## 3 Method
### Semantic Segmentation Network for Decoupling Body and Edge
In addition, to ensure smoother performance of the body feature and reduce noise and discontinuities in the prediction results, we applied the \(L_{2}\) loss [40] to bootstrapping the body generation branch learning, as shown in Equation (8). \[L_{body}=\sqrt{\sum_{s=1}^{H\times W\times C}(F_{body}^{(s)})^{2}}, \tag{8}\]  
where \(s\) denotes the positional index of the element in \(\forall F\in\mathbb{R}^{H\times W\times C}\), and \(s=1,2,...\), \(H\times W\times C\). **Edge preservation branch:** This branch is dedicated to handling high-frequency terms \(F_{high}\) in the image, where high-frequency features usually encompass more detailed edge information. To obtain the high-frequency edge feature, we subtracted the body feature \(F_{body}\) from the original feature \(F\), i.e., \((F-F_{body})\). Drawing inspiration from recent work on decoder design [41], we outputted a low-level feature \(F_{detail}\) through the backbone's low layer, which served as a complement to the missing fine-detail information and augmented the high-frequency terms in \(F_{edge}\). Finally, \((F-F_{body})\) and \(F_{detail}\) were cascaded, and then a \(1\times 1 Conv\) was used for channel adjustment to obtain \(F_{edge}\). The implementation is expressed in Equation (9). \[F_{edge}=h_{\text{conv}}((F-F_{body})||F_{detail}), \tag{9}\]  
where \(F_{edge}\in\mathbb{R}^{H\times W\times C}\). The edge preservation branch focuses more on edge detail features and does not require body features. Unlike the \(L_{2}\) loss, the \(L_{1}\) loss can obtain a sparse solution so that certain features have zero weight. This makes the boundary sparser and reduces unnecessary body features, contributing to an accurate boundary prediction feature map. Therefore, the \(L_{1}\) loss [40] was utilized to guide the learning of the edge preservation branch, as shown in Equation (10). \[L_{edge}=\sum_{s=1}^{H\times W\times C}|F_{edge}^{(s)}|. \tag{10}\]  
The final decoupling loss is:  
\[L_{de}=L_{body}+\lambda_{3}L_{edge}, \tag{11}\]  
Both the \(L_{body}\) and \(L_{edge}\) losses complement each other by sampling pixels from different regions of the image, which was beneficial for showing the performance of the experimental results. Since the edge portion is not a large part of the overall image, \(\lambda_{3}\) is used to balance the weight of \(L_{edge}\) in \(L_{de}\), which was set to 0.4 in the experiments. Figure 3: Decoupling module for body generation and edge preservation. In this module, \(X\) represents the input image, \(F\) is derived from the backbone network and a dilated convolution, and \(F_{detail}\) represents the high-frequency detailed feature which is output through the low layer of the backbone network. In the body generation branch, \(F\) and \(F_{up}\) are cascaded and input to \(1\times 1 Conv\). Notably, \(F_{low}\) was not added to the cascade. Subsequently, average pooling and feature relocation were performed to obtain the body feature \(F_{body}\), which had an obvious body but fuzzy edges. In the edge preservation branch, \((F-F_{body})\) was cascaded with \(F_{detail}\) and input to \(1\times 1 Conv\) to obtain the edge feature \(F_{edge}\) with a clear boundary. The final segmentation predicted \(\tilde{F}=F_{body}+F_{edge}\). In this paper, \(G_{seg}\) acquired the body feature map \(F_{body}\) and edge feature map \(F_{edge}\) of the input image \(X\) through the body generation branch \(\rho\) and the edge preservation branch \(\delta\), respectively. Moreover, the edge features were supplemented by the high-frequency detailed features \(F_{detail}\) output from the lower layer of the backbone network. By employing distinct body and edge losses, the segmentation performance was enhanced, and the final segmentation map \(F\) was obtained through \(F_{body}+F_{edge}\).