## 3 The Proposed Method
### The GEA Attention Module  
The GEA attention module, serves as an attention mechanism to enhance the extraction of water features and refine the segmentation effect of the model. In the encoding process, downsampling is employed to reduce resolution and obtain semantic features at different levels. However, these shallow features possess rich spatial information while lacking in semantic details [55; 56], leading to potential loss or the misclassification of a significant number of water bodies. In the GEA module, the spatial features are first extracted by depth convolution. The depth convolution uses a convolution of 3 \(\times\) 3 size and the number of groups is the same as the feature dimension. The proposed method performs convolution operations on each layer of channels, emphasizing the global semantic information within the channels. Figure 5: Residual network structure. Point convolution is employed using a 1 \(\times\) 1 kernel to effectively fuse features across the channel vector. The depth separable convolutions not only captures the features of individual channels but also extracts inter-channel information within the same spatial context. After applying the Gaussian error linear unit (GELU) activation function, we employ the global response normalization (GRN) module to effectively mitigate noise and eliminate the redundant information in the image. The GRN module performs aggregation, normalization, and the calibration of global features, thereby enhancing the efficiency of feature learning. The formula is as follows:  
\[X\in R^{H\times W\times C} \tag{1}\]  
where \(R\) is the original input image, \(H\) and \(W\) are the height and width of the input image, respectively, \(C\) is the number of channels in the image, \(X\) represents the feature obtained from the image. The entire spatial feature is aggregated by the \(g\) function to obtain a compressed feature vector. The expression of \(g\) function is as follows:  
\[g(X)=gX=\{\|X_{1}\|+\|X_{2}\|+\cdots\|X_{i}\|\}\in R^{C} \tag{2}\]  
\[X\in R^{H\times W\times X}\to gX\in R^{C} \tag{3}\]  
where \(g\) in Equations (2) and (3) represents the feature vector after the aggregation of the input \(X\). After obtaining the feature expression \(X\), we propose \(g\) to represent the high-level aggregation of features. Based on research [51], the \(L_{2}\) norm of \(X\) can be used as a measure for feature aggregation by \(g\), aggregates the feature of each channel into a set of vectors after generating a value, and the \(L_{2}\) norm of \(Xi\) represents the statistical information scalar of the \(i\) channel. Next, the channel characteristics after aggregation will be normalized, with the following expression:  
\[N(\|X_{i}\|)\approx\|X_{i}\|\in R\rightarrow\frac{\|X_{i}\|}{\sum_{j=1,-C}\|X_ {j}\|}\in R \tag{4}\]  
where \(N\) in Equation (4) denotes the normalization operation performed on the \(i\) channel, while the fractional formula represents a means to calculate the relative significance of other channels in achieving this normalization operation by considering their influence on the current channel. Finally, it is necessary to calibrate the original input response by employing the computed feature-normalized score, and its specific expression is provided as follows:  
\[X_{i}=\gamma\times X_{i}\times N(g(X)_{i})+\beta+X_{i} \tag{5}\]  
In Formula (5), to streamline the optimization process, we introduced two additional learnable parameters, \(\gamma\) and \(\beta\), which were initialized to zero. Furthermore, a residual connection was incorporated between the input and output of the GRN layer. The resulting equation is presented as Equation (5). \(Xi\) represents the ultimate output, which is adjusted through the addition of hyperparameters \(\gamma\) and \(\beta\) to the residual structure. The inclusion of residuals and hyperparameters aims to enhance the corrective capacity for the initial input.