特征点
特征点是图像中具有代表性的点，这些点在图像发生变化时，比如图像的旋转、缩放，将保持不变。图像中的角点和边缘相对来说更加“特别”，因为它们在不同的图像中辨识度更强。因此一种直观的提取特征的方式就是在图像之间辨认角点，并确定对应关系。角点的提取算法有Harris角点、FAST角点、GFTT角点，等等。但是在很多应用中角点不能满足需求，因为从远处看上去是角点的地方当相机离近时就不是角点了，或者当发生旋转时就认不出是角点了。因此研究人员设计了更加稳定的局部图像特征，如：SIFT、SURF、ORB等等。这些人工设计的特征点具有以下性质：
- 可重复性:相同的特征可以在不同的图像中找到
- 可区别性:不同的特征有不同的表达
- 高效率：同一图像中特征点的数量小于像素的数量
- 本地性：特征只与一小片图像区域有关
特征点是由关键点（Key-point）和描述子（Discriptor）组成，关键点是指该特征点在图像中的位置，描述子通常是一个向量，描述了该关键点周围的像素信息。
ORB特征
ORB特征由关键点与描述子组成。它的关键点称为“Oriented FAST”，是一种改进的FAST角点，它的描述子为BRIEF。
提取ORB特征分为如下两个步骤：
- oFAST角点提取：找出图像中的角点，与原来的FAST算法相比，ORB中计算了特征点的主方向，为BRIEF描述子增加了旋转不变性
- BRIEF描述子：对前一步找到的关键点周围的像素区域进行描述，由于BRIEF对于图像旋转十分敏感，因此ORB对BRIEF进行了改进，利用上一步计算出的方向信息增强BRIEF的旋转不变性。
oFAST角点提取
先来了解一下FAST关键点：有一个像素点p，快速的将p像素点的亮度与其周围16个像素点的亮度进行比较。这16个像素点将被划分为三类(比p点亮、比p点暗、与p点亮度相似)。如果超过8个像素点比p点更亮互更暗，则把p点作为一个关键点。
FAST角点没有方向信息，而且由于它取固定半径为3的圆因此也存在尺度问题（远看是角点，近看就不是角点了）。因此ORB算法使用了图像金字塔（image pyramid）来解决尺度问题。图像金子塔每往上一层就对图像进行一个固定倍率的缩放，较小的图像可以当作远景，如图：
ORB通过对图像的每一层进行关键点的提取从而部分解决了尺度问题。
在旋转方面，ORB根据关键点周围灰度值的变化为每个关键点分配一个方向。为了检测灰度值的变化ORB使用了图像灰度质心（intensity centroid），图像灰度质心假设一个点的灰度强度是偏离中心的，计算步骤如下：
-
在一个图像块（patch）中定义图像块的矩为：
-
通过矩找到图像块的质心
-
由图像块的中心O与质心O构建一个方向向量OC,所以特征点的方向可以定义为：
下图是一个例子：
通过以上的方法，FAST角点便具有了尺度与旋转的描述，提升了其在不同图像中的鲁棒性，因此ORB中这种改进的FAST称为Oriented FAST （oFAST）。
BRIEF 描述子（Binary robust independent elementary feature）
提取了oFAST关键点后需要对每一个关键点计算描述子。BRIEF是一种二进制描述子，描述向量由多个0和1组成。简而言之，每个关键点由一个128-512位的二进制字符串表示
二进制特征向量的每一位取0还是取1是由关键点周围两个随机像素（比如p和q）的大小关系决定的：如果p大于q则取1，反之取0。如果取128对这样的p和q,最后就得到一个128维由0和1组成的向量。由于是随机选取关键点附近的点对（p,q），BRIEF对高频噪声敏感，因此应该先对图像进行高斯滤波。ORB中这两个点（p，q）的选取是服从以图像块为中心的高斯分布的，并且选择的二进制特征向量维数为256维。
在BRIEF的论文原文中，点对（p和q）的采样有5种方式：
- 第一种（G I）服从均匀分布
- 第二次 (G II) 服从以图像块几何中心为中心的高斯分布
- 第三种 （G III）第一个采样点服从以图像块几何中心为中心的高斯分布，第二种服从以第一个采样点为中心的高斯分布
- 后面两种是极坐标采样
由于第二种方式效果更好，所以论文中使用的是第二种采样方式。原始的BRIEF描述子不具有旋转不变性（对旋转很敏感）,因此在图像旋转时容易丢失。而ORB在关键点提取阶段计算了关键点的方向，所以利用方向信息计算旋转之后的“Steer BRIEF”特征，使描述子具有良好的旋转不变性。
下面我写了一段代码用于生成G I、G II 、G III中的采样坐标构成的 “模板”（pattern）：
#include <iostream>
#include <stdlib.h>
#include <math.h>
#include <time.h>
using namespace std;
template<class T>
class Point
{
private:
T X;
T Y;
public:
T getX() {
return X;
}
T getY() {
return Y;
}
Point(){
X = (T)0;
Y = (T)0;
}
Point(T x, T y) {
X = x;
Y = y;
}
};
typedef Point<double> Point2f;
class Random
{
private:
const static int NSUM = 100;//N个独立同分布变量
constexpr static double PI = 3.141592654;
public:
static double gaussRand(void);//静态成员变量，使用类名调用
static double gaussRandBM(void);//通过Box-Muller算法生成一个高斯随机数
static Point2f randPointGauss();//产生一个中心为原点（均值为0），服从二维标准正态分布的采样点
static Point2f randPointGauss(Point2f center, double sd);//产生一个服从以center为中心点（均值），标准差为sd的高斯分布采样点
static Point2f randPointUniform(int a, int b);//服从均匀分布的采样坐标点
static int * Orb_PatternI(const int N, int a, int b);//产生由n个点对构成的pattern
static int * Orb_PatternII(const int N, double sd, int boundrySize);//产生由n个点对构成的pattern, 以原点为中心采集两次
static int * Orb_PatternIII(const int N, double sd, int boundrySize);
};
/**
* 利用中心极限定理，生成一个符合标准正太分布的随机数
* @return 返回一个double类型的符合高斯分布的随机数
*/
double Random::gaussRand() {
double x = 0;//用于求和
//产生NSUM个0-1之间的随机数求和
//srand((unsigned)time(NULL));
for (int i = 0; i < NSUM; i++) {
x += (double) rand() / (RAND_MAX+1.0);
}
x = (x - NSUM * 0.5) / sqrt(NSUM/12);//标准化，转化为标准正态分布
return x;
}
double Random::gaussRandBM() {
static double U, V;
static int phase = 0;
double z;
if(phase == 0)
{
U = rand() / (RAND_MAX + 1.0);
V = rand() / (RAND_MAX + 1.0);
z = sqrt(-2.0 * log(U))* sin(2.0 * PI * V);
}
else
{
z = sqrt(-2.0 * log(U)) * cos(2.0 * PI * V);
}
phase = 1 - phase;
return z;
}
Point2f Random::randPointUniform(int a, int b) {
Point2f p((rand() % (b-a+1))+ a,(rand() % (b-a+1))+ a);
return p;
}
Point2f Random::randPointGauss() {
Point2f p(gaussRandBM(),gaussRandBM());
return p;
}
Point2f Random::randPointGauss(Point2f center, double sd){
Point2f p(center.getX()+gaussRandBM()*sd,center.getY() + gaussRandBM() * sd);
return p;
}
int *Random::Orb_PatternI(const int N, int a, int b){
static int * orb_pattern;//延长生命周期
orb_pattern = new int[4*N];
for(int i = 0; i < 4 * N; i+=2) {
Point2f p1 = randPointUniform(a,b);
orb_pattern[i] = p1.getX();
orb_pattern[i + 1] = p1.getY();
}
return orb_pattern;
}
int * Random::Orb_PatternII(const int N, double sd, int boundrySize) {
static int * orb_pattern;//延长生命周期
orb_pattern = new int[4*N];
Point2f center(0,0);
for(int i = 0; i < 4 * N; i+=2) {
Point2f p1 = randPointGauss(center,sd/5.0);
if (p1.getX() < -boundrySize || p1.getY() < -boundrySize ||p1.getX() > boundrySize || p1.getY() > boundrySize) {
i-=2;
continue;
}
orb_pattern[i] = p1.getX();
orb_pattern[i + 1] = p1.getY();
}
return orb_pattern;
}
int * Random::Orb_PatternIII(const int N, double sd, int boundrySize) {
static int * orb_pattern;//延长生命周期
orb_pattern = new int[4*N];
Point2f center(0,0);
Point2f p1, p2;
for(int i = 0; i < 4 * N; i+=4) {
p1 = randPointGauss(center,sd/5.0);
if (p1.getX() < -boundrySize || p1.getY() < -boundrySize ||p1.getX() >= boundrySize-1 || p1.getY() >= boundrySize-1) {
i-=4;
continue;
}
orb_pattern[i] = p1.getX();
orb_pattern[i + 1] = p1.getY();
}
for(int i = 2; i < 4 * N; i+=4) {
p2 = randPointGauss(p1,sd/10.0);
if (p2.getX() < -boundrySize || p2.getY() < -boundrySize ||p2.getX() >= boundrySize-1 || p2.getY() >= boundrySize-1) {
i-=4;
continue;
}
orb_pattern[i] = p2.getX();
orb_pattern[i + 1] = p2.getY();
}
return orb_pattern;
}
int main() {
int * pattern = Random::Orb_PatternII(256,16,13);
for(int i = 0; i < 4*256; i+=4) {
cout<< pattern[i] << ","<< pattern[i+1] <<","<< pattern[i+2] <<","<< pattern[i+3] <<","<<endl; ;
}
// int * pattern = Random::Orb_PatternI(256,-13,13);
// for(int i = 0; i < 4*256; i+=4) {
// cout<< pattern[i] << ","<< pattern[i+1] <<","<< pattern[i+2] <<","<< pattern[i+3] <<","<<endl; ;
// }
}
BRIEF具有一个重要的特性，即每个位特征具有较大的方差，且均值接近0.5。 但是，一旦将其沿关键点方向定向，它就会失去此属性并变得更加分散。 大的方差使特征更具区分性，因为它对输入的响应不同。 另一个理想的特性是使二进制特征向量不相关，因为这样每一个向量都有助于结果。 为了解决所有这些问题，ORB在所有可能的二进制向量中进行贪婪搜索，以找到方差高且均值接近0.5且不相关的向量。 结果称为rBRIEF。
在OpenCV orb.cpp的源码中有这样一个数组bit_pattern_31_，如图：
这是orb使用某种学习算法（论文里有说明）训练好的256个点对，使用这256个点对的效果会比较好，当然也可以使用自己生成的随机采样点对。
特征匹配
不同图像之间提取完成特征点后就可以进行特征匹配，找到不同图像之间特征点的对应关系。最简单的匹配算法是暴力匹配 （Brute-Force Matcher）：对图像I中的每一个特征点与图像II中的所有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。描述子距离表示两个特征点之间的相似程度。对于rBRIEF这种二进制描述子，通常使用汉明距离（Hamming distance）:两个二进制串不同位数的个数。
实践
下面代码演示了opencv中ORB的使用方法：
#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
vector<KeyPoint> keypoints_1, keypoints_2;//关键点
Mat descriptors_1, descriptors_2;//描述子
Ptr<FeatureDetector> detector = ORB::create();
Ptr<DescriptorExtractor> descriptor = ORB::create();
Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");//暴力匹配
//--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
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("-- Mat dist : %f
", max_dist);
printf("-- Mat 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。但是有时最小距离会非常小，所以要设置一个经验值30作为下限
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);
DMatch m{0,0,256};
return 0;
}
运行效果如下：
下面代码演示如何手写ORB特征，代码中ORB_pattern数组使用的是ORB训练好的采样点数据，当然也可以使用前文提到的代码自己生成随机采样的数据，但是效果较差。
#include <iostream>
#include <opencv2/opencv.hpp>
#include <string>
#include <nmmintrin.h>
#include <chrono>
using namespace std;
//global varluables
string first_file = "./1.png";
string second_file = "./2.png";
//unsigned int is 32bit, will have 8, so is 8*32 = 256 bit
typedef vector<uint32_t> DescType;//Descriptor type
/**
* compute descriptor of orb keypoints
* @param img input image
* @param ketpoints detected by fast keypoints
* @param descriptors descriptors
*
*/
void ComputeORB(const cv::Mat &img, vector<cv::KeyPoint> &keypoints, vector<DescType> & descriptors);
/**
* brute-force match two sets of decriptors
* @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, CV_LOAD_IMAGE_GRAYSCALE);
cv::Mat second_image = cv::imread(second_file, CV_LOAD_IMAGE_GRAYSCALE);
assert(first_image.data != nullptr && second_image.data != nullptr);
//detect FAST keypoints, using threshold = 40
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
vector<cv::KeyPoint> keypoints1;
cv::FAST(first_image, keypoints1, 40);
//compute descriptors by keypoints1
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)*/
};
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) {
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;
}
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);//以当前关键点为原点
m10 += dx * pixel;
m01 += 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;
DescType desc(8,0);
for(int i = 0; i < 8; i++) {
uint32_t d = 0;//d的每一位初始化为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，利用三角函数旋转pq两个点，并转化为以kp为原点
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.x + 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
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);
}
}
}
下面是运行效果
参考
-
https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_feature2d/py_orb/py_orb.html
-
https://medium.com/analytics-vidhya/introduction-to-orb-oriented-fast-and-rotated-brief-4220e8ec40cf
-
Rublee E , Rabaud V , Konolige K , et al. ORB: An efficient alternative to SIFT or SURF[C]// 2011 International Conference on Computer Vision. IEEE, 2012.
-
Calonder M , Lepetit V , Strecha C , et al. BRIEF: Binary Robust Independent Elementary Features[C]// Computer Vision - ECCV 2010, 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part IV. Springer, Berlin, Heidelberg, 2010.
-
视觉SLAM十四讲