自学SLAM(9)《第五讲:特征点法视觉里程计》作业

文章目录

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


在这里插入图片描述

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。
在这里插入图片描述

1.2 ORB描述

在这里插入图片描述

1.3 暴力匹配

在这里插入图片描述
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:

#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 imagecv::Mat first_image = cv::imread(first_file, 0);    // load grayscale imagecv::Mat second_image = cv::imread(second_file, 0);  // load grayscale image// plot the imagecv::imshow("first image", first_image);cv::imshow("second image", second_image);cv::waitKey(0);// detect FAST keypoints using threshold=40vector<cv::KeyPoint> keypoints;cv::FAST(first_image, keypoints, 40);cout << "keypoints: " << keypoints.size() << endl;// compute angle for each keypointcomputeAngle(first_image, keypoints);// compute ORB descriptorsvector<DescType> descriptors;computeORBDesc(first_image, keypoints, descriptors);// plot the keypointscv::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 secondvector<cv::KeyPoint> keypoints2;cv::FAST(second_image, keypoints2, 40);cout << "keypoints: " << keypoints2.size() << endl;// compute angle for each keypointcomputeAngle(second_image, keypoints2);// compute ORB descriptorsvector<DescType> descriptors2;computeORBDesc(second_image, keypoints2, descriptors2);// find matchesvector<cv::DMatch> matches;bfMatch(descriptors, descriptors2, matches);cout << "matches: " << matches.size() << endl;// plot the matchescv::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 edgeint 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=0for(int i=-half_patch_size;i<half_patch_size;i++){    //-8<i<8,-8<j<8for(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_minif(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 HEREfor (auto &m: matches) {cout << m.queryIdx << ", " << m.trainIdx << ", " << m.distance << endl;}return;
}

CMakeLists.txt:

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
在这里插入图片描述
在这里插入图片描述

在这里插入图片描述
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。
在这里插入图片描述
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。
在这里插入图片描述
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
在这里插入图片描述

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? 在这里插入图片描述
运行时间如图所示,使用快速近似最近邻的方法(FLANN)。
在这里插入图片描述

2.从 E 恢复 R,t

在这里插入图片描述
首先说一下运行中碰到的问题吧:
第一个问题:
在这里插入图片描述
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:

在这里插入图片描述
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

#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,tMatrix3d R;Vector3d t;// SVD and fix sigular values// START YOUR CODE HEREJacobiSVD<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 HEREMatrix3d 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 HEREcout << "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 scaleMatrix3d tR = t_wedge1 * R1;cout << "t^R = " << tR << endl;return 0;
}

CMakeLists.txt:

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:
在这里插入图片描述

3.用 G-N 实现 Bundle Adjustment

在这里插入图片描述
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

#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 HEREifstream 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 HEREassert(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 posefor (int iter = 0; iter < iterations; iter++) {Matrix<double, 6, 6> H = Matrix<double, 6, 6>::Zero();Vector6d b = Vector6d::Zero();cost = 0;// compute costfor (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 jacobianMatrix<double, 2, 6> J;// START YOUR CODE HEREdouble 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 HEREH += J.transpose() * J;b += -J.transpose() * e;}// solve dx Vector6d dx;// START YOUR CODE HERE dx = H.ldlt().solve(b);// END YOUR CODE HEREif (isnan(dx[0])) {cout << "result is nan!" << endl;break;}if (iter > 0 && cost >= lastCost) {// cost increase, update is not goodcout << "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 HERElastCost = cost;cout << "iteration " << iter << " cost=" << cout.precision(12) << cost << endl;}cout << "estimated pose: \n" << T_esti.matrix() << endl;return 0;
}

CMakeLists.txt:

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:
在这里插入图片描述
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:
在这里插入图片描述
写成矩阵形式为Siui=KTPi

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:
在这里插入图片描述
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?
在这里插入图片描述

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

在这里插入图片描述
icp.cpp

#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 massint 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 centerfor (int i = 0; i < N; i++) {q1[i] = pts1[i] - p1;q2[i] = pts2[i] - p2;}// compute q1*q2^TEigen::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 WEigen::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 trajectorypangolin::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:

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1305031526.771481 0.013978966 -0.013082317 -0.010869596 0.043280017 0.032526672 0.003260542 0.998528004 1305031526.772200 1.5119 0.9142 1.4651 -0.8502 -0.1262 0.0954 0.5021
1305031526.807455 -0.001601209 -0.011404546 -0.026841529 0.073491804 0.052071322 0.000915701 0.995935082 1305031526.812100 1.5152 0.9063 1.4724 -0.8341 -0.1188 0.0871 0.5316
1305031526.871446 -0.004428456 -0.001333938 -0.042973492 0.115341254 0.070847765 -0.006601509 0.990774155 1305031526.872200 1.5177 0.8921 1.4824 -0.8172 -0.1124 0.0738 0.5605
1305031526.907484 -0.006487503 -0.003464771 -0.058195263 0.135408968 0.081248961 -0.010381512 0.987398207 1305031526.912200 1.5189 0.8828 1.4886 -0.8039 -0.1062 0.0656 0.5816
1305031526.939618 -0.014331216 -0.013660092 -0.078787915 0.147756621 0.091927201 -0.015138508 0.984625876 1305031526.942100 1.5196 0.8752 1.4926 -0.7958 -0.1012 0.0594 0.5941
1305031526.971510 -0.018625503 -0.015494643 -0.089080200 0.165385425 0.100416750 -0.017430481 0.980948687 1305031526.972200 1.5197 0.8664 1.4958 -0.7881 -0.0951 0.0537 0.6058
1305031527.007595 -0.020048823 -0.005540572 -0.097900160 0.181910872 0.106515355 -0.017926607 0.977364600 1305031527.012100 1.5209 0.8569 1.4996 -0.7795 -0.0899 0.0483 0.6180
1305031527.039512 -0.023435375 -0.009148147 -0.106970325 0.195644155 0.113224901 -0.019022474 0.973931015 1305031527.042100 1.5218 0.8500 1.5023 -0.7711 -0.0861 0.0444 0.6292
1305031527.071487 -0.026807848 0.004425369 -0.112307228 0.213958293 0.120352432 -0.020585811 0.969181776 1305031527.072300 1.5234 0.8450 1.5043 -0.7608 -0.0831 0.0422 0.6422
1305031527.107498 -0.031070728 0.004864503 -0.118102826 0.221194029 0.125381440 -0.019031256 0.966949105 1305031527.112200 1.5243 0.8380 1.5057 -0.7542 -0.0789 0.0399 0.6506
1305031527.139473 -0.030610107 0.008234076 -0.122761726 0.232777029 0.129590198 -0.020409001 0.963641405 1305031527.142100 1.5258 0.8327 1.5068 -0.7480 -0.0759 0.0366 0.6583
1305031527.171540 -0.032993812 0.018031888 -0.131125793 0.240357533 0.133578792 -0.019260569 0.961256444 1305031527.172200 1.5266 0.8284 1.5067 -0.7443 -0.0716 0.0348 0.6630
1305031527.207588 -0.036744710 0.020500474 -0.137645885 0.239894286 0.135950848 -0.017296137 0.961076975 1305031527.212200 1.5271 0.8251 1.5055 -0.7444 -0.0708 0.0335 0.6631
1305031527.271501 -0.043445326 0.041889958 -0.136677355 0.232142463 0.137271211 -0.013112986 0.962857485 1305031527.272100 1.5270 0.8228 1.5007 -0.7554 -0.0680 0.0323 0.6509
1305031527.307472 -0.046960510 0.043947175 -0.127684563 0.222602263 0.136040613 -0.011219901 0.965305805 1305031527.312200 1.5265 0.8244 1.4961 -0.7622 -0.0684 0.0363 0.6427
1305031527.339636 -0.045433633 0.050494798 -0.122109100 0.214023039 0.131844014 -0.006879775 0.967865646 1305031527.322100 1.5263 0.8245 1.4947 -0.7647 -0.0680 0.0377 0.6397
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
1305031527.707520 -0.062977917 0.080318302 -0.075421400 0.081575632 0.118124433 0.010604718 0.989585578 1305031527.712200 1.5059 0.8406 1.4390 -0.8461 -0.0839 0.0480 0.5241
1305031527.771461 -0.063968100 0.079457901 -0.070676021 0.062909685 0.104486309 0.013305012 0.992445469 1305031527.772100 1.4984 0.8395 1.4327 -0.8526 -0.0880 0.0560 0.5121
1305031527.807581 -0.067149058 0.071368024 -0.072235338 0.050288275 0.096843056 0.014775201 0.993918598 1305031527.812200 1.4922 0.8378 1.4290 -0.8564 -0.0930 0.0630 0.5039
1305031527.839601 -0.084145665 0.083385780 -0.065109350 0.049927417 0.091642611 0.016088929 0.994409442 1305031527.842200 1.4867 0.8363 1.4265 -0.8574 -0.0980 0.0705 0.5003
1305031527.871464 -0.094857678 0.090055093 -0.066003457 0.044405133 0.080871582 0.012684624 0.995654106 1305031527.872100 1.4804 0.8341 1.4237 0.8603 0.1070 -0.0783 -0.4922
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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
1305031528.039560 -0.149975643 0.084671959 -0.052950244 0.036809143 0.004435565 -0.046019781 0.998252273 1305031528.042200 1.4350 0.8113 1.4166 0.8395 0.1968 -0.1235 -0.4911
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
1305031528.439469 -0.294514090 0.129935056 -0.100482926 0.113646500 -0.217375934 -0.202731520 0.948014855 1305031528.442100 1.3372 0.6902 1.4400 -0.7103 -0.4054 0.2555 0.5156
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
1305031528.539626 -0.329695433 0.143418118 -0.155989200 0.111015044 -0.298002064 -0.219036371 0.922438860 1305031528.542200 1.3180 0.6526 1.4496 0.6736 0.4500 -0.3218 -0.4902
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
1305031528.707447 -0.339044899 0.179300487 -0.177713454 0.078025557 -0.396103621 -0.245452717 0.881343842 1305031528.712200 1.3036 0.5843 1.4413 0.6416 0.5122 -0.3716 -0.4335
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
1305031529.807516 -0.782125950 0.550134659 -0.398882180 -0.178626403 -0.136654928 -0.177510321 0.958075225 1305031529.812200 1.0347 0.0182 1.3067 0.8683 0.3721 -0.1418 -0.2957
1305031529.839505 -0.801752090 0.562361419 -0.403514504 -0.164821103 -0.120010868 -0.171232879 0.963903904 1305031529.842200 1.0205 0.0123 1.3077 0.8720 0.3619 -0.1364 -0.3002
1305031529.875495 -0.825005233 0.565140069 -0.403103828 -0.163723126 -0.107326634 -0.161056474 0.967334747 1305031529.872100 1.0056 0.0061 1.3092 0.8768 0.3496 -0.1342 -0.3015
1305031529.939498 -0.862981617 0.568239570 -0.402119935 -0.153819934 -0.099035807 -0.135157794 0.973788321 1305031529.942300 0.9664 -0.0101 1.3143 0.8831 0.3236 -0.1383 -0.3102
1305031529.975501 -0.880968273 0.572280824 -0.404322088 -0.150892213 -0.094667107 -0.124493204 0.976099968 1305031529.972100 0.9487 -0.0181 1.3172 0.8879 0.3138 -0.1360 -0.3078
1305031530.007409 -0.905366302 0.569447100 -0.406524211 -0.154951453 -0.086226285 -0.112701796 0.977677524 1305031530.012200 0.9251 -0.0287 1.3230 0.8943 0.2970 -0.1364 -0.3057
1305031530.039454 -0.928224921 0.566439390 -0.410196871 -0.157523975 -0.081151128 -0.098109439 0.979272783 1305031530.042100 0.9078 -0.0374 1.3294 0.8982 0.2858 -0.1387 -0.3039
1305031530.075443 -0.950253010 0.559827328 -0.416947931 -0.162434965 -0.077827856 -0.086941622 0.979795277 1305031530.072100 0.8912 -0.0468 1.3372 0.9025 0.2763 -0.1397 -0.2994
1305031530.107445 -0.969959199 0.551806927 -0.419147462 -0.166437954 -0.076426215 -0.074270479 0.980276167 1305031530.112100 0.8702 -0.0598 1.3504 0.9063 0.2617 -0.1441 -0.2991
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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:

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:
在这里插入图片描述
在这里插入图片描述

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