## 3 Method
### Semantic Segmentation Network for Decoupling Body and Edge  
Currently, mainstream semantic segmentation methods primarily focus on enhancing the internal consistency of the object through global modeling or refining the object details along the boundaries through multi-scale feature fusion. However, it is worth noting that foreground boundary regions typically harbor more spatial detail and higher-frequency feature information. In view of this, we introduced the semantic segmentation network \(G_{seg}\) for decoupling body and edge, which contains a body generation branch \(\rho\) and an edge preservation branch \(\delta\). Unlike previous studies, we do not require the input image's ground truth map and trained two branches with distinct losses to predict the body feature map and edge feature map, respectively. The implementation details are described below. **Decoupling segmentation framework:** In this paper, we assume that the spatial features of the image conform to the addition rule, i.e., \(\hat{F}=F_{\text{body}}+F_{\text{edge}}\). Accordingly, the body feature \(F_{body}\) can be generated first, and the edge feature \(F_{edge}\) can be obtained by a specific subtraction operation. If we make \(F_{body}=\rho(F)\), then \(F_{edge}=F-F_{body}\), as shown in Equation (7). \[ \begin{split}\hat{F}&=\rho(F)+\delta(F_{edge})\\ &=F_{body}+\delta(F-F_{body}),\end{split}  \tag{7}\]  
where \(\rho\) represents the body generation branch mapping which is used to aggregate contextual information within objects to form a distinct body for each object. On the other hand, \(\delta\) denotes the edge preservation branch mapping, which is designed to extract spatially detailed features from the boundary region. **Body generation branch:** This branch is responsible for the generation of more consistent feature representations for pixels that are part of the same object in an image. Low-resolution feature maps typically contain low-frequency terms, with the low-spatial-frequency portion representing the image as a whole. Therefore, the low-resolution feature maps represent the most salient parts. In order to achieve this goal, as illustrated in Figure 3, \(X\) is the input image, and we utilized an encoder-decoder architecture after the backbone to extract \(F\). Specifically, the encoder downsamples \(F\) using dilated convolution, which downsamples \(F\) into a low-resolution representation of the low-spatial-frequency portion, denoted as \(F_{low}\). In some cases, low-resolution features might still contain high-frequency information. We assumed that this compressed representation encapsulates the most obvious object portions and leads to rough representation which ignores details or high-frequency portions. Therefore, we used bilinear interpolation to upsample \(F_{low}\) to the same size as \(F\) to obtain \(F_{up}\). Then, we cascaded \(F\) and \(F_{up}\) and used a \(1\times 1 Conv\) to adjust the channel dimensions to \(\mathbb{R}^{H\times W\times C}\) to obtain \(F_{conv}\), i.e., \(F_{conv}=h_{conv}(F||F_{up})\), where \(h_{conv}\) denotes the \(1\times 1\) convolutional layer, and \(||\) denotes the channel dimensionality join operation. This branch also contains an average pooling layer by average pooling \(F_{conv}\) to generate a feature map \(F_{ap}\) with a more distinct body, i.e., \(F_{ap}=h_{ap}(F_{conv})\) and \(F_{ap}\in\mathbb{R}^{H\times W\times C}\), where \(h_{ap}\) denotes the average pooling operation. To increase the spatial accuracy of body features in segmentation results, we first mapped each pixel \(p\) in the default spatial grid \(\Omega_{l}\) on \(F_{ap}\) to a new pixel point \(p\) via feature relocation. Then, we used a variable bilinear sampling mechanism [38, 39] to approximate the value of each pixel point \(p\) in \(F_{body}\), i.e., \(F_{body}(\hat{p})=\sum_{p\in l(o)}F_{ap}(p)\), where \(l\) denotes the pixels in the four fields around \(p\), \(o\) is the center point, and \(F_{body}\in\mathbb{R}^{H\times W\times C}\).