## 2 Materials and Methods
### Proposed Method
#### 2.3.4 Support Vector Machine Classification Based on Texture Features  
Gray level co-occurrence matrix (GLCM) is an image analysis method based on statistical methods for reflecting image texture features that carry spatial relationships between pixels. The method describes the probability of occurrence of a pair of image elements with gray levels \(i\) and \(j\), respectively, separated by a distance of d image elements in the direction [38; 39]. The calculation is as follows:  
\[P(i,j,d,\theta)=\left\{((x,y),(x+D_{x},y+D_{y})|f(x,y)=i;\big{|}f(x+D_{x},y+D_{ y})=j)\right\} \tag{19}\]  
where \((x,y)\) is the pixel coordinate of any point on the image; \(i\) is the pixel gray level of the point; \((x+D_{x},y+D_{y})\) is the pixel distance D from the point in the direction \(\theta\) of the deviation point; \(j\) is the pixel gray level of the deviation point; \(\theta\) is the direction that can be selected, generally \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) and \(135^{\circ}\); \(d\) is the computation step length of the gray level coevolution matrix. The gray level co-occurrence matrix does not provide a direct reference for texture feature extraction, while the secondary statistics derived from it provide an important basis for measuring texture features. The secondary statistics used include the following:  
1. Angular Second Moment (ASM), which reflects the degree of uniformity of the image grayscale distribution and texture coarseness and fineness, is calculated as follows:\[ASM=\sum_{i}\sum_{j}P(i,j)^{2} \tag{20}\]
2. Entropy (ENT), which reflects the randomness of the amount of information contained in the image, is calculated as follows: \[ENT=-\sum_{i}\sum_{j}P(i,j)\times\log[P(i,j)]\] (21)
3. Contrast (CON), reflecting the sharpness of the image and the depth of the texture grooves, is calculated as follows: \[CON=\sum_{i}\sum_{j}(i-j)^{2}\times P(i,j)\] (22)
4. Inverse Differential Moment (IDM), reflecting the clarity and regularity of the texture, is calculated as follows: \[IDM=\sum_{i}\sum_{j}P(i,j)/[1+(i-j)^{2}]\] (23)
5. Correlation (COR), reflecting the degree of similarity of spatial gray scale covariance matrix elements in the row or column direction, is calculated as follows: \[COR=\sum_{i}\sum_{j}(i-mean)\times(j-mean)\times P(i,j)^{2}/\mathrm{var}\] (24)  
where \(P(i,j)\) is the number of occurrences of a pair of image elements with gray level \(i\) and \(j\), respectively; \(mean\) is the mean of the gray level covariance matrix; and \(\mathrm{var}\) is the standard deviation. The support vector machine is a method based on statistical learning theory, which can apply undifferentiated learning ability to seek the best mathematical model in limited and complex sample information [40; 41]. A major advantage of the support vector machine is that if the appropriate decision hyperplane cannot be solved under the original dimension, the feature data in the low-latitude space can be mapped to the high-dimensional space using a nonlinear mapping function. The appropriate decision hyperplane can be researched in the high-dimensional space to achieve the purpose of classification [42]. Take two-dimensional space as an example; let \(x_{i}\) be the eigenvalue and \(y_{i}\) be the data category the positive hyperplane is 1, and the negative hyperplane is \(-1\). As shown in Figure 7, the optimal solution solved by the support vector machine is to find the decision hyperplane having the maximum soft interval with proper allowance for outliers. The larger the soft interval, the better the classification results. Figure 7: Support vector machine model. Mathematically, the original problem solved by the support vector machine is the minimization problem \(f(w)\) under constraint \(g_{i}(w,b)\).