视觉十四讲：第七讲_ORB特征点

1.特征点

特征点是图像里一些特别的地方,如角点、边缘和区块。比较著名有SIFT、SURF、ORB等。SIFT充分考虑了图像变换过程中出现的光照、尺度、旋转等变换，但是计算量非常大。而ORB是质量和性能之间比较好的折中。
特征点包含：

• 关键点
• 描述子

2. ORB特性

提取ORB特性有两个步骤:FAST角点提取、BRIEF描述子

1.FAST关键点:

1.在图像中选取像素p,假设它的亮度为({I}_{p}).
2.设置一个阀值T,比如({I}_{p})的20%
3.以像素点p为中心,选取半径为3的圆上的16个像素点
4.假如选取的圆上有连续N个点的亮度大于({I}_{p})+T或小于({I}_{p})-T,则p可认为是特征点(N取12的话,就是FAST-12)
5.循环上面的四步,对每一个像素执行相同的操作

ORB添加了尺度和旋转的描述.

• 尺度不变由构造图像金字塔,并在金字塔的每一层上检测焦点来实现.
• 旋转由计算特征点附近的图像灰度质心求得.步骤为:
  1.在一个小的图像块B中,定义图像块的矩为:({m}_{pq} = sum_{x,yin B}x^py^qI(x,y)) p,q={0,1}
  2.通过矩可以找到图像快的质心: (C=(frac{m_{10}}{m_{00}},frac{m_{01}}{m_{00}}))
  3.连接图像块的几何中心O与质心C,得到一个向量(vec{OC})
  4.特征点的方向可以定义为: ( heta=arctan(m_{01}/m_{10}))

2.BRIEF描述子:

BRIEF是一种二进制描述子,由0和1组成,这里0和1编码了关键点附近两个随机像素比如(p和q)的大小关系:如果p比q大,取1,反之取0.如果取了128个这样的p,q.则最后得到128维由0,1组成的向量.BRIEF使用了随机选点的比较,速度非常快.

3.特征匹配:

最简单的匹配模式是暴力匹配.对两个时刻的图像取得的特征点,测量描述子的距离,然后排序,取最近的一个作为匹配点.对于浮点型的描述子,使用欧氏距离进行度量,对于二进制,使用汉明距离进行度量-两个二进制串的汉明距离,指的是其不同位数的个数.
当特征点数量很大的时候,暴力匹配的计算量会很大,使用快速近似最近邻(FLANN)更适合匹配点数极多的情况.

4.ORB特征点

#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <chrono>

using namespace std;
using namespace cv;

int main(int argc, char **argv) {
  if (argc != 3) {
    cout << "usage: feature_extraction img1 img2" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
  Mat img_2 = imread(argv[2], CV_LOAD_IMAGE_COLOR);
  assert(img_1.data != nullptr && img_2.data != nullptr);

  //-- 初始化
  std::vector<KeyPoint> keypoints_1, keypoints_2;
  Mat descriptors_1, descriptors_2;
  Ptr<FeatureDetector> detector = ORB::create();
  Ptr<DescriptorExtractor> descriptor = ORB::create();
  Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");

  //-- 第一步:检测 Oriented FAST 角点位置
  chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
  detector->detect(img_1, keypoints_1);
  detector->detect(img_2, keypoints_2);

  //-- 第二步:根据角点位置计算 BRIEF 描述子
  descriptor->compute(img_1, keypoints_1, descriptors_1);
  descriptor->compute(img_2, keypoints_2, descriptors_2);
  chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
  chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "extract ORB cost = " << time_used.count() << " seconds. " << endl;

  Mat outimg1;
  drawKeypoints(img_1, keypoints_1, outimg1, Scalar::all(-1), DrawMatchesFlags::DEFAULT);
  imshow("ORB features", outimg1);

  //-- 第三步:对两幅图像中的BRIEF描述子进行匹配，使用 Hamming 距离
  vector<DMatch> matches;
  t1 = chrono::steady_clock::now();
  matcher->match(descriptors_1, descriptors_2, matches);
  t2 = chrono::steady_clock::now();
  time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "match ORB cost = " << time_used.count() << " seconds. " << endl;

  //-- 第四步:匹配点对筛选
  // 计算最小距离和最大距离
  auto min_max = minmax_element(matches.begin(), matches.end(),
                                [](const DMatch &m1, const DMatch &m2) { return m1.distance < m2.distance; });
  double min_dist = min_max.first->distance;
  double max_dist = min_max.second->distance;

  printf("-- Max dist : %f 
", max_dist);
  printf("-- Min dist : %f 
", min_dist);

  //当描述子之间的距离大于两倍的最小距离时,即认为匹配有误.但有时候最小距离会非常小,设置一个经验值30作为下限.
  std::vector<DMatch> good_matches;
  for (int i = 0; i < descriptors_1.rows; i++) {
    if (matches[i].distance <= max(2 * min_dist, 30.0)) {
      good_matches.push_back(matches[i]);
    }
  }

  //-- 第五步:绘制匹配结果
  Mat img_match;
  Mat img_goodmatch;
  drawMatches(img_1, keypoints_1, img_2, keypoints_2, matches, img_match);
  drawMatches(img_1, keypoints_1, img_2, keypoints_2, good_matches, img_goodmatch);
  imshow("all matches", img_match);
  imshow("good matches", img_goodmatch);
  waitKey(0);

  return 0;
}

CMakeLists.txt:

cmake_minimum_required(VERSION 2.8)
project(orb)

set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
include_directories(inc)
aux_source_directory(src DIR_SRCS)
SET(SOUR_FILE ${DIR_SRCS})
find_package(OpenCV 3 REQUIRED)
find_package(G2O REQUIRED)
find_package(Sophus REQUIRED)

include_directories(
        ${OpenCV_INCLUDE_DIRS}
        ${G2O_INCLUDE_DIRS}
        ${Sophus_INCLUDE_DIRS}
        "/usr/include/eigen3/"
)


add_executable(orb ${SOUR_FILE})
target_link_libraries(orb ${OpenCV_LIBS})

5.手写ORB特征点

//
// Created by xiang on 18-11-25.
//

#include <opencv2/opencv.hpp>
#include <string>
#include <nmmintrin.h>
#include <chrono>

using namespace std;

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

// 32 bit unsigned int, will have 8, 8x32=256
typedef vector<uint32_t> DescType; // Descriptor type

/**
 * compute descriptor 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 computed and will be left 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 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);
  cv::Mat second_image = cv::imread(second_file, 0);
  assert(first_image.data != nullptr && second_image.data != nullptr);

  // detect FAST keypoints1 using threshold=40
  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;
  vector<DescType> descriptor2;
  cv::FAST(second_image, keypoints2, 40);
  ComputeORB(second_image, keypoints2, descriptor2);
  chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
  chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "extract ORB cost = " << time_used.count() << " seconds. " << endl;

  // find matches
  vector<cv::DMatch> matches;
  t1 = chrono::steady_clock::now();
  BfMatch(descriptor1, descriptor2, matches);
  t2 = chrono::steady_clock::now();
  time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "match ORB cost = " << 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
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 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) {

    //不计算图像边的特征点
    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;
    }

   //计算旋转角度
    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);
        m01 += dx * pixel;
        m10 += dy * pixel;
      }
    }

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

    // 计算描述子，256维，8个uint32位
    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 * 8 + 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]);  //随机选点算法

        
        cv::Point2f pp = cv::Point2f(cos_theta * p.x - sin_theta * p.y, sin_theta * p.x + cos_theta * p.y)  //选点坐标，包含旋转信息
                         + kp.pt;
        cv::Point2f qq = cv::Point2f(cos_theta * q.x - sin_theta * q.y, sin_theta * q.x + cos_theta * q.y)
                         + kp.pt;
        if (img.at<uchar>(pp.y, pp.x) < img.at<uchar>(qq.y, qq.x)) {   //比较p和q的大小
          d |= 1 << k;
        }
      }
      desc[i] = d;
    }
    descriptors.push_back(desc);
  }

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

// 匹配描述子
void BfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches) {
  const int d_max = 40;

  for (size_t i1 = 0; i1 < desc1.size(); ++i1) {
    if (desc1[i1].empty()) continue;
    cv::DMatch m{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);
    }
  }
}