## 3 The Proposed Method
### The GEA Attention Module
The selection of the depth separable convolution and global response normalization (GRN) module enables the effective feature extraction and global normalization in consideration of both spatial and channel characteristics. This design not only accelerates model convergence but also facilitates efficient aggregation and the extraction of features by utilizing GRN for global feature normalization. After the aforementioned module, we will perform point convolution to further enhance the extraction of feature information for the highly aggregated data. Subsequently, these features will be passed into the coordinate attention (CA) mechanism, which generates separate outputs from two directions. The spatial attention mechanism CA [57] employed here differs from self-attention in terms of feature calculation through matrices. CA focuses more on capturing spatial information and channel relationships within features [50]. The challenge in lake segmentation lies in accurately delineating water body edges and detecting small water bodies. \[X=[x_{1},x_{2},\cdots x_{c}]\in R^{H\times W\times C} \tag{6}\]  
After the previous feature aggregation, assuming that the incoming intermediate feature is denoted by \(R\) and \(X\) in Equation (6). Represents the feature tensor, this facilitates subsequent pooling operations in both the \(H\) and \(W\) directions. However, conventional global pooling compresses spatial information into channel information, thus necessitating a decomposition of the global pooling operation. The specific formula for this decomposition is provided as follows:  
\[Z_{c}=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}x_{c}(i,j) \tag{7}\]  
\[Z_{c}^{h}(h)=\frac{1}{W}\sum_{0<i<W}x_{c}(h,i) \tag{8}\]  
\[Z_{c}^{w}(w)=\frac{1}{H}\sum_{0<j<H}x_{c}(j,w) \tag{9}\]  
Equation (7) represents the global pooling operation of the original feature vector, whereas we employ pooling convolution with \((H,1)\) and \((1,W)\) to perform pooling along the horizontal \(X\) direction and vertical \(Y\) direction, respectively. Subsequently, Formulas (8) and (9) yield the expressions for the obtained features. In Formula (8), \(Z_{c}^{h}\) denotes the output feature of channel \(c\) with a height \(h\), while \(Z_{c}^{w}\) in Formula (9) represents the output feature of channel \(c\) with a height \(w\). Following this extraction of directional features, an aggregation transformation operation is conducted as follows:  
\[X\in R^{H\times W\times C} \tag{1}\]0  
The formula incorporates the integrated features (represented by \(f\)), the nonlinear activation function (denoted by \(\delta\)), and the concatenate function (indicated by \(F\)) that connects the features bidirectionally. Subsequently, the resulting output is fed into convolutional processing, which can be expressed as follows:  
\[X\in R^{H\times W\times C} \tag{1}\]1  
\[X\in R^{H\times W\times C} \tag{1}\]2  
The features of \(h\) and \(w\) in the given formula should be separated initially, where \(\sigma\) represents the sigmoid function, \(F\) denotes the convolution operation, and \(g\) signifies the feature obtained in this direction. Ultimately, by connecting the residual input, we obtain the final output as follows:  
\[X\in R^{H\times W\times C} \tag{1}\]3  
The \(y_{c}(i,j)\) in the aforementioned equation represents the ultimate output, and the aforementioned realization conducts attention learning based on both horizontal (\(h\)) and vertical (\(w\)) directions for the previously fused features. The structure diagram of GEA module is shown in \[X\in R^{H\times W\times C} \tag{1}\]4 The overarching concept of this model is to achieve feature enhancement extraction while minimizing parameter increase and computational complexity. Consequently, the GEA module consists of depth-wise separable convolution combined with global normalized response, complemented by CA feature learning. The final experimental results substantiate that this model enhances accuracy without an excessive surge in parameter quantity.