## 2 Materials and Methods
### Polarization Feature Extraction
#### 2.2.2 Cloude-Pottier Decomposition  
Under conditions of backscattering, the coherence matrix for media exhibiting scattering symmetry characteristics can be parameterized in terms that incorporate the parameters \(\lambda\), \(\alpha\), \(\beta\), \(\delta\), and \(\gamma\):  
\[\mathbf{T}=\mathbf{U}_{3}\left[\begin{array}{ccc}\lambda_{1}&0&0\\ 0&\lambda_{2}&0\\ 0&0&\lambda_{3}\end{array}\right]\mathbf{U}_{3}{}^{*}{}^{T} \tag{6}\]  
\[[U_{3}]=\left[\begin{array}{ccc}\cos\alpha_{1}&\cos\alpha_{2}&\cos\alpha_{3 }\\ \sin\alpha_{1}\cos\beta_{1}e^{i\delta_{1}}&\sin\alpha_{2}\cos\beta_{2}e^{i \delta_{2}}&\sin\alpha_{3}\cos\beta_{3}e^{i\delta_{3}}\\ \sin\alpha_{1}\sin\beta_{1}e^{i\gamma_{1}}&\sin\alpha_{2}\sin\beta_{2}e^{i \gamma_{2}}&\sin\alpha_{3}\sin\beta_{3}e^{i\gamma_{3}}\end{array}\right] \tag{7}\]  
where \(\vec{\lambda}=(\lambda_{1},\lambda_{2},\lambda_{3})\) is the eigenvector, \(\vec{\alpha}=(\alpha_{1},\alpha_{2},\alpha_{3})\) indicates the decomposition coefficient of the scattering mechanism, \(\vec{\beta}=(\beta_{1},\beta_{2},\beta_{3})\) is the referenced orientation angle, \(\vec{\delta}=(\delta_{1},\delta_{2},\delta_{3})\) represents the phase difference between \(S_{hh}-S_{vv}\) and \(S_{hh}+S_{vv}\), \(\vec{\gamma}=(\gamma_{1},\gamma_{2},\gamma_{3})\) represents the phase difference between \(S_{hh}+S_{vv}\) and \(S_{hw}\), and \(\mathbf{U}_{3}\) represents the dominant matrix, which is determined by the maximum eigenvector of the coherence matrix and exhibits a certain level of randomness. This randomness is characterized by entropy:  
\[H=\sum_{i=1}^{3}-P_{i}\log_{3}P_{i}, \tag{8}\]  
\[P_{i}=\frac{\lambda_{i}}{\sum_{j=1}^{3}\lambda_{j}}. \tag{9}\]  
According to Equation (9), it is easy to find that \(P_{1}+P_{2}+P_{3}=1\). The \(P_{i}\) parameter can be considered as a kind of probability. According to the theory of optimal estimation, the \(\alpha\) parameter can be defined as follows:  
\[\alpha=P_{1}\alpha_{1}+P_{2}\alpha_{2}+P_{3}\alpha_{3}. \tag{10}\]  
For random media, the \(\alpha\) parameter is generally employed to assess the main scattering mechanism \[S=\mathrm{e}^{\mathrm{j}\phi}+k_{H}\mathrm{e}^{\mp\mathrm{j}2\theta}\left\{ \mathrm{e}^{\mathrm{j}\phi\mathrm{S}}k_{S}\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right]+k_{D}\left[\begin{array}{cc}\cos 2\theta&\sin 2\theta\\ \sin 2\theta&-\cos 2\theta\end{array}\right]+k_{H}\mathrm{e}^{\mp\mathrm{j}2 \theta}\left[\begin{array}{cc}1&\pm\mathrm{j}\\ \pm\mathrm{j}&-1\end{array}\right]\right\} \tag{12}\]  
where \(K_{S}\), \(K_{D}\), and \(K_{H}\) respectively denote the contributions from the sphere, dihedral corner reflector, and helical components, while \(\theta\) indicates the orientation angle. By calculating the relative magnitudes of these three components within the target scattering mechanism, we can determine that  
\[K_{o}=\frac{|k_{S}|}{|k_{S}|+|k_{D}|+|k_{H}|}, \tag{13}\]  
\[K_{e}=\frac{|k_{D}|}{|k_{S}|+|k_{D}|+|k_{H}|}, \tag{14}\]  
\[K_{h}=1-K_{o}-K_{e}. \tag{15}\]  
The parameters \(K_{o}\), \(K_{e}\), and \(K_{h}\) are the polarization characteristics of Krogager decomposition, and respectively represent the contributions of the odd-order scattering, even-order scattering, and helical scattering mechanisms to the overall scattering mechanism.