>tz1>>qx1>>qy1>>qz1>>qw1>>t2>>tx2>>ty2>>tz2>>qx2>>qy2>>qz2>>qw2;
        pts_e.push_back(Point3f(tx1,ty1,tz1));
        pts_g.push_back(Point3f(tx2,ty2,tz2));
        poses_e.push_back(Sophus::SE3(Quaterniond(qw1,qx1,qy1,qz1),Vector3d(tx1,ty1,tz1)));
        poses_g.push_back(Sophus::SE3(Quaterniond(qw2,qx2,qy2,qz2),Vector3d(tx2,ty2,tz2)));
    }

    Matrix3d R;
    Vector3d t;
    pose_estimation_3d3d(pts_e,pts_g,R,t);
    Sophus::SE3 T_eg(R,t);
    for(auto SE_g:poses_g)    {
        Sophus::SE3 T_e=T_eg*SE_g;
        poses_gt.push_back(T_e);
    }
    DrawTrajectory(poses_e,poses_g," Before Align");
    DrawTrajectory(poses_e,poses_gt," After Align");
    return 0;
}

void pose_estimation_3d3d(const vector<Point3f> &pts1,
                          const vector<Point3f> &pts2,
                          Eigen::Matrix3d &R_, Eigen::Vector3d &t_) {
    Point3f p1, p2;     // center of mass
    int N = pts1.size();
    for (int i = 0; i < N; i++) {
        p1 += pts1[i];
        p2 += pts2[i];
    }
    p1 = Point3f(Vec3f(p1) / N);
    p2 = Point3f(Vec3f(p2) / N);
    vector<Point3f> q1(N), q2(N); // remove the center
    for (int i = 0; i < N; i++) {
        q1[i] = pts1[i] - p1;
        q2[i] = pts2[i] - p2;
    }

    // compute q1*q2^T
    Eigen::Matrix3d W = Eigen::Matrix3d::Zero();
    for (int i = 0; i < N; i++) {
        W += Eigen::Vector3d(q1[i].x, q1[i].y, q1[i].z) * Eigen::Vector3d(q2[i].x, q2[i].y, q2[i].z).transpose();
    }
    cout << "W=" << W << endl;

    // SVD on W
    Eigen::JacobiSVD<Eigen::Matrix3d> svd(W, Eigen::ComputeFullU | Eigen::ComputeFullV);
    Eigen::Matrix3d U = svd.matrixU();
    Eigen::Matrix3d V = svd.matrixV();

    cout << "U=" << U << endl;
    cout << "V=" << V << endl;

    R_ = U * (V.transpose());
    if (R_.determinant() < 0) {
        R_ = -R_;
    }
    t_ = Eigen::Vector3d(p1.x, p1.y, p1.z) - R_ * Eigen::Vector3d(p2.x, p2.y, p2.z);
}

void DrawTrajectory(vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_e,
        vector<Sophus::SE3, Eigen::aligned_allocator<Sophus::SE3>> poses_g,
        const string& ID) {
    if (poses_e.empty() || poses_g.empty()) {
        cerr << "Trajectory is empty!" << endl;
        return;
    }

    string windowtitle = "Trajectory Viewer" + ID;
    // create pangolin window and plot the trajectory
    pangolin::CreateWindowAndBind(windowtitle, 1024, 768);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

    pangolin::OpenGlRenderState s_cam(
            pangolin::ProjectionMatrix(1024, 768, 500, 500, 512, 389, 0.1, 1000),
            pangolin::ModelViewLookAt(0, -0.1, -1.8, 0, 0, 0, 0.0, -1.0, 0.0)
    );

    pangolin::View &d_cam = pangolin::CreateDisplay()
            .SetBounds(0.0, 1.0, pangolin::Attach::Pix(175), 1.0, -1024.0f / 768.0f)
            .SetHandler(new pangolin::Handler3D(s_cam));


    while (pangolin::ShouldQuit() == false) {
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        d_cam.Activate(s_cam);
        glClearColor(1.0f, 1.0f, 1.0f, 1.0f);

        glLineWidth(2);
        for (size_t i = 0; i < poses_e.size() - 1; i++) {
            glColor3f(1.0f, 0.0f, 0.0f);
            glBegin(GL_LINES);
            auto p1 = poses_e[i], p2 = poses_e[i + 1];
            glVertex3d(p1.translation()[0], p1.translation()[1], p1.translation()[2]);
            glVertex3d(p2.translation()[0], p2.translation()[1], p2.translation()[2]);
            glEnd();
        }
        for (size_t i = 0; i < poses_g.size() - 1; i++) {
            glColor3f(0.0f, 0.0f, 1.0f);
            glBegin(GL_LINES);
            auto p1 = poses_g[i], p2 = poses_g[i + 1];
            glVertex3d(p1.translation()[0], p1.translation()[1], p1.translation()[2]);
            glVertex3d(p2.translation()[0], p2.translation()[1], p2.translation()[2]);
            glEnd();
        }
        pangolin::FinishFrame();
        usleep(5000);   // sleep 5 ms
    }
}

compare.txt:

cpp 复制代码 
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1305031527.539741 -0.040670216 0.068688609 -0.094280347 0.155639857 0.128989607 0.007390451 0.979327977 1305031527.532200 1.5213 0.8354 1.4665 -0.7993 -0.0665 0.0447 0.5955
1305031527.671547 -0.059779059 0.086170383 -0.080027580 0.096256085 0.124875024 0.008046621 0.987459481 1305031527.672100 1.5107 0.8404 1.4443 -0.8388 -0.0797 0.0411 0.5370
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1305031527.939566 -0.114897557 0.077028573 -0.058029801 0.028592139 0.054828048 0.000756203 0.998086035 1305031527.942100 1.4628 0.8271 1.4192 0.8586 0.1365 -0.0964 -0.4847
1305031527.971502 -0.125279635 0.082915515 -0.061315395 0.033042073 0.038314771 -0.013166402 0.998632491 1305031527.972200 1.4545 0.8231 1.4180 0.8531 0.1537 -0.1048 -0.4875
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1305031528.071546 -0.160694852 0.087861642 -0.055381063 0.043458812 -0.012107812 -0.061667852 0.997076631 1305031528.072100 1.4269 0.8052 1.4168 0.8321 0.2141 -0.1310 -0.4947
1305031528.107513 -0.176289976 0.090757042 -0.055422220 0.049189046 -0.027869513 -0.077940412 0.995353699 1305031528.112200 1.4157 0.7957 1.4172 0.8213 0.2395 -0.1415 -0.4982
1305031528.139513 -0.182451800 0.096339859 -0.055684097 0.055754602 -0.047568955 -0.096469797 0.992633939 1305031528.142100 1.4076 0.7880 1.4177 -0.8129 -0.2579 0.1482 0.5008
1305031528.171523 -0.189394832 0.097757049 -0.056705259 0.059309058 -0.062220436 -0.113738760 0.989785075 1305031528.172100 1.3999 0.7798 1.4182 -0.8057 -0.2750 0.1516 0.5023
1305031528.207527 -0.202431262 0.095546886 -0.061502121 0.064778626 -0.071393289 -0.133537352 0.986344039 1305031528.212100 1.3902 0.7684 1.4191 -0.7934 -0.2930 0.1537 0.5109
1305031528.239493 -0.211042851 0.098279119 -0.066208452 0.074096076 -0.080469146 -0.148469865 0.982848525 1305031528.242200 1.3834 0.7599 1.4203 -0.7816 -0.3053 0.1570 0.5208
1305031528.275450 -0.223710716 0.104189500 -0.073275700 0.081444807 -0.093165532 -0.159726724 0.979374468 1305031528.272200 1.3757 0.7500 1.4218 -0.7755 -0.3204 0.1620 0.5193
1305031528.307665 -0.244773716 0.107162125 -0.078257680 0.089617550 -0.112386964 -0.174391136 0.974128127 1305031528.312100 1.3670 0.7361 1.4255 -0.7607 -0.3420 0.1774 0.5223
1305031528.339593 -0.267502815 0.119377658 -0.079869874 0.100359902 -0.131352678 -0.185550600 0.968630672 1305031528.342100 1.3592 0.7261 1.4284 -0.7470 -0.3576 0.1940 0.5259
1305031528.375435 -0.277227014 0.122483246 -0.086401798 0.105153799 -0.156168520 -0.190717027 0.963421524 1305031528.372100 1.3526 0.7159 1.4316 -0.7373 -0.3709 0.2099 0.5242
1305031528.407459 -0.286472470 0.125400484 -0.096434973 0.109714307 -0.185297355 -0.197440162 0.956370771 1305031528.412200 1.3435 0.7011 1.4363 -0.7218 -0.3905 0.2364 0.5202
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1305031528.475342 -0.309931368 0.129882887 -0.129739463 0.111446232 -0.240962654 -0.210141197 0.940934300 1305031528.472100 1.3311 0.6784 1.4431 -0.7014 -0.4167 0.2744 0.5090
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1305031528.575449 -0.329237044 0.149565578 -0.154559985 0.106090672 -0.328091890 -0.223088816 0.911773980 1305031528.572300 1.3133 0.6410 1.4507 0.6649 0.4635 -0.3380 -0.4782
1305031528.607841 -0.340293765 0.151535481 -0.160942093 0.099514537 -0.350554526 -0.228903219 0.902669191 1305031528.612200 1.3094 0.6251 1.4510 0.6549 0.4788 -0.3560 -0.4638
1305031528.639487 -0.340425193 0.165493459 -0.169357076 0.096142113 -0.372110546 -0.231576025 0.893679440 1305031528.642100 1.3070 0.6131 1.4497 0.6474 0.4893 -0.3666 -0.4550
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1305031528.739609 -0.342159748 0.189583004 -0.177449271 0.070908576 -0.403506339 -0.253377467 0.876330137 1305031528.742100 1.3022 0.5717 1.4362 0.6380 0.5205 -0.3731 -0.4277
1305031528.775443 -0.341898620 0.206203520 -0.174872875 0.064870313 -0.407845527 -0.261114776 0.872509539 1305031528.772100 1.3019 0.5591 1.4304 0.6397 0.5275 -0.3680 -0.4209
1305031528.807559 -0.348404497 0.222904056 -0.195781291 0.056483749 -0.403348863 -0.271214008 0.872102201 1305031528.812100 1.3009 0.5418 1.4213 0.6417 0.5382 -0.3614 -0.4098
1305031528.839572 -0.353144258 0.236203671 -0.200213343 0.045424741 -0.405389339 -0.278263241 0.869577825 1305031528.842200 1.2998 0.5287 1.4140 0.6412 0.5445 -0.3598 -0.4036
1305031528.875433 -0.357103825 0.256649941 -0.206021339 0.036655750 -0.406093627 -0.286254942 0.867065430 1305031528.872100 1.2985 0.5151 1.4065 0.6435 0.5524 -0.3545 -0.3939
1305031528.907519 -0.363840312 0.273261279 -0.213352874 0.023924233 -0.403293431 -0.293037355 0.866551280 1305031528.912100 1.2962 0.4966 1.3960 0.6491 0.5605 -0.3457 -0.3808
1305031528.939602 -0.373810410 0.280675173 -0.220558763 0.005930781 -0.399948001 -0.299453437 0.866218269 1305031528.942100 1.2942 0.4819 1.3883 0.6557 0.5642 -0.3396 -0.3692
1305031528.975465 -0.383288622 0.293885916 -0.225069121 -0.007588292 -0.398547530 -0.297109455 0.867656767 1305031528.972100 1.2922 0.4665 1.3810 0.6627 0.5621 -0.3385 -0.3610
1305031529.007487 -0.387591243 0.312122375 -0.228814498 -0.022781339 -0.395879656 -0.293224841 0.869930744 1305031529.012100 1.2880 0.4447 1.3704 0.6751 0.5606 -0.3311 -0.3470
1305031529.039494 -0.396930993 0.326887786 -0.233368337 -0.039953087 -0.387588739 -0.290734917 0.873871803 1305031529.042100 1.2848 0.4279 1.3625 0.6879 0.5564 -0.3221 -0.3367
1305031529.075422 -0.409061730 0.334867179 -0.235107094 -0.057665374 -0.375858516 -0.282847494 0.880569339 1305031529.072100 1.2813 0.4105 1.3549 0.7035 0.5454 -0.3135 -0.3306
1305031529.107523 -0.420381188 0.348994136 -0.244129315 -0.070332937 -0.359931797 -0.270585924 0.890104294 1305031529.112100 1.2759 0.3862 1.3451 0.7244 0.5267 -0.3032 -0.3256
1305031529.139597 -0.432475984 0.367254645 -0.253846556 -0.084366389 -0.344622523 -0.252671927 0.900152504 1305031529.142200 1.2710 0.3666 1.3378 0.7418 0.5092 -0.2977 -0.3190
1305031529.175411 -0.442705750 0.384032130 -0.264635384 -0.099091217 -0.330286026 -0.234458074 0.908912241 1305031529.172100 1.2660 0.3461 1.3310 0.7603 0.4912 -0.2910 -0.3100
1305031529.207466 -0.461968184 0.417857319 -0.283306688 -0.107409544 -0.308710963 -0.220306739 0.919035196 1305031529.212100 1.2578 0.3180 1.3227 0.7825 0.4731 -0.2775 -0.2947
1305031529.239515 -0.474564463 0.434241831 -0.290974945 -0.122858316 -0.295257181 -0.214269757 0.922939599 1305031529.242200 1.2501 0.2972 1.3166 0.7943 0.4646 -0.2658 -0.2874
1305031529.275389 -0.488497406 0.454518944 -0.299479723 -0.134992152 -0.277170092 -0.211710542 0.927433312 1305031529.272100 1.2422 0.2763 1.3115 0.8063 0.4580 -0.2489 -0.2797
1305031529.307413 -0.505657196 0.462695599 -0.306875080 -0.152041495 -0.259664267 -0.206709743 0.930982769 1305031529.312200 1.2305 0.2483 1.3063 0.8194 0.4484 -0.2302 -0.2732
1305031529.339486 -0.530183196 0.486928225 -0.326155573 -0.160189480 -0.237766638 -0.205552071 0.935710788 1305031529.342100 1.2210 0.2270 1.3029 0.8282 0.4457 -0.2162 -0.2622
1305031529.375399 -0.554967403 0.482978404 -0.331514835 -0.181723729 -0.229372948 -0.205984905 0.933774471 1305031529.372100 1.2104 0.2063 1.3008 0.8301 0.4456 -0.2115 -0.2602
1305031529.407513 -0.573170364 0.494490802 -0.336653709 -0.182107240 -0.230446473 -0.207627431 0.933071375 1305031529.412100 1.1956 0.1791 1.2997 0.8299 0.4472 -0.2081 -0.2607
1305031529.439502 -0.592521727 0.509317398 -0.348569959 -0.176561520 -0.225443274 -0.212392747 0.934286177 1305031529.442100 1.1843 0.1600 1.3000 0.8304 0.4464 -0.2028 -0.2645
1305031529.475403 -0.613592625 0.520123661 -0.360875040 -0.172136515 -0.218513519 -0.214253858 0.936331213 1305031529.472100 1.1729 0.1418 1.3008 0.8303 0.4460 -0.1983 -0.2690
1305031529.507485 -0.633599639 0.528568029 -0.369254827 -0.166303858 -0.213266820 -0.219033107 0.937488556 1305031529.512100 1.1577 0.1193 1.3029 0.8290 0.4453 -0.1917 -0.2788
1305031529.539489 -0.651074648 0.528935075 -0.378143847 -0.160415858 -0.206384078 -0.221350908 0.939508438 1305031529.542200 1.1462 0.1041 1.3046 0.8290 0.4417 -0.1865 -0.2879
1305031529.607479 -0.686017632 0.545031309 -0.394158632 -0.154660717 -0.191093341 -0.215704605 0.945005238 1305031529.612300 1.1179 0.0732 1.3064 0.8350 0.4311 -0.1765 -0.2927
1305031529.639746 -0.701905608 0.552717209 -0.398970723 -0.154912621 -0.184921563 -0.209788874 0.947520316 1305031529.642300 1.1057 0.0620 1.3067 0.8404 0.4225 -0.1734 -0.2919
1305031529.675618 -0.719306707 0.559796870 -0.401483953 -0.157197714 -0.176389754 -0.200863779 0.950699389 1305031529.672100 1.0934 0.0521 1.3067 0.8466 0.4127 -0.1705 -0.2897
1305031529.707557 -0.735418081 0.563297987 -0.403395295 -0.162735164 -0.169739127 -0.191895753 0.952828407 1305031529.712100 1.0772 0.0401 1.3062 0.8540 0.4020 -0.1668 -0.2851
1305031529.739568 -0.746963501 0.566777885 -0.403324068 -0.165786088 -0.164117917 -0.185986936 0.954457521 1305031529.742100 1.0645 0.0324 1.3057 0.8593 0.3933 -0.1610 -0.2845
1305031529.775501 -0.761871457 0.562885761 -0.403146863 -0.173444703 -0.152099952 -0.180582851 0.956123650 1305031529.772100 1.0519 0.0257 1.3054 0.8653 0.3833 -0.1532 -0.2845
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1305031547.512114 -0.969141722 0.690587997 -0.436644912 -0.112998858 -0.028315512 -0.070585296 0.990680158 1305031547.512600 0.8920 -0.1464 1.2457 0.8999 0.2336 -0.1049 -0.3529
1305031547.544015 -0.969343126 0.685919464 -0.435732603 -0.115559071 -0.027669447 -0.071633816 0.990327775 1305031547.542600 0.8918 -0.1458 1.2463 0.8997 0.2338 -0.1044 -0.3535
1305031547.576437 -0.969174564 0.686703444 -0.435318053 -0.112849854 -0.027105195 -0.070552461 0.990733325 1305031547.572800 0.8918 -0.1446 1.2464 0.8993 0.2324 -0.1049 -0.3553
1305031547.612296 -0.970078647 0.689395785 -0.435169339 -0.112708598 -0.026355622 -0.070317492 0.990786374 1305031547.612600 0.8919 -0.1431 1.2459 0.9003 0.2329 -0.1051 -0.3523
1305031547.644160 -0.968304217 0.684383154 -0.432779491 -0.115552612 -0.027641958 -0.069583893 0.990475416 1305031547.642700 0.8920 -0.1419 1.2458 0.8996 0.2314 -0.1062 -0.3549
1305031547.677287 -0.966275394 0.690610170 -0.433439136 -0.111170650 -0.027089374 -0.068664201 0.991056204 1305031547.672700 0.8922 -0.1407 1.2451 0.9005 0.2309 -0.1046 -0.3533
1305031547.712338 -0.964709222 0.686679959 -0.430968702 -0.118181951 -0.026665349 -0.069269933 0.990213931 1305031547.712700 0.8925 -0.1396 1.2441 0.9020 0.2315 -0.1028 -0.3497
1305031547.744332 -0.963581026 0.684470177 -0.429666400 -0.117340922 -0.025876738 -0.069295891 0.990333080 1305031547.742800 0.8929 -0.1386 1.2441 0.9011 0.2307 -0.1025 -0.3526
1305031547.776390 -0.964229822 0.688230872 -0.429996789 -0.114284322 -0.024022026 -0.070344165 0.990663290 1305031547.772700 0.8935 -0.1379 1.2440 0.9008 0.2318 -0.1015 -0.3529
1305031547.812317 -0.964506626 0.684349477 -0.429410160 -0.117394648 -0.022055248 -0.071717598 0.990246713 1305031547.812700 0.8942 -0.1371 1.2441 0.9011 0.2310 -0.0996 -0.3532
1305031547.844564 -0.962979019 0.686277032 -0.429381162 -0.114744045 -0.021526016 -0.070772044 0.990637004 1305031547.842800 0.8946 -0.1365 1.2442 0.9008 0.2305 -0.0994 -0.3543
1305031547.876362 -0.963006616 0.688939631 -0.429479182 -0.113952808 -0.021306587 -0.070929334 0.990721881 1305031547.872800 0.8950 -0.1360 1.2442 0.9016 0.2311 -0.0993 -0.3520
1305031547.912744 -0.960898936 0.685296535 -0.428291798 -0.116005875 -0.021983700 -0.069795489 0.990549266 1305031547.912800 0.8956 -0.1352 1.2445 0.9016 0.2297 -0.0992 -0.3529
1305031547.944304 -0.960632503 0.685537279 -0.428972363 -0.115375742 -0.021099383 -0.069957919 0.990630627 1305031547.943100 0.8959 -0.1347 1.2447 0.9019 0.2297 -0.0988 -0.3522

CMakeLists.txt:

cpp 复制代码 
cmake_minimum_required(VERSION 3.0)

project(E2RT)
set(CMAKE_CXX_STANDARD 11)
set(CMAKE_BUILD_TYPE "Release")

#添加头文件
include_directories( "/usr/include/eigen3")
find_package(Sophus REQUIRED)
find_package(Pangolin REQUIRED)
find_package(OpenCV REQUIRED)
#添加头文件
include_directories( ${OpenCV_INCLUDE_DIRS})
include_directories(${Pangolin_INCLUDE_DIRS})
include_directories(${Sophus_INCLUDE_DIRS})


add_executable(useICP icp.cpp)

#链接OpenCV库
target_link_libraries(useICP ${Sophus_LIBRARIES} ${Pangolin_LIBRARIES} ${OpenCV_LIBS})

运行结果如下：

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