BRISK算法是2011年ICCV上《BRISK:Binary Robust Invariant Scalable Keypoints》文章中,提出来的一种特征提取算法,也是一种二进制的特征描述算子。
它具有较好的旋转不变性、尺度不变性,较好的鲁棒性等。在图像配准应用中,速度比较:SIFT<SURF<BRISK<FREAK<ORB,在对有较大模糊的图像配准时,BRISK算法在其中表现最为出色。
BRISK算法主要利用FAST9-16进行特征点检测(为什么是主要?因为用到一次FAST5-8),可参见博客:FAST特征点检测算法。要解决尺度不变性,就必须在尺度空间进行特征点检测,于是BRISK算法中构造了图像金字塔进行多尺度表达。
构造n个octave层(用ci表示)和n个intra-octave层(用di表示),文章中n=4,i={0,1,...,n-1}。假设有图像img,octave层的产生:c0层就是img原图像,c1层是c0层的2倍下采样,c2层是c1层的2倍下采样,以此类推。intra-octave层的产生:d0层是img的1.5倍下采样,d1层是d0层的2倍下采样(即img的2*1.5倍下采样),d2层是d1层的2倍下采样,以此类推。
则ci、di层与原图像的尺度关系用t表示为:,
ci、di层与原图像大小关系为:
由于n=4,所以一共可以得到8张图,octave层之间尺度(缩放因子)是2倍关系,intra-octave层之间尺度(缩放因子)也是2倍关系。
对这8张图进行FAST9-16角点检测,得到具有角点信息的8张图,对原图像img进行一次FAST5-8角点检测(当做d(-1)层,虚拟层),总共会得到9幅有角点信息的图像。
对这9幅图像,进行空间上的非极大值抑制(同SIFT算法的非极大值抑制):特征点在位置空间(8邻域点)和尺度空间(上下层2x9个点),共26个邻域点的FAST的得分值要最大,否则不能当做特征点;此时得到的极值点还比较粗糙,需要进一步精确定位。
进过上面步骤,得到了图像特征点的位置和尺度,在极值点所在层及其上下层所对应的位置,对FAST得分值(共3个)进行二维二次函数插值(x、y方向),得到真正意义上的得分极值点及其精确的坐标位置(作为特征点位置);再对尺度方向进行一维插值,得到极值点所对应的尺度(作为特征点尺度)。
现在,我们得到了特征点的位置和尺度(t)后,要对特征点赋予其描述符。均匀采样模式:以特征点为中心,构建不同半径的同心圆,在每个圆上获取一定数目的等间隔采样点(所有采样点包括特征点,一共N个),由于这种邻域采样模式会引起混叠效应,所以需要对同心圆上的采样点进行高斯滤波。
采样模式如下图,蓝圈表示;以采样点为中心,为方差进行高斯滤波,滤波半径大小与高斯方差的大小成正比,红圈表示。最终用到的N个采样点是经过高斯平滑后的采样点。下图是t=1时的。(文章中:N=60)
由于有N个采样点,则采样点两两组合成一对,共有N(N-1)/2钟组合方式,所有组合方式的集合称作采样点对,用集合表示,其中像素分别是、,δ表示尺度。用表示特征点局部梯度集合,则有:
定义短距离点对子集、长距离点对子集(L个):
其中,,,t是特征点所在的尺度。
现在要利用上面得到的信息,来计算特征点的主方向(注意:此处只用到了长距离子集),如下:
要解决旋转不变性,则需要对特征点周围的采样区域进行旋转到主方向,旋转后得到新的采样区域,采样模式同上。BRISK描述子是二进制的特征,由采样点集合可得到N(N-1)/2对采样点对,就可以得到N(N-1)/2个距离的集合(包含长、短距离子集),考虑其中短距离子集中的512个短距离点对,进行二进制编码,判断方式如下:
其中,带有上标,表示经过旋转a角度后的,新的采样点。由此可得到,512Bit的二进制编码,也就是64个字节(BRISK64)。
汉明距离进行比较,与其他二进制描述子的匹配方式一样。
#include <cv.h> #include <opencv2/highgui/highgui.hpp> #include <opencv2/core/core.hpp> #include <opencv2/nonfree/features2d.hpp> #include <opencv2/nonfree/nonfree.hpp> #include <Windows.h> using namespace cv; using namespace std; int main() { //Load Image Mat c_src1 = imread( "1.png"); Mat c_src2 = imread("2.png"); Mat src1 = imread( "1.png", CV_LOAD_IMAGE_GRAYSCALE); Mat src2 = imread( "2.png", CV_LOAD_IMAGE_GRAYSCALE); if( !src1.data || !src2.data ) { cout<< "Error reading images " << std::endl; return -1; } //feature detect BRISK detector; vector<KeyPoint> kp1, kp2; double start = GetTickCount(); detector.detect( src1, kp1 ); detector.detect( src2, kp2 ); //cv::BRISK extractor; Mat des1,des2;//descriptor detector.compute(src1, kp1, des1); detector.compute(src2, kp2, des2); Mat res1,res2; int drawmode = DrawMatchesFlags::DRAW_RICH_KEYPOINTS; drawKeypoints(c_src1, kp1, res1, Scalar::all(-1), drawmode);//画出特征点 drawKeypoints(c_src2, kp2, res2, Scalar::all(-1), drawmode); cout<<"size of description of Img1: "<<kp1.size()<<endl; cout<<"size of description of Img2: "<<kp2.size()<<endl; BFMatcher matcher(NORM_HAMMING); vector<DMatch> matches; matcher.match(des1, des2, matches); double end = GetTickCount(); cout<<"耗时:"<<(end - start) <<"ms"<<endl; Mat img_match; drawMatches(src1, kp1, src2, kp2, matches, img_match); cout<<"number of matched points: "<<matches.size()<<endl; imshow("matches",img_match); cvWaitKey(0); cvDestroyAllWindows(); return 0; }
// construct the image pyramids(构造图像金字塔) void BriskScaleSpace::constructPyramid(const cv::Mat& image) { // set correct size: pyramid_.clear(); // fill the pyramid: pyramid_.push_back(BriskLayer(image.clone())); if (layers_ > 1) { pyramid_.push_back(BriskLayer(pyramid_.back(), BriskLayer::CommonParams::TWOTHIRDSAMPLE));//d0层是2/3 } const int octaves2 = layers_; for (uchar i = 2; i < octaves2; i += 2) { pyramid_.push_back(BriskLayer(pyramid_[i - 2], BriskLayer::CommonParams::HALFSAMPLE));//c?层是前两层的1/2 pyramid_.push_back(BriskLayer(pyramid_[i - 1], BriskLayer::CommonParams::HALFSAMPLE));//d?层是前两层的1/2(除d0层外) } }
//提取特征点 void BriskScaleSpace::getKeypoints(const int threshold_, std::vector<cv::KeyPoint>& keypoints) { // make sure keypoints is empty keypoints.resize(0); keypoints.reserve(2000); // assign thresholds int safeThreshold_ = (int)(threshold_ * safetyFactor_); std::vector<std::vector<cv::KeyPoint> > agastPoints; agastPoints.resize(layers_); // go through the octaves and intra layers and calculate fast corner scores: for (int i = 0; i < layers_; i++) { // call OAST16_9 without nms BriskLayer& l = pyramid_[i]; l.getAgastPoints(safeThreshold_, agastPoints[i]); } if (layers_ == 1) { // just do a simple 2d subpixel refinement... const size_t num = agastPoints[0].size(); for (size_t n = 0; n < num; n++) { const cv::Point2f& point = agastPoints.at(0)[n].pt; // first check if it is a maximum: if (!isMax2D(0, (int)point.x, (int)point.y)) continue; // let's do the subpixel and float scale refinement: BriskLayer& l = pyramid_[0]; int s_0_0 = l.getAgastScore(point.x - 1, point.y - 1, 1); int s_1_0 = l.getAgastScore(point.x, point.y - 1, 1); int s_2_0 = l.getAgastScore(point.x + 1, point.y - 1, 1); int s_2_1 = l.getAgastScore(point.x + 1, point.y, 1); int s_1_1 = l.getAgastScore(point.x, point.y, 1); int s_0_1 = l.getAgastScore(point.x - 1, point.y, 1); int s_0_2 = l.getAgastScore(point.x - 1, point.y + 1, 1); int s_1_2 = l.getAgastScore(point.x, point.y + 1, 1); int s_2_2 = l.getAgastScore(point.x + 1, point.y + 1, 1); float delta_x, delta_y; float max = subpixel2D(s_0_0, s_0_1, s_0_2, s_1_0, s_1_1, s_1_2, s_2_0, s_2_1, s_2_2, delta_x, delta_y); // store: keypoints.push_back(cv::KeyPoint(float(point.x) + delta_x, float(point.y) + delta_y, basicSize_, -1, max, 0)); } return; } float x, y, scale, score; for (int i = 0; i < layers_; i++) { BriskLayer& l = pyramid_[i]; const size_t num = agastPoints[i].size(); if (i == layers_ - 1) { for (size_t n = 0; n < num; n++) { const cv::Point2f& point = agastPoints.at(i)[n].pt; // consider only 2D maxima... if (!isMax2D(i, (int)point.x, (int)point.y)) continue; bool ismax; float dx, dy; getScoreMaxBelow(i, (int)point.x, (int)point.y, l.getAgastScore(point.x, point.y, safeThreshold_), ismax, dx, dy); if (!ismax) continue; // get the patch on this layer: int s_0_0 = l.getAgastScore(point.x - 1, point.y - 1, 1); int s_1_0 = l.getAgastScore(point.x, point.y - 1, 1); int s_2_0 = l.getAgastScore(point.x + 1, point.y - 1, 1); int s_2_1 = l.getAgastScore(point.x + 1, point.y, 1); int s_1_1 = l.getAgastScore(point.x, point.y, 1); int s_0_1 = l.getAgastScore(point.x - 1, point.y, 1); int s_0_2 = l.getAgastScore(point.x - 1, point.y + 1, 1); int s_1_2 = l.getAgastScore(point.x, point.y + 1, 1); int s_2_2 = l.getAgastScore(point.x + 1, point.y + 1, 1); float delta_x, delta_y; float max = subpixel2D(s_0_0, s_0_1, s_0_2, s_1_0, s_1_1, s_1_2, s_2_0, s_2_1, s_2_2, delta_x, delta_y); // store: keypoints.push_back( cv::KeyPoint((float(point.x) + delta_x) * l.scale() + l.offset(), (float(point.y) + delta_y) * l.scale() + l.offset(), basicSize_ * l.scale(), -1, max, i)); } } else { // not the last layer: for (size_t n = 0; n < num; n++) { const cv::Point2f& point = agastPoints.at(i)[n].pt; // first check if it is a maximum: if (!isMax2D(i, (int)point.x, (int)point.y)) continue; // let's do the subpixel and float scale refinement: bool ismax=false; score = refine3D(i, (int)point.x, (int)point.y, x, y, scale, ismax); if (!ismax) { continue; } // finally store the detected keypoint: if (score > float(threshold_)) { keypoints.push_back(cv::KeyPoint(x, y, basicSize_ * scale, -1, score, i)); } } } } }
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