# Water Extraction in PolSAR Image Based on Superpixel and Graph Convolutional Network
## 4 Discussion  
Based on superpixel segmentation, this study transforms a regular image into irregular graph structure data. Another more direct method is to take each pixel as the vertex, the pixel value as the features of the node, and the second-order neighborhood as the adjacency relationship. This causes two problems: the first is the network size and computational burden. Taking a single-channel small image (size of 1024 \(\times\) 1024) as an example, 1,048,576 vertices and nearly 10 million edges are generated. Assuming that the superpixel is composed of 200 pixels on average, the number of vertices is reduced by 200 times, from one million to five thousand, which also means that the number of network calculations is reduced by 200 times. The second problem is the speckle noise. Different from an optical image, any pixel-level algorithm on SAR data is greatly affected by speckle noise. Statistical values on an adjacent area are more robust and meaningful than a single pixel value and are thus more often used for PolSAR classification tasks. Moreover, a prior knowledge graph can be constructed by superpixel segmentation. Thus, superpixels are preferred in a GNN network. However, the usage of superpixels still causes some problems. First, several segmentation methods have been recently proposed for multi-polarization and single-polarization SAR data. Often, we need to choose the optimal method according to the data, and its precision and efficiency directly affect the GNN results. On the one hand, some small targets are ignored when the original size of the superpixel is too large. On the other hand, compared to simple TS methods, over-segmentation is time-consuming, especially for a large area. However, once superpixels are acquired, a GNN can classify them as quickly as other methods. Another problem is how to express the features of nodes. In this paper, a series of features were designed and analyzed, including statistical values of the scattering matrix, texture, covariance matrix, and LWR. For different data, the feature values probably have different expressions. Like texture value, several calculation methods are available. These features tend to be redundant because some of them are linearly dependent. However, the GNN network can deal with this redundancy, and the accuracy does not reduce, even when all available features are inputted. Moreover, the importance of features differs greatly. Through experiments, we determined that the texture and LWR are the most important, and the second most important are the scattering values of the HH polarization. For single-polarization data, texture and HH are the most important. The parameters affecting the GNN results mainly include the sampling number of surrounding neighbors and the layer number. A large sampling number causes lots of redundant information and computation, while a small number leads to a feature deficiency in adjacent nodes. Usually, the mean value of neighbor nodes is the optimal number. Meanwhile, the layer number depends on how many layers of information you want to aggregate. If there are too many layers, the characteristics of the nodes in the same area converge, and the nodes are not separable because they all contain a lot of the same neighborhood information. Generally, graph convolution should not have more than five layers. We also tried the graph convolution network of GAT and found that the accuracy in this task is not as good as the GraphSAGE. That may be because GAT more easily smooths features between different nodes.