图像特征描述与匹配（一）——BRIEF特征点描述与匹配
传统的特征点描述子如SIFT,SURF描述子，每个特征点采用128维(SIFT)或者64维(SURF)向量去描述，每个维度上占用4字节，SIFT需要128×4=512字节内存，SURF则需要256字节。如果对于内存资源有限的情况下，这种描述子方法显然不适应。同时，在形成描述子的过程中，也比较耗时。后来有人提出采用PCA降维的方法，但没有解决计算描述子耗时的问题。
鉴于上述的缺点Michael Calonder等人在论文提出BRIEF描述特征点的方法(BRIEF:Binary Robust Independent Elementary Features)。BRIEF描述子采用二进制码串(每一位非1即0)作为描述子向量，论文中考虑长度有128,256,512几种，同时形成描述子算法的过程简单，由于采用二进制码串，匹配上采用汉明距离，（一个串变成另一个串所需要的最小替换次数）。但由于BRIEF描述子不具有方向性，大角度旋转会对匹配上有很大的影响。
主要思路就是在特征点附近随机选取若干点对，将这些点对的灰度值的大小，组合成一个二进制串，并将这个二进制串作为该特征点的特征描述子。 摈弃了利用区域灰度直方图描述特征点的传统方法，大大的加快了特征描述符建立的速度，同时也极大的降低了特征匹配的时间，是一种非常快速，很有潜力的算法。
由于BRIEF仅仅是特征描述子，所以事先要得到特征点的位置，可以利用FAST特征点检测算法或Harris角点检测算法或SIFT、SURF等算法检测特征点的位置，论文中建议与Fast结合，因为会更能体现出Brirf速度快等优点。
相关：Fast原理及源码解析
Harris原理及源码解析
SIFT原理及源码解析
SURF原理及源码解析
BRIEF具体算法
原理解析：
__1.关于做τ测试前，需要对随机点做高斯平滑，由于采用单个的像素灰度值做比较，会对噪声很敏感；采用高斯平滑图像，会降低噪声的影响，使得 brief描述子更加稳定。论文中建议采用9×9的kernal。
__2.在窗口中随机选取N对随机点，重复步骤2的二进制赋值，形成一个二进制编码，这个编码就是对特征点的描述，即特征描述子。（一般N=256）。关于一对随机点的选择方法，论文中对随机取N对点采用了5中不同的方法做测试，论文中建议采用G II的方法：
这5种方法生成的256对随机点如下（一条线段的两个端点是一对）：
__3.利用BRIEF特征进行配准
经过上面的特征提取算法，对于一幅图中的每一个特征点，都得到了一个256bit的二进制编码。接下来对有相似或重叠部分的两幅图像进行配准。
特征配对是利用的汉明距离进行判决，直接比较两二进制码串的距离，距离定义为：其中一个串变成另一个串所需要的最少操作。因而比欧氏距离运算速度快.： 如果取N=128,即每个特征点需要128/8=16个字节内存大小作为其描述子。对于原论文来说
1、两个特征编码对应bit位上相同元素的个数小于128的，一定不是配对的。
2、一幅图上特征点与另一幅图上特征编码对应bit位上相同元素的个数最多的特征点配成一对。
OPENCV源码解析：
#include
#include
#include "cv.h"
#include "opencv2/highgui/highgui.hpp"
#include "opencv2/core/core.hpp"
#include "opencv2/features2d/features2d.hpp"
#include "opencv2/nonfree/nonfree.hpp"
using namespace std;
using namespace cv;
int main( int argc, char** argv )
{
Mat img_1 = imread( "F:\\Picture\\book.jpg", CV_LOAD_IMAGE_GRAYSCALE );
Mat img_2 = imread( "F:\\Picture\\book_2.jpg", CV_LOAD_IMAGE_GRAYSCALE );
if( !img_1.data || !img_2.data )
{
return -1; }
//-- Step 1: Detect the keypoints using SURF Detector
int minHessian = 400;
SurfFeatureDetector detector( minHessian); //采用Surf特征点检测
std::vector keypoints_1, keypoints_2;
detector.detect( img_1, keypoints_1 );
detector.detect( img_2, keypoints_2 );
//-- Step 2: Calculate descriptors (feature vectors)
BriefDescriptorExtractor extractor(64); //参数表示字节数,采用长度为64×8=512的向量表示，见下方分析
Mat descriptors_1, descriptors_2;
extractor.compute( img_1, keypoints_1, descriptors_1 );
extractor.compute( img_2, keypoints_2, descriptors_2 );
//-- Step 3: Matching descriptor vectors with a brute force matcher
BFMatcher matcher(NORM_HAMMING); //汉明距离匹配特征点
std::vector< DMatch > matches;
matcher.match( descriptors_1, descriptors_2, matches );
//-- Draw matches
Mat img_matches;
drawMatches( img_1, keypoints_1, img_2, keypoints_2, matches, img_matches );
////-- Show detected matches
imshow("Matches", img_matches );
waitKey(0);
return 0;
} Brief描述子的类定义：
注意bytes参数表示的是描述子占用的字节数不是描述子长度，如默认采用32字节对应描述子长度为32×8=256；
/*
* BRIEF Descriptor
*/
class CV_EXPORTS BriefDescriptorExtractor : public DescriptorExtractor
{
public:
static const int PATCH_SIZE = 48; //邻域范围
static const int KERNEL_SIZE = 9;//平滑积分核大小
// bytes is a length of descriptor in bytes. It can be equal 16, 32 or 64 bytes.
BriefDescriptorExtractor( int bytes = 32 ); //占用字节数32,对应描述子长度为32×8=256;
virtual void read( const FileNode& );
virtual void write( FileStorage& ) const;
virtual int descriptorSize() const;
virtual int descriptorType() const;
/// @todo read and write for brief
AlgorithmInfo* info() const;
protected:
virtual void computeImpl(const Mat& image, vector& keypoints, Mat& descriptors) const; //计算特征描述子函数
typedef void(*PixelTestFn)(const Mat&, const vector&, Mat&); //不同长度的描述子调用不同的函数
int bytes_;//占用字节数
PixelTestFn test_fn_;
}; 计算特征描述子函数：
void BriefDescriptorExtractor::computeImpl(const Mat& image, std::vector& keypoints, Mat& descriptors) const
{
// Construct integral image for fast smoothing (box filter)
Mat sum;
Mat grayImage = image;
if( image.type() != CV_8U ) cvtColor( image, grayImage, CV_BGR2GRAY );
///TODO allow the user to pass in a precomputed integral image
//if(image.type() == CV_32S)
// sum = image;
//else
integral( grayImage, sum, CV_32S); //计算积分图像
//Remove keypoints very close to the border
KeyPointsFilter::runByImageBorder(keypoints, image.size(), PATCH_SIZE/2 + KERNEL_SIZE/2);//剔除落在边界外的角点
descriptors = Mat::zeros((int)keypoints.size(), bytes_, CV_8U);
test_fn_(sum, keypoints, descriptors); //计算特征点描述子
} 关于对随机点平滑，不采用论文中高斯平滑，而是采用随机点邻域内积分和代替，同样可以降低噪声的影响：
inline int smoothedSum(const Mat& sum, const KeyPoint& pt, int y, int x)
{
static const int HALF_KERNEL = BriefDescriptorExtractor::KERNEL_SIZE / 2;
int img_y = (int)(pt.pt.y + 0.5) + y;
int img_x = (int)(pt.pt.x + 0.5) + x;
return sum.at(img_y + HALF_KERNEL + 1, img_x + HALF_KERNEL + 1)
- sum.at(img_y + HALF_KERNEL + 1, img_x - HALF_KERNEL)
- sum.at(img_y - HALF_KERNEL, img_x + HALF_KERNEL + 1)
+ sum.at(img_y - HALF_KERNEL, img_x - HALF_KERNEL);
} 描述子向量的形成（以长度为16字节×8=128为例）：
数组des每一个元素占用一个字节，源码位置：...\modules\features2d\src\generated_16.i
// Code generated with '$ scripts/generate_code.py src/test_pairs.txt 16'
#define SMOOTHED(y,x) smoothedSum(sum, pt, y, x)
desc[0] = (uchar)(((SMOOTHED(-2, -1) < SMOOTHED(7, -1)) << 7) + ((SMOOTHED(-14, -1) < SMOOTHED(-3, 3)) << 6) + ((SMOOTHED(1, -2) < SMOOTHED(11, 2)) << 5) + ((SMOOTHED(1, 6) < SMOOTHED(-10, -7)) << 4) + ((SMOOTHED(13, 2) < SMOOTHED(-1, 0)) << 3) + ((SMOOTHED(-14, 5) < SMOOTHED(5, -3)) << 2) + ((SMOOTHED(-2, 8) < SMOOTHED(2, 4)) << 1) + ((SMOOTHED(-11, 8) < SMOOTHED(-15, 5)) << 0));
desc[1] = (uchar)(((SMOOTHED(-6, -23) < SMOOTHED(8, -9)) << 7) + ((SMOOTHED(-12, 6) < SMOOTHED(-10, 8)) << 6) + ((SMOOTHED(-3, -1) < SMOOTHED(8, 1)) << 5) + ((SMOOTHED(3, 6) < SMOOTHED(5, 6)) << 4) + ((SMOOTHED(-7, -6) < SMOOTHED(5, -5)) << 3) + ((SMOOTHED(22, -2) < SMOOTHED(-11, -8)) << 2) + ((SMOOTHED(14, 7) < SMOOTHED(8, 5)) << 1) + ((SMOOTHED(-1, 14) < SMOOTHED(-5, -14)) << 0));
desc[2] = (uchar)(((SMOOTHED(-14, 9) < SMOOTHED(2, 0)) << 7) + ((SMOOTHED(7, -3) < SMOOTHED(22, 6)) << 6) + ((SMOOTHED(-6, 6) < SMOOTHED(-8, -5)) << 5) + ((SMOOTHED(-5, 9) < SMOOTHED(7, -1)) << 4) + ((SMOOTHED(-3, -7) < SMOOTHED(-10, -18)) << 3) + ((SMOOTHED(4, -5) < SMOOTHED(0, 11)) << 2) + ((SMOOTHED(2, 3) < SMOOTHED(9, 10)) << 1) + ((SMOOTHED(-10, 3) < SMOOTHED(4, 9)) << 0));
desc[3] = (uchar)(((SMOOTHED(0, 12) < SMOOTHED(-3, 19)) << 7) + ((SMOOTHED(1, 15) < SMOOTHED(-11, -5)) << 6) + ((SMOOTHED(14, -1) < SMOOTHED(7, 8)) << 5) + ((SMOOTHED(7, -23) < SMOOTHED(-5, 5)) << 4) + ((SMOOTHED(0, -6) < SMOOTHED(-10, 17)) << 3) + ((SMOOTHED(13, -4) < SMOOTHED(-3, -4)) << 2) + ((SMOOTHED(-12, 1) < SMOOTHED(-12, 2)) << 1) + ((SMOOTHED(0, 8) < SMOOTHED(3, 22)) << 0));
desc[4] = (uchar)(((SMOOTHED(-13, 13) < SMOOTHED(3, -1)) << 7) + ((SMOOTHED(-16, 17) < SMOOTHED(6, 10)) << 6) + ((SMOOTHED(7, 15) < SMOOTHED(-5, 0)) << 5) + ((SMOOTHED(2, -12) < SMOOTHED(19, -2)) << 4) + ((SMOOTHED(3, -6) < SMOOTHED(-4, -15)) << 3) + ((SMOOTHED(8, 3) < SMOOTHED(0, 14)) << 2) + ((SMOOTHED(4, -11) < SMOOTHED(5, 5)) << 1) + ((SMOOTHED(11, -7) < SMOOTHED(7, 1)) << 0));
desc[5] = (uchar)(((SMOOTHED(6, 12) < SMOOTHED(21, 3)) << 7) + ((SMOOTHED(-3, 2) < SMOOTHED(14, 1)) << 6) + ((SMOOTHED(5, 1) < SMOOTHED(-5, 11)) << 5) + ((SMOOTHED(3, -17) < SMOOTHED(-6, 2)) << 4) + ((SMOOTHED(6, 8) < SMOOTHED(5, -10)) << 3) + ((SMOOTHED(-14, -2) < SMOOTHED(0, 4)) << 2) + ((SMOOTHED(5, -7) < SMOOTHED(-6, 5)) << 1) + ((SMOOTHED(10, 4) < SMOOTHED(4, -7)) << 0));
desc[6] = (uchar)(((SMOOTHED(22, 0) < SMOOTHED(7, -18)) << 7) + ((SMOOTHED(-1, -3) < SMOOTHED(0, 18)) << 6) + ((SMOOTHED(-4, 22) < SMOOTHED(-5, 3)) << 5) + ((SMOOTHED(1, -7) < SMOOTHED(2, -3)) << 4) + ((SMOOTHED(19, -20) < SMOOTHED(17, -2)) << 3) + ((SMOOTHED(3, -10) < SMOOTHED(-8, 24)) << 2) + ((SMOOTHED(-5, -14) < SMOOTHED(7, 5)) << 1) + ((SMOOTHED(-2, 12) < SMOOTHED(-4, -15)) << 0));
desc[7] = (uchar)(((SMOOTHED(4, 12) < SMOOTHED(0, -19)) << 7) + ((SMOOTHED(20, 13) < SMOOTHED(3, 5)) << 6) + ((SMOOTHED(-8, -12) < SMOOTHED(5, 0)) << 5) + ((SMOOTHED(-5, 6) < SMOOTHED(-7, -11)) << 4) + ((SMOOTHED(6, -11) < SMOOTHED(-3, -22)) << 3) + ((SMOOTHED(15, 4) < SMOOTHED(10, 1)) << 2) + ((SMOOTHED(-7, -4) < SMOOTHED(15, -6)) << 1) + ((SMOOTHED(5, 10) < SMOOTHED(0, 24)) << 0));
desc[8] = (uchar)(((SMOOTHED(3, 6) < SMOOTHED(22, -2)) << 7) + ((SMOOTHED(-13, 14) < SMOOTHED(4, -4)) << 6) + ((SMOOTHED(-13, 8) < SMOOTHED(-18, -22)) << 5) + ((SMOOTHED(-1, -1) < SMOOTHED(-7, 3)) << 4) + ((SMOOTHED(-19, -12) < SMOOTHED(4, 3)) << 3) + ((SMOOTHED(8, 10) < SMOOTHED(13, -2)) << 2) + ((SMOOTHED(-6, -1) < SMOOTHED(-6, -5)) << 1) + ((SMOOTHED(2, -21) < SMOOTHED(-3, 2)) << 0));
desc[9] = (uchar)(((SMOOTHED(4, -7) < SMOOTHED(0, 16)) << 7) + ((SMOOTHED(-6, -5) < SMOOTHED(-12, -1)) << 6) + ((SMOOTHED(1, -1) < SMOOTHED(9, 18)) << 5) + ((SMOOTHED(-7, 10) < SMOOTHED(-11, 6)) << 4) + ((SMOOTHED(4, 3) < SMOOTHED(19, -7)) << 3) + ((SMOOTHED(-18, 5) < SMOOTHED(-4, 5)) << 2) + ((SMOOTHED(4, 0) < SMOOTHED(-20, 4)) << 1) + ((SMOOTHED(7, -11) < SMOOTHED(18, 12)) << 0));
desc[10] = (uchar)(((SMOOTHED(-20, 17) < SMOOTHED(-18, 7)) << 7) + ((SMOOTHED(2, 15) < SMOOTHED(19, -11)) << 6) + ((SMOOTHED(-18, 6) < SMOOTHED(-7, 3)) << 5) + ((SMOOTHED(-4, 1) < SMOOTHED(-14, 13)) << 4) + ((SMOOTHED(17, 3) < SMOOTHED(2, -8)) << 3) + ((SMOOTHED(-7, 2) < SMOOTHED(1, 6)) << 2) + ((SMOOTHED(17, -9) < SMOOTHED(-2, 8)) << 1) + ((SMOOTHED(-8, -6) < SMOOTHED(-1, 12)) << 0));
desc[11] = (uchar)(((SMOOTHED(-2, 4) < SMOOTHED(-1, 6)) << 7) + ((SMOOTHED(-2, 7) < SMOOTHED(6, 8)) << 6) + ((SMOOTHED(-8, -1) < SMOOTHED(-7, -9)) << 5) + ((SMOOTHED(8, -9) < SMOOTHED(15, 0)) << 4) + ((SMOOTHED(0, 22) < SMOOTHED(-4, -15)) << 3) + ((SMOOTHED(-14, -1) < SMOOTHED(3, -2)) << 2) + ((SMOOTHED(-7, -4) < SMOOTHED(17, -7)) << 1) + ((SMOOTHED(-8, -2) < SMOOTHED(9, -4)) << 0));
desc[12] = (uchar)(((SMOOTHED(5, -7) < SMOOTHED(7, 7)) << 7) + ((SMOOTHED(-5, 13) < SMOOTHED(-8, 11)) << 6) + ((SMOOTHED(11, -4) < SMOOTHED(0, 8)) << 5) + ((SMOOTHED(5, -11) < SMOOTHED(-9, -6)) << 4) + ((SMOOTHED(2, -6) < SMOOTHED(3, -20)) << 3) + ((SMOOTHED(-6, 2) < SMOOTHED(6, 10)) << 2) + ((SMOOTHED(-6, -6) < SMOOTHED(-15, 7)) << 1) + ((SMOOTHED(-6, -3) < SMOOTHED(2, 1)) << 0));
desc[13] = (uchar)(((SMOOTHED(11, 0) < SMOOTHED(-3, 2)) << 7) + ((SMOOTHED(7, -12) < SMOOTHED(14, 5)) << 6) + ((SMOOTHED(0, -7) < SMOOTHED(-1, -1)) << 5) + ((SMOOTHED(-16, 0) < SMOOTHED(6, 8)) << 4) + ((SMOOTHED(22, 11) < SMOOTHED(0, -3)) << 3) + ((SMOOTHED(19, 0) < SMOOTHED(5, -17)) << 2) + ((SMOOTHED(-23, -14) < SMOOTHED(-13, -19)) << 1) + ((SMOOTHED(-8, 10) < SMOOTHED(-11, -2)) << 0));
desc[14] = (uchar)(((SMOOTHED(-11, 6) < SMOOTHED(-10, 13)) << 7) + ((SMOOTHED(1, -7) < SMOOTHED(14, 0)) << 6) + ((SMOOTHED(-12, 1) < SMOOTHED(-5, -5)) << 5) + ((SMOOTHED(4, 7) < SMOOTHED(8, -1)) << 4) + ((SMOOTHED(-1, -5) < SMOOTHED(15, 2)) << 3) + ((SMOOTHED(-3, -1) < SMOOTHED(7, -10)) << 2) + ((SMOOTHED(3, -6) < SMOOTHED(10, -18)) << 1) + ((SMOOTHED(-7, -13) < SMOOTHED(-13, 10)) << 0));
desc[15] = (uchar)(((SMOOTHED(1, -1) < SMOOTHED(13, -10)) << 7) + ((SMOOTHED(-19, 14) < SMOOTHED(8, -14)) << 6) + ((SMOOTHED(-4, -13) < SMOOTHED(7, 1)) << 5) + ((SMOOTHED(1, -2) < SMOOTHED(12, -7)) << 4) + ((SMOOTHED(3, -5) < SMOOTHED(1, -5)) << 3) + ((SMOOTHED(-2, -2) < SMOOTHED(8, -10)) << 2) + ((SMOOTHED(2, 14) < SMOOTHED(8, 7)) << 1) + ((SMOOTHED(3, 9) < SMOOTHED(8, 2)) << 0));
#undef SMOOTHEDBRIEF算法优劣
优点
1、计算速度快
缺点
1、对噪声敏感（因为二进制编码是通过比较具体像素值来判定的）
2、不具备旋转不变性
3、不具备尺度不变性
参考文章：
https://blog.csdn.net/luoshixian099/article/details/48338273
https://blog.csdn.net/hujingshuang/article/details/46910259
https://blog.csdn.net/songzitea/article/details/18272559