# COMA: Propagating Complementary Multi-Level Aggregation Network for Polyp Segmentation
## 2 Materials and Methods
### Boundary Propagation Module  
Explicit boundary information contributes to a more elaborate discrimination of polyps in ambiguous contexts. Existing studies [25; 26] generated edge information by ensembling both low- and relatively high-level representations. They only utilized this information to refine the highest-level feature or adjacent pair of encoder-decoder outputs, rather than the entire network. In contrast to existing methods, the BPM is designed not only to detect explicit boundary information but also to propagate the boundary to complementary multi-level features by incorporating the lowest- and highest-level representations. Although both levels exhibit a large distribution discrepancy, we overcome the discrepancy with a property of each level to obtain a detailed boundary. The low-level encoder output contains sufficient boundary information including background noise; in contrast, the high-level output contains abstracted position information such that it exhibits ambiguous boundaries [14; 15; 16]. Based on these properties, we consider both the lowest and highest levels to maximize boundary detection performance. To verify the effectiveness of this adoption, we conducted an ablation study related on the representation level for boundary generation in Section 4.2.  
We denoise the boundary noise at the lowest-level \(E_{1}^{(1)}\) through the highest-level representation \(D_{4}^{(1)}\) to obtain a high-quality boundary, as follows:  
\[\begin{split} X=\mathcal{F}(E_{1}^{(1)})\otimes Up(D_{4}^{(1)}) \\ B=\sigma(\mathcal{F}(X))\end{split} \tag{3}\]  
A convolutional operation \(\mathcal{F}(\cdot)\) removing background noise [35; 36] is applied to \(E_{1}^{(1)}\). \(D_{4}^{(1)}\) for the effective aggregation of two different levels is directly rescaled to the same size as \(E_{1}^{(1)}\) by the bilinear upsampling \(Up(\cdot)\). Subsequently, we refine the fused feature \(X\) using \(\mathcal{F}(\cdot)\) and employ a sigmoid function to discriminate the boundary representation \(B\). After generating the explicit boundary \(B\), the BPM propagates downsampled \(B\) to complementary representations \(E_{i}^{(2)}\), which are the CMM outputs of the first decoder, to clarify the fine information, as follows:  
\[E_{i}^{(2)}=E_{i}^{(2)}\otimes Down(B)+E_{i}^{(2)},\;\textit{where}\;i=2,3,4 \tag{4}\]  
Here, \(Down(\cdot)\) indicates bilinear downsampling to the same size as \(E_{i}^{(2)}\). We emphasize boundary information in \(E_{i}^{(2)}\) using resized \(B\) to each \(E_{i}^{(2)}\). By enhancing the fine features at each \(E_{i}^{(2)}\), which is the input of the second decoder, the second decoder can more easily detect ambiguous polyps compared to the first. That is, boundary propagation is capable of learning a robust network against ambiguous edge information. To verify the effectiveness of boundary propagation, we present experimental results depending on the BPM application in Section 4.1. Finally, as demonstrated in existing studies [20; 23; 37], we generate a boundary ground truth \(GT_{B}\) to improve the boundary detection performance. To support the explainability of the module, we visualize feature maps corresponding to the BPM application state in Section 4.3.