## 3 Results and Discussion
### Discrimination of Different Human Skin Tissues Using Vectorial Retardance  
#### 3.2.1 Quantitative Classification  
A dataset of 853 normal cases, 851 BE cases, and 847 MM cases is detected. The specific information on training and testing sets is listed in Table 2. To quantitatively differentiate normal skin, BE, and MM, the SVM algorithm is applied. The basic idea of the SVM algorithm is to create a separated hyperplane that can correctly partition the training dataset with maximum geometric separation [71; 72]. It is mainly used in solving small samples, nonlinear, and high-dimensional classification problems [73; 74], which fits well with the sample characteristics of this paper. SVM has been commonly used and performs well in pattern recognition [73; 74; 75; 76; 77; 78; 79]. To demonstrate the performance of retardance-related parameters in discriminating skin tissues with different lesions, eight SVM classifiers with three classifications were established and evaluated according to different retardance-related parameters in conjunction with the one-against-one (OAO) method. The relationships between the eight SVM classifiers are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{4}{c}{**Train Set**} & \multicolumn{4}{c}{**Test Set**} \\ \cline{2-9}  & **Normal** & **BE** & **MM** & **Total** & **Normal** & **BE** & **MM** & **Total** \\ \hline Cases & 500 & 500 & 500 & 1500 & 353 & 351 & 347 & 1051 \\ \hline \end{tabular}
\end{table} 
Table 2: The specific information on training and testing sets. Figure 4: Birefringence-related imaging results: (**a**) horizontal retardance; (**b**) 45\({}^{\circ}\)-linear retardance; (**c**) circle retardance; (**d**) scalar retardance; (**e**) orientation of linear retardance; (**f**) true-color vectorial retardance image. For constructing the SVM classifiers, five characteristics are extracted from the measured retardance-related parameters, including mean (\(M\)), standard deviation (\(S_{td}\)), skewness (\(S_{ke}\)), kurtosis (\(K_{ur}\)), and entropy (\(E_{n}\)) shown as Equations (8)-(12) [80,81]. \(M\) and \(S_{td}\) describe the mean value and standard deviation of the retardance-related parameters, respectively. \(S_{ke}\) measures the distribution of the values around the mean and gives its shape. \(K_{ur}\) calculates from the histogram and extends up to the shape of the distribution equal to the normal distribution. \(E_{n}\) describes the randomness of the structures displayed in the image. \[M=\frac{1}{m\times n}{\sum_{i=1}^{m}{\sum_{j=1}^{n}{R_{(i,j)}}}} \tag{8}\]  
\[S_{td}=\sqrt{\frac{1}{m\times n}{\sum_{i=1}^{m}{\sum_{j=1}^{n}{\Big{(}{R_{(i,j )}}-M\Big{)}^{2}}}}} \tag{9}\]  
\[S_{ke}=\frac{1}{S_{td}}^{3}\frac{1}{m\times n}{\sum_{i=1}^{m}{\sum_{j=1}^{n}{ \Big{(}{R_{(i,j)}}-M\Big{)}^{3}}}} \tag{10}\]  
\[K_{ur}=\frac{1}{S_{td}}^{4}\frac{1}{m\times n}{\sum_{i=1}^{m}{\sum_{j=1}^{n}{ \Big{(}{R_{(i,j)}}-M\Big{)}^{4}}}} \tag{11}\]  
\[E_{n}=\sum_{i=1}^{m}{\sum_{j=1}^{n}{q(i,j)\log_{2}{q(i,j)}}} \tag{12}\]  
where \(R_{(i,j)}\) is the value at the \(i\)-th and \(j\)-th pixel in the horizontal and vertical directions, respectively, and \(q(i,j)\) represents the probability of \(R_{(i,j)}\). \(m\) and \(n\) are the total number of pixels in the horizontal and vertical directions, respectively. Each of the eight SVM classifiers is trained by five tissue microstructural features (including \(M\), \(S_{td}\), \(S_{ke}\), \(K_{ur}\), and \(E_{n}\)) with the RBF kernel and five-fold cross-validation approach for accurate prediction. Cross-validation accuracy and prediction accuracy are used to assess the performance of classifiers. For a fair comparison, the feature selection is not performed for each classifier, and all features of each classifier are normalized to avoid systematic bias [71,72]. The classification tasks are carried out with the reference to practical guidance [71,72]. It is worth noting from Table 3 that the three components show comparable accuracy, albeit with slightly different [82,83].