## 4 Method
### Edge-Enhanced Feature Extraction Module  
Considering the distinct characteristics of global features and edge features, we employ a dual-branch network architecture to separately extract features from the original image and the corresponding edge image. As shown in Figure 3, these branches are called the Global Feature Extraction Branch \(F_{rgb}:\ x_{rgb}\to f_{rgb}\) and the Edge Feature Extraction Branch \(F_{e}:\ x_{e}\to f_{e}\). During the feature learning process, edge features are incorporated into corresponding layers of the Global Feature Extraction Branch, aiming to enhance the network's ability to extract global features. Specifically, to efficiently learn deep features of the image and mitigate the issue of gradient vanishing during training, ResNet-50 is used as the backbone network of the Global Feature Extraction Branch, while ResNet-18 is used as the backbone network of the Edge Feature Extraction Branch. In addition, considering that features in different channels and regions have different importance, we added a hybrid attention module to the global feature extraction branch. As shown in Figure 4, the hybrid attention module consists of a channel attention block and a spatial attention block. It dynamically assigns greater weights to important channels and regions in the features, allowing the network to learn critical information while ignoring less relevant details. Finally, global features and edge features are fused by a feature fusion module (see Section 4.5 for a detailed description) to obtain the output features of this module, which enhances the comprehensive feature representation. The channel attention block includes a global average pooling layer, a global maximum pooling layer, a \(1\times 1\) convolutional layer, and a sigmoid function. The spatial attention block comprises a cross-channel average pooling layer, a cross-channel maximum pooling layer, a \(7\times 7\) convolutional layer, and another sigmoid function. For a given global feature map \(X^{i}_{rgb}\) and edge feature map \(X^{i}_{e}\) output from the i-th layer of the network,  
Figure 4: Hybrid attention module. Figure 3: Edge-enhanced Feature Extraction Module. \(X^{i}_{rgb}\in\mathbb{R}^{C^{i}_{rgb}\times H_{i}\times W_{i}}\), \(X^{i}_{e}\in\mathbb{R}^{C^{i}_{c}\times H_{i}\times W_{i}}\). \(X^{i}_{rgb}\) and \(X^{i}_{e}\) are first concatenated along the channel dimension. The concatenated features are then subjected to global average pooling and global max pooling operations, respectively. The pooled features are concatenated along the channel dimension and fed into a \(1\times 1\) convolutional layer, where the number of input channels is \(C^{i}_{rgb}+C^{i}_{e}\), and the number of output channels is \(C^{i}_{rgb}\). Finally, the convolution features are activated using a sigmoid function and expanded via broadcasting along the spatial dimension to match the dimensions of \(X^{i}_{rgb}\). The channel attention map can be expressed as follow:  
\[A_{C}\Big{(}X^{i}_{rgb},X^{i}_{e}\Big{)}=Broadcast_{S}\Big{(} \sigma\Big{(}Conv_{1\times 1}\Big{(}cat\Big{(}GAvgPool\Big{(}cat\Big{(}X^{i}_{rgb},X^{i}_{e }\Big{)}\Big{)},GMaxPool\Big{(}cat\Big{(}X^{i}_{rgb},X^{i}_{e}\Big{)}\Big{)} \Big{)}\Big{)}\Big{)}\Big{)} \tag{4}\]  
here, \(A_{C}\in\mathbb{R}^{C^{i}_{rgb}\times H_{i}\times W_{i}}\) is the channel attention map, \(Broadcast_{S}(\cdot)\) denotes broadcast operation along the spatial dimension, \(\sigma\) denotes the sigmoid function, \(cat(\cdot)\) represents the concatenation operation, \(Conv_{1\times 1}(\cdot)\) represents the convolutional layer with a kernel size of \(1\times 1\), \(GAvgPool(\cdot)\) and \(GMaxPool(\cdot)\) represent the global average pooling layer and the global maximum pooling layer, respectively. Embedding \(A_{C}\) into \(X^{i}_{rgb}\) through element-wise multiplication, the embedded feature can be expressed as \(X^{i}_{C}=\overset{\sim}{A_{C}}\bigotimes\underset{X^{i}_{rgb}}{\overset{i}{ \sim}}\), where \(\otimes\) denotes element-wise multiplication.