## 3 Methodology
### Conflict Resolution of Local Consistency Optimization  
For enforcing the local consistency on pixel labels, optimization by probability theory is used to smooth labels based on the above three classification maps. Conflict resolution is used to determine the class of pixel \(p(i,j)\) in conflict labels as follows on the SAR image, and \(1\leq i\leq I_{1},1\leq j\leq I_{2}\).  
In no-conflict situations, \(cou_{k}^{i,j}\) denotes the classification times that each pixel \(p(i,j)\) is classified as class \(k\) in three classification maps, \(m\) is the class number, and then final class label \(l\) can be obtained by the maximum count value, that is  
\[Lab_{i,j}^{non}=\Big{\{}l\Big{|}cou_{l}^{i,j}=\max(cou_{1}^{i,j},\cdots,cou_{k}^{ i,j},\cdots,cou_{m}^{i,j}),0<=cou_{k}^{i,j}<=3.\Big{\}}. \tag{21}\]  
In conflict situations, where a pixel has three different classification maps' labels, it is hard to choose the right map's label as the final result. To address this issue, a probability is solved to determine the label of a pixel based on image feature information quality. The equivalent number of looks (ENL) [33] is an index to measure the smoothness of uniform regions. The higher the value, the less the noise affects the feature information and the better the feature quality. In order to further improve the reliability of labels, confidence level is combined with ENL to make decisions. A confidence level is defined with the initiation value zero for each map, and the valid decision times of each \(F_{fea}^{flag}\) feature information are counted according to classification map \(Lab_{i,j}^{non}\) in no-conflict situations. The label of largest probability is selected, the probability is defined as  
\[Pro_{flag}=\frac{CL_{flag}}{\sum\limits_{flag=G}^{W}CL_{flag}}+\frac{M_{flag }}{\sum\limits_{flag=G}^{W}M_{flag}}, \tag{22}\]  
\[\text{where }M_{flag}=\delta_{flag}^{2}/\mu_{flag}^{2}, \tag{23}\]  
\[CL_{flag}=\text{Countif}\Big{(}classmap_{i,j}(F_{fea}^{flag})=Lab_{i,j}^{non }\Big{)}. \tag{24}\]  
The ENL values \(M_{flag}\) are denoted as \(M_{G},M_{A},M_{W},flag\) is a member of \(\{G,A,W\}\). They equal to the square ratio of the standard deviation \(\sigma_{flag}\) and the expectation \(\mu_{flag}\) of intensity in SAR image area. Formula (24) calculates the confidence level of each classification map. If \(classmap_{i,j}(F_{fea}^{flag})\), that is the pixel label at positions \((i,j)\) in classification map of feature \(F_{fea}^{flag}\), is equal to the same position pixel label \(Lab_{i,j}^{non}\), which is final label result in the no-conflict case, then the confidence level \(CL_{flag}\) of feature \(F_{fea}^{flag}\) is increased by 1, that is, count the number of labels in each feature classification map that are equal to the final label results in the no-conflict case. \(CL_{G},CL_{A},CL_{W}\) count the number of times that each feature \(F_{fea}^{flag}\) classification map is consistent with the result of \(Lab_{i,j}^{non}\) in no-conflict situations obtained by (21). Finally, the undetermined test pixel sample \(p(i,j)\) label is the label in \(F_{fea}^{flag}\) classification map with the highest probability value \(Pro_{flagx}\) in conflict situations, which is  
\[Lab_{i,j}^{conflict}=\Big{\{}l\Big{|}Pro_{flagx}=\max(Pro_{G},Pro_{A},Pro_{W}) \text{, then }l=\text{classmap}_{i,j}(F_{fea}^{flag})\Big{\}}. \tag{25}\]  
In the end, the label matrix \(Lab\) of classification result is obtained. The procedure of multi-feature fusion and adaptive kernel combination algorithm is outlined in Algorithm 1.