slambook2+ch7+orb_self代码理解

算法部分

1. 获取关键点
   • 使用cv::FAST函数获取图像特征点，cv::FAST中自带高斯金字塔，实现了尺度不变性
2. 计算描述子
   • 剔除边缘不稳定的关键点
   • 求关键点局部区域的旋转方向
   • 在关键点附近的局部区域(patch)组成的图像块，定义图像块的像素矩m01、m10，然后求图像块的像素质心（类似于重心）C=(m10/m_sqrt , m01/m_sqrt)
   • 连接图像块几何中心O与质心C，得到方向向量OC，定义特征点方向为 theta
   • 在关键点附近选取256对随机像素点(像素点对的选取方式为pattern,pattern服从随机分布、高斯分布等，特征点的分布方式不影响旋转结果)，每对像素点都旋转 theat 角度。
   • 比较每对像素点，p大于q取1，小于取0。则每对关键点都由附近的像素点比较后组成了256位的描述子。
3. 比较描述子
   • 每个特征点x(t)与所有x(t+1)计算汉明距离并排序，取最近点为匹配点

//
// Created by wcm on 2020/6/1.
//

//nmmintrin与SSE指令集有关
//SSE指令集提供标量和包裹式浮点运算
#include 
#include 
#include 
#include 

using namespace std;

//global variables
string first_file= "/home/automobile/wcm/slambook2/ch7/01.png";
string second_file= "/home/automobile/wcm/slambook2/ch7/02.png";

//Descriptor type
//32 bit unsigned int, will have 8, 8*32=256
typedef vector<uint32_t> DescType;

/**
 * compute descriptors of ORB keypoints
 * @param img input image
 * @param keypoints detected fast keypoints
 * @param descriptors descriptors
 *
 * Note:if a keypoint goes outside the image boundary(8 pixels),
 * descriptors will not be compute and leave as empty
 */
void ComputeORB(const cv::Mat &img, vector<cv::KeyPoint> &keypoints, vector<DescType> &descriptors);

/**
 * Brute-Force match two sets of descriptors
 * @param desc1 the first descriptors
 * @param desc2 the second descriptors
 * @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, CV_LOAD_IMAGE_COLOR);
    cv::Mat second_image = cv::imread(second_file, CV_LOAD_IMAGE_COLOR);
    assert(first_image.data != nullptr && second_image.data != nullptr );

    //detect fast keypoints using threshold=40
    //ORB使用FAST算法检测特征点
    //OpenCV中的ORB采用了图像金字塔来解决尺度变换一致性
    //自定义ComputeORB函数来描述ORB特征点，并旋转使其具备旋转尺度不变性
    chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
    vector<cv::KeyPoint> keypoints1;
    cv::FAST(first_image, keypoints1, 40);
    vector<DescType> descriptor1;
    ComputeORB(first_image, keypoints1, descriptor1);

    //same for the second
    vector<cv::KeyPoint> keypoints2;
    cv::FAST(second_image, keypoints2, 40);
    vector<DescType> descriptor2;
    ComputeORB(second_image, keypoints2, descriptor2);
    chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
    chrono::duration<double> time_used_extract = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
    cout << " extract ORB cost = " << time_used_extract.count() << " seconds. "<< endl;

    //find matches
    //自定义BfMatch函数，匹配特征点
    vector<cv::DMatch> matches;
    chrono::steady_clock::time_point t3 = chrono::steady_clock::now();
    BfMatch(descriptor1, descriptor2, matches);
    chrono::steady_clock::time_point t4 = chrono::steady_clock::now();
    chrono::duration<double> time_used_match = chrono::duration_cast<chrono::duration<double>>(t4 - t3);
    cout << " match ORB cost " << time_used_match.count() << " seconds" <<endl;
    chrono::duration<double> ORB_total_time_used = chrono::duration_cast<chrono::duration<double>>(time_used_extract + time_used_match);
    cout << " extract and match ORB cost = " << ORB_total_time_used.count() << " seconds" <<endl;
    cout << " matches: " << matches.size() <<endl;



    //plot the matches
    cv::Mat image_show;
    cv::drawMatches(first_image, keypoints1, 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;
}

//-------------------------------------------------------------//
//ORB pattern
//特征点附近256次像素比较，每次比较两个像素点
//patter选取的两个像素点的分布方式，如高斯分布，随机分布，每种分布的结果应该差不多
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
//将特征点领域看成patch
//patch size of comparison
void ComputeORB (const cv::Mat &img, vector<cv::KeyPoint> &keypoints, vector<DescType> &descriptors) {
    const int half_patch_size = 8;
    const int half_boundary = 16;
    int bad_points = 0;
    for (auto &kp : keypoints) {    //剔除边缘关键点
        if (kp.pt.x < half_boundary || kp.pt.y < half_boundary ||
            kp.pt.x >= img.cols - half_boundary || kp.pt.y >= img.rows - half_boundary) {
            //outside
            bad_points++;
            descriptors.push_back({});
            continue;
        }

        //计算局部区域内所有像素点
        //以关键点为圆心，patch为特征点领域，m10、m01为领域像素灰度质心
        float m01 = 0, m10 = 0;
        for (int dx = -half_patch_size; dx < half_patch_size; ++dx) {
            for (int dy = -half_patch_size; dy < half_patch_size; ++dy) {
                uchar pixel = img.at<uchar>(kp.pt.y + dy, kp.pt.x + dx);
                m10 += dx * pixel;
                m01 += dy * pixel;
            }
        }

        //angle should be arc tan(m01/m10)
        float m_sqrt = sqrt(m01 * m01 + m10 * m10) + 1e-18;//avoid divided by zero;
        float sin_theta = m01 / m_sqrt;
        float cos_theta = m10 / m_sqrt;

        //compute the angle of the point
        //计算局部区域内所有像素点角度
        //描述子为二进制描述子，p大于q取1，小于取0
        DescType desc(8, 0);
        for (int i = 0; i < 8; i++) {
            uint32_t d = 0;
            for (int k = 0; k < 32; k++) {
                int idx_pq = i * 32 + k;
                cv::Point2f p(ORB_pattern[idx_pq * 4], ORB_pattern[idx_pq * 4 + 1]);
                cv::Point2f q(ORB_pattern[idx_pq * 4 + 2], ORB_pattern[idx_pq * 4 + 3]);

                //rotate with theta,关键点邻域需要旋转
                //p,q为关键点附近两个比较的像素，像素分布为pattern
                //pp、qq表达式为图像中任意点(x1,y1)绕另一坐标点(x2,y2)旋转坐标表达式
                //旋转角度为特征点到质心构成的向量的角度
                //p.x=x1-x2、p.y=y1-y2
                cv::Point2f pp = cv::Point2f(cos_theta * p.x - sin_theta * p.y,
                                             sin_theta * p.x + cos_theta * p.y) + kp.pt;
                cv::Point2f qq = cv::Point2f(cos_theta * q.x - sin_theta * q.y,
                                             sin_theta * q.y + cos_theta * q.y) + kp.pt;
                if (img.at<uchar>(pp.y, pp.x) < img.at<uchar>(qq.y, qq.x)) {
                    d |= 1 << k;
                }
            }
            desc[i] = d;
        }
        descriptors.push_back(desc);
    }

    cout << " bad/total: " << bad_points << " / " << keypoints.size() << endl;
}

    //brute-force matching
    //每个描述子DescType均为32*8=256位二进制
    //desc1、desc2为32*8的二维向量
    //desc.size()为图像的描述子的数量
    //每个特征点x(t)与所有x(t+1)测量描述子的距离
    //比较排序，取最近的作为匹配点，记录ℹi匹配的i2
    void BfMatch(
            const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches
    ) {
    const int d_max = 20;

    for(size_t i1 = 0; i1 < desc1.size(); ++i1){
        if (desc1[i1].empty()) continue;
        cv::DMatch m{int(i1), 0, 256};
        for (size_t i2 = 0; i2 < desc2.size(); ++i2){
            if (desc2[i2].empty()) continue;
            int distance = 0;
            for (int k = 0; k < 8; k++){
                distance += _mm_popcnt_u32(desc1[i1][k] ^ desc2[i2][k]);
            }
            if (distance < d_max && distance < m.distance){
                m.distance = distance;
                m.trainIdx = i2;
            }
        }
        if (m.distance < d_max){
            matches.push_back(m);
        }
    }
}