# Breast Microcalcification Detection Algorithm Based on Contourlet and ASVM
## 3 Method
### Feature Extraction  
Before SVM classification of ROI, some features need to be extracted from ROI as input to the SVM classifier. The characteristics of the super pixel region are currently described as grayscale feature, shape feature, Histogram of Oriented Gradient (HOG) feature, etc. Table 1 shows that some feature algorithm. Researchers use some statistics based on it as the texture classification feature. Choosing the appropriate features can improve the computational efficiency and classification effect. Commonly used texture features for analyzing mammogram image textures are as the following:  
(1) Angular Second Moment (ASM)  
\[ASM=\sum_{i}\sum_{j}\left(P(i,j)\right)^{2} \tag{2}\]  
(2) Entropy (ENT)  
\[ENT=-\sum_{i}\sum_{j}P(i,j)\log(P(i,j)) \tag{3}\]  
(3) Relativity (CORRLN)  
\[COR=[\sum_{i}\sum_{j}\left((ij)P(i,j)\right)-\mu_{\mathrm{x}}\mu_{\mathrm{y}}] /\sigma_{\mathrm{x}}\sigma_{\mathrm{y}} \tag{4}\]  
(4) Contrast (CON)  
\[CON=\sum_{i}\sum_{j}\left(i-j\right)^{2}P(i,j) \tag{5}\]  
Local binary pattern (LBP) is a feature used in the field of machine vision for classification. It was first proposed by [PERSON], [PERSON] and [PERSON] [24; 25] in 1994 for the texture feature extraction. It has significant advantages, such as rotation and gray invariances. It is a very effective feature that compares each pixel with its neighboring pixels and saves the result as a binary number. Due to its strong discriminative power and simple calculation, the local binary pattern texture operator has been applied in different scenarios. The most important attribute of the LBP is the robustness to grayscale changes, such as illumination changes. Another important feature of it is its simple calculation, which allows it to analyze images in real time. A combination of local binary pattern features and gray level co-occurrence matrix are used in the present study, which can effectively \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Definition** & **Description** \\ \hline \multirow{4}{*}{Grayscale feature (4)} & Maximum value & \\  & Minimum value & \\  & Mean & \\  & variance & \\ \hline \multirow{6}{*}{Shape feature (13)} & \multirow{6}{*}{\
\begin{tabular}{c} Area \\ Convex area \\ perimeter \\ \end{tabular} } & The number of pixels in the area boundary; \\  & & The length of the long axis of the ellipse; \\  & Long axis length & The short axis length of the ellipse; \\  & Short axis length & Length to width ratio; \\  & Aspect ratio & The diameter of a circle having the same \\  & Equivalent diameter & area; \\  & Convexity & The area ratio of the area to its smallest \\  & & convex polygon; \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Angular Second Moment \\ Entropy \\ Relativity \\ Contrast \\ \end{tabular} } & Formulas (2)–(5) shows four features in \\ \cline{1-1}  & LBP & The following is a detailed introduction \\ \hline HOG feature (200) & Histogram of Oriented Gradient & The following is a detailed introduction \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the feature used to describe each region of interest (ROI). improve the detection effect on some sets. Algorithms 2 shows that, LBP feature algorithm steps. Formulas (6) and (7) are complementary to Algorithm 2, which is more intuitive to understand. ```
Input: image I(m, n) Output: the feature vector
1 Dividing block 16*16
2 If \(\mathrm{I_{x,y}}\geq\mathrm{I_{x=1,y\pm 1}}\)
3 \(\mathrm{I_{x,y}}=0\)
4 Else
5 \(\mathrm{I_{x,y}}=1\)
6 Binary\(\rightarrow\)decimal
7 Normalization of the frequency histogram
```  
\[LBP(i_{x,y})=\sum_{p=0}^{p-1}2^{p}s(i_{p}-i_{x,y}) \tag{6}\]  
where \((i_{x})\), \(i_{p}\) and s are coordinates of the center pixel with gray values, the gray value of the surrounding P Pixel and a symbol function, respectively. The symbol function is defined as:  
\[\mathrm{s}(x)=\left\{ \begin{array}{ll}1&if\ x\geq 0\\ 0&else\end{array} \right\} \tag{7}\]  
These two functions are calculated to obtain a binary LBP value.