## 2 Background  
In this section, we briefly review texture information representations of SAR images, which are gray-level co-occurrence matrix (GLCM), wavelet (WL), and attribute profile (AP). In addition, the information entropy, image entropy, and entropy rate superpixel methods are introduced. SAR image size is \(I_{1}\times I_{2}\). A gray-level co-occurrence matrix (GLCM) can express the imaging mechanism and the statistical characteristics of SAR images [20; 21]. Derived from the co-occurrence matrix on four directions, \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), and \(135^{\circ}\), six measures named contrast, correlation, homogeneity, energy, mean value, and median value are selected, then the average value of four directions on each measure is computed to represent the image pixel, and the feature vector of each pixel is represented as  
\[F_{ij}^{\rm G}=(f_{ij1}^{\rm G},f_{ij2}^{\rm G},f_{ij3}^{\rm G},f_{ij4}^{\rm G },f_{ij5}^{\rm G},f_{ij6}^{\rm G}),1\leq i\leq I_{1},1\leq j\leq I_{2}. \tag{1}\]  
Then, the 3D GLCM feature tensor of \(I_{1}\times I_{2}\times 6\) size is obtained for the SAR image, which is  
\[F_{feu}^{\rm G}=\left[ \begin{array}{cccc}F_{11}^{\rm G}&F_{12}^{\rm G}&\cdots &F_{1I_{2}}^{\rm G}\\ F_{21}^{\rm G}&F_{22}^{\rm G}&\cdots&F_{2I_{2}}^{\rm G}\\ \cdots&\cdots&\cdots&\cdots\\ F_{1I_{1}}^{\rm G}&F_{12}^{\rm G}&\cdots&F_{I_{1}I_{2}}^{\rm G}\end{array}  \right]. \tag{2}\]  
The GLCM feature is very good for contrast enhancement and despeckling, and effectively describes spatial information about the relative position of pixels, but does not involve structural relationships and weak the target signal or edge information. The characteristics of texture and noise are not essentially distinguished. Fortunately, WL and AP can make up for GLCM. WL transform provides frequency information through multi-resolution analysis [22], which can essentially distinguish the characteristics of texture and noise. Inspired by reference [23], the two-level four-tap Daubechies wavelet decomposition is performed over a 9 \(\times\) 9 window for each pixel of the SAR image in this section. The wavelet energy is extracted from seven channels, and the feature vector of each pixel is denoted as  
\[F_{ij}^{W}=(f_{ij1}^{W},f_{ij2}^{W},f_{ij3}^{W},f_{ij4}^{W},f_{ij5}^{W},f_{ij6 }^{W},f_{ij7}^{W}),1<=i<=I_{1},1<=j<=I_{2}. \tag{3}\]Then, a 3D WL feature tensor of \(I_{1}\times I_{2}\times 7\) size can be obtained [4; 24], and is represented as  
\[F_{fea}^{\rm W}=\left[ \begin{array}{cccc}F_{11}^{\rm W}&F_{12}^{\rm W}&\cdots& F_{1I_{2}}^{\rm W}\\ F_{21}^{\rm W}&F_{22}^{\rm W}&\cdots&F_{2I_{2}}^{\rm W}\\ \cdots&\cdots&\cdots&\cdots\\ F_{I1}^{\rm W}&F_{I12}^{\rm W}&\cdots&F_{I_{1}I_{2}}^{\rm W}\end{array} \right]. \tag{4}\]  
AP provides a multi-level characterization of an image, which is created by the sequential application of morphological attribute filters (AFs). AFs are the operators of the connection, which only consider the connected components of the image. Thus, they do not distort or insert new edges when processing images, but simply merge existing flat areas. So, AP can be used to model different kinds of structural information of the scene in order to increase the effectiveness of classification. The four SAR attributes of area, the diagonal, moment of inertia, and standard deviation are applied [5; 6]. There are three thresholds for each attribute, and the feature vector of each pixel is represented as  
\[F_{ij}^{A}=(f_{ij1}^{A},f_{ij2}^{A},f_{ij3}^{A},\cdots f_{ij23}^{A},f_{ij24}^{A },f_{ij25}^{A}),1\leq i\leq I_{1},1\leq j\leq I_{2}. \tag{5}\]  
Then, a 3D attribute profile tensor of \(I_{1}\times I_{2}\times 25\) size is obtained on the SAR image according to the thickening and thinning operation, which is  
\[F_{fea}^{A}=\left[ \begin{array}{cccc}F_{11}^{A}&F_{12}^{A}&\cdots&F_{1I_{2}} ^{A}\\ F_{21}^{A}&F_{22}^{A}&\cdots&F_{2I_{2}}^{A}\\ \cdots&\cdots&\cdots&\cdots\\ F_{I1}^{A}&F_{I12}^{A}&\cdots&F_{I_{1}I_{2}}^{A}\end{array} \right]. \tag{6}\]  
Information entropy was proposed by [PERSON].