## 3 Materials and Methods
### Boundary Constraint Reverse Attention Module  
In the realm of machine vision, most existing deep salience models are fine-tuned from image classification networks, and they often struggle to effectively capture residual details. However, reverse attention [32] highlights the potential of the reverse attention module in guiding side output residual learning in a top-down fashion. This guidance swiftly directs the network's focus toward previously undetected regions for residual capture, ultimately leading to improved performance. On this basis, the spatial resolution of the deeper features is low, which may lead to rough boundaries if polyp masks are generated on these layers. Studies such as Inf-Net [33], ETNet [34], and EGNet [35] all demonstrated that integrating edge and positional information can lead to clearer boundaries in segmentation results. Inspired by BCNet [36], we chose to generate polyp masks on the shallow feature maps using the positional information extracted from the deeper layers as a bilateral guide, which helps to enhance the polyp boundary features and suppress the non-polyp boundary features.  
Hence, we propose a boundary constraint reverse attention module (BCRA). As we stated before, the global map generated by the parallel partial decoder was employed as the initial anchor region, as shown in Figure 4. First, the lower branch feature \(S_{i+1}\) is multiplied with \(f_{2}^{{}^{\prime}}\) after doing sigmoid and reverse operations to obtain the foreground feature \(B_{s}\)  
Figure 3: Efficient atrous convolution attention module structure. The yellow dashed box signifies a standard convolution with a kernel size of 3, which is employed for local feature extraction. The red dashed box utilizes atrous convolutions to extract contextual features from the surrounding area. The blue dashed box concatenates the local features and the surrounding context features through concatenation. Within the purple dashed box resides the global feature extractor.  
Subsequently, the upper branch feature \(f_{i}^{{}^{\prime}}\) is directly multiplied with \(f_{2}^{{}^{\prime}}\) after normalization of the width and height to obtain the background feature \(B_{f}\), and finally, \(B_{s}\) is summed with \(B_{f}\) to obtain the boundary constraint feature \(B_{i}\). Finally, \(S_{i+1}\) is added with \(B_{i}\) after doing a down-sampling to obtain the boundary information graph \(S_{g}\). This progressive top-down reverse erasure of foreground information continues until the third layer outputs at \(S_{3}\), with the sigmoid applied to \(S_{3}\) yielding the global prediction, as shown in Figure 1.  
\[\left\{\begin{array}{c}B_{f}=c(U(f_{i}^{{}^{\prime}})\odot f_{2}^{{}^{\prime }})\\ B_{s}=c(\epsilon(\ominus(U(S_{i+1}\odot f_{2}^{{}^{\prime}}))))\end{array}\right. \tag{1}\]  
\[B_{i}=B_{f}+B_{s} \tag{2}\]  
where \(c(\cdot)\) indicates the operation consisting of the \(3\times 3\) convolution + BN + ReLU, \(U(\cdot)\) indicates the double up-sampling operation, \(\epsilon\) indicates the sigmoid operation, \(\ominus\) indicates the reverse operation of subtracting the input from the matrix E, and \(\odot\) indicates the point multiplication operation.