From 67d825b4d58d8a625effdb2d2688caaee8f32c34 Mon Sep 17 00:00:00 2001 From: zhaobenx Date: Sun, 1 Apr 2018 20:13:26 +0800 Subject: [PATCH] =?UTF-8?q?=E5=A2=9E=E5=8A=A0ORB=E8=A7=A3=E6=9E=90?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .gitignore | 1 + .../img/BRIEF\347\202\271\345\257\271.png" | Bin 0 -> 187355 bytes .../img/descriptor.png" | Bin 0 -> 13932 bytes .../img/fast\350\247\222\347\202\271.png" | Bin 0 -> 46162 bytes .../img/keypoints.png" | Bin 0 -> 18059 bytes .../img/runtime.png" | Bin 0 -> 2250 bytes .../orb\350\247\243\346\236\220.md" | 296 ++++++++++++++++++ 7 files changed, 297 insertions(+) create mode 100644 "doc/orb\350\247\243\346\236\220/img/BRIEF\347\202\271\345\257\271.png" create mode 100644 "doc/orb\350\247\243\346\236\220/img/descriptor.png" create mode 100644 "doc/orb\350\247\243\346\236\220/img/fast\350\247\222\347\202\271.png" create mode 100644 "doc/orb\350\247\243\346\236\220/img/keypoints.png" create 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zYk%oS2U`U5g4>Qnlug@O&EH5EbQ3O&Z1VI$x Ye|jEVdm-G5Q2+n{07*qoM6N<$g4n83zyJUM literal 0 HcmV?d00001 diff --git "a/doc/orb\350\247\243\346\236\220/orb\350\247\243\346\236\220.md" "b/doc/orb\350\247\243\346\236\220/orb\350\247\243\346\236\220.md" new file mode 100644 index 0000000..bbe874d --- /dev/null +++ "b/doc/orb\350\247\243\346\236\220/orb\350\247\243\346\236\220.md" @@ -0,0 +1,296 @@ +--- +typora-copy-images-to: img +--- + +# ORB算法与源码解析 + +来自opencv + +## 算法介绍 + +是ORB特征是将**FAST**特征点的检测方法与**BRIEF**特征描述子结合起来,并在它们原来的基础上做了改进与优化。 + +1. 利用**FAST**特征点检测的方法来检测特征点。 +2. 利用**Harris**角点的度量方法,从**FAST**特征点从挑选出Harris角点响应值最大的$N$个特征点。 +3. 解决局部不变性(尺度不变性和旋转不变性),即选择从不同高斯金字塔进行检测和对特征点添加角度特征。 +4. 为特征点增加特征描述即描述子。 + + +### FAST检测 + +**FAST**特征点的检测方式即寻找一个像素点周围半径为3中的角点,如图示: + +![fast角点](img/fast角点.png) + + + +### Harris评判 + +**Harris**方法是一种特征点评判方式。 + +其中**Harris**角点的响应函数定义为: + + +$$ +R=det \boldsymbol{M} - \alpha(trace\boldsymbol{M})^2 +$$ + +(其中 $det$指的是矩阵行列式的值;值得指的是矩阵的迹,即对角线元素之和;$M$指的是像素矩阵) + +### 旋转不变性 + +尺度不变性的解决通过构建不同高斯金字塔(即对图像进行缩放)分别进行特征检测。而旋转不变性则是为每个特征点增加角度特征,角度的计算公式即: + +$$ +m_{pq} = \sum_{x,y}x^py^qI(x,y) +$$ + +$$ +C = \left(\frac{m_{10}}{m_{00}},\frac{m_{01}}{m_{00}}\right) +$$ + +$$ +\theta = arctan(m_{01},m_{10}) +$$ + +其中$M_{pq}$的定义是在以特征点为中心的一个园内,对所有像素值(以灰度为单位)以x,y坐标为权进行的加权和。即算出像素的“重心”。从而可利用*公式(4)*来计算出特征点的方向。 + +### 描述子计算 + +描述子使用**BRIEF**方法来进行的特征描述方式,其原理即在特征点一定邻域内按照一定的股则选取一些点对,并对这些点对的灰度值进行比较,将结果的布尔值储存下来,最终结果为长度为128/256/512长度的比特串。 + +下图为一些点对的选择方法: + +​ ![BRIEF点对](img/BRIEF点对.png) + +(上图分别为:1. x,y方向平均分布采样 2. x,y均服从Gauss(0,S^2/25)各向同性采样 3. x服从Gauss(0,S^2/25),y服从Gauss(0,S^2/100)采样 4. x,y从网格中随机获取 5. x一直在(0,0),y从网格中随机选取) + +为了解决旋转不变性,这里选择了**Steer BREIF**,即在计算描述值时考虑到旋转后的结果,其公式为: + +$$ +S_{\theta} = R_{\theta}S +$$ + +其中的$S$为选取的点对($x_n$与$y_n$是一个点对两个点的灰度值),$R_{\theta}$为旋转不变性(公式(4))求得的旋转角度。 +$$ +S =\begin{pmatrix}x_1&x_2&\cdots&x_{2n} \\ y_1&y_2&\cdots&y_{2n}\end{pmatrix} +$$ + +$$ +R_{\theta} = \begin{bmatrix}cos\theta & sin\theta \\ –sin\theta &cos\theta\end{bmatrix} +$$ + +### 匹配 + +由以上几部即完成了ORB特征的提取,提取后将输出两个值,分别为关键点和描述值,其中关键点的结构如下: + +```c++ +class KeyPoint +{ +public: + Point2f pt; //!< 特征点坐标 + float size; //!< 特征点描述区域大小 + float angle; //!< 特征点朝向,取[0, 360),取-1代表不可用 + float response; //!< 被选取的强度,可用于排序 + int octave; //!< 描述此点属于第几层金字塔 + int class_id; //!< 分类id,如果特征点需要被分类 +}; +``` + +而描述值则为Mat类型,用于储存点对。 + +最终匹配时跟剧描述值之间的**汉明距离**(即bit相同的个数)来进行比较。 + + + +## 代码解析 + +代码实现于`opencv\modules\features2d\src\orb.cpp`,采用OpenCV版本号为3.4.1。 + +### FAST检测 + +代码833-837行,利用Fast检测方法,检测出若干潜在关键点 + +```c++ + // Detect FAST features, 20 is a good threshold + { + Ptr fd = FastFeatureDetector::create(fastThreshold, true); + fd->detect(img, keypoints, mask); + } +``` + +### Harris评价 + +888行, + +```c++ + HarrisResponses(imagePyramid, layerInfo, allKeypoints, 7, HARRIS_K); +``` + +而其具体实现在本文件131-172行 + +```c++ +static void +HarrisResponses(const Mat& img, const std::vector& layerinfo, + std::vector& pts, int blockSize, float harris_k) +{ + CV_Assert( img.type() == CV_8UC1 && blockSize*blockSize <= 2048 ); + + size_t ptidx, ptsize = pts.size(); + + const uchar* ptr00 = img.ptr(); + int step = (int)(img.step/img.elemSize1()); + int r = blockSize/2; + + float scale = 1.f/((1 << 2) * blockSize * 255.f); + float scale_sq_sq = scale * scale * scale * scale; + + AutoBuffer ofsbuf(blockSize*blockSize); + int* ofs = ofsbuf; + for( int i = 0; i < blockSize; i++ ) + for( int j = 0; j < blockSize; j++ ) + ofs[i*blockSize + j] = (int)(i*step + j); + + for( ptidx = 0; ptidx < ptsize; ptidx++ ) + { + int x0 = cvRound(pts[ptidx].pt.x); + int y0 = cvRound(pts[ptidx].pt.y); + int z = pts[ptidx].octave; + + const uchar* ptr0 = ptr00 + (y0 - r + layerinfo[z].y)*step + x0 - r + layerinfo[z].x; + int a = 0, b = 0, c = 0; + + for( int k = 0; k < blockSize*blockSize; k++ ) + { + const uchar* ptr = ptr0 + ofs[k]; + int Ix = (ptr[1] - ptr[-1])*2 + (ptr[-step+1] - ptr[-step-1]) + (ptr[step+1] - ptr[step-1]); + int Iy = (ptr[step] - ptr[-step])*2 + (ptr[step-1] - ptr[-step-1]) + (ptr[step+1] - ptr[-step+1]); + a += Ix*Ix; + b += Iy*Iy; + c += Ix*Iy; + } + pts[ptidx].response = ((float)a * b - (float)c * c - + harris_k * ((float)a + b) * ((float)a + b))*scale_sq_sq; + } +} +``` + +代码最后几行即为计算我们公式(1)的具体计算,其中用到了这样的公式,即在矩阵$\boldsymbol{M}=\begin{bmatrix}A&C\\C&B\end{bmatrix}$中: +$$ +det\boldsymbol{M} = \lambda_1\lambda_2=AB-C^2 +$$ + +$$ +trace\boldsymbol{M}=\lambda_2+\lambda_2=A+B +$$ + +### 旋转不变性 + +角度的计算有下代码实现,实现在176-210行。 + + +```cpp +static void ICAngles(const Mat& img, const std::vector& layerinfo, + std::vector& pts, const std::vector & u_max, int half_k) +{ + int step = (int)img.step1(); + size_t ptidx, ptsize = pts.size(); + + for( ptidx = 0; ptidx < ptsize; ptidx++ ) + { + const Rect& layer = layerinfo[pts[ptidx].octave]; + const uchar* center = &img.at(cvRound(pts[ptidx].pt.y) + layer.y, cvRound(pts[ptidx].pt.x) + layer.x); + + int m_01 = 0, m_10 = 0; + + // Treat the center line differently, v=0 + for (int u = -half_k; u <= half_k; ++u) + m_10 += u * center[u]; + + // Go line by line in the circular patch + for (int v = 1; v <= half_k; ++v) + { + // Proceed over the two lines + int v_sum = 0; + int d = u_max[v]; + for (int u = -d; u <= d; ++u) + { + int val_plus = center[u + v*step], val_minus = center[u - v*step]; + v_sum += (val_plus - val_minus); + m_10 += u * (val_plus + val_minus); + } + m_01 += v * v_sum; + } + + pts[ptidx].angle = fastAtan2((float)m_01, (float)m_10); + } +} +``` + +### 计算描述子 + +实现在214行到415行,摘取重要部分: + +```c++ +static void +computeOrbDescriptors( const Mat& imagePyramid, const std::vector& layerInfo, + const std::vector& layerScale, std::vector& keypoints, + Mat& descriptors, const std::vector& _pattern, int dsize, int wta_k ) +{ +// ... + //矩阵相乘 + #define GET_VALUE(idx) \ + (x = pattern[idx].x*a - pattern[idx].y*b, \ + y = pattern[idx].x*b + pattern[idx].y*a, \ + ix = cvRound(x), \ + iy = cvRound(y), \ + *(center + iy*step + ix) ) + //... + //实现公式(5) + for (i = 0; i < dsize; ++i, pattern += 16) + { + int t0, t1, val; + t0 = GET_VALUE(0); t1 = GET_VALUE(1); + val = t0 < t1; + t0 = GET_VALUE(2); t1 = GET_VALUE(3); + val |= (t0 < t1) << 1; + t0 = GET_VALUE(4); t1 = GET_VALUE(5); + val |= (t0 < t1) << 2; + t0 = GET_VALUE(6); t1 = GET_VALUE(7); + val |= (t0 < t1) << 3; + t0 = GET_VALUE(8); t1 = GET_VALUE(9); + val |= (t0 < t1) << 4; + t0 = GET_VALUE(10); t1 = GET_VALUE(11); + val |= (t0 < t1) << 5; + t0 = GET_VALUE(12); t1 = GET_VALUE(13); + val |= (t0 < t1) << 6; + t0 = GET_VALUE(14); t1 = GET_VALUE(15); + val |= (t0 < t1) << 7; + + desc[i] = (uchar)val; + } + //... +} +``` + +## 代码运行时数据 + +在运行时,选取的特征描述子是256bit的,即32个`unsigned char`的大小,可以由下图的运行数据大小得知: + + + +运行后的数据: + +![1522583392970](img/1522583392970.png) + +部分关键点及其数据: + +![keypoints](img/keypoints.png) + +对应的描述子: + +![1522583860543](img/1522583860543.png) + + + +(三十二个为一个描述子,图中并未截全一个描述子) \ No newline at end of file