## 3 Methods
### Three-Branch Attention Mechanism  
A significant disparity in semantic understanding exists between the encoder and decoder components within the UNet network. Directly merging low-level semantic feature maps with high-level semantic feature maps can substantially diminish the feature information. To mitigate this issue, a lightweight three-branch attention (TA) mechanism has been integrated into the skip connections. As described in reference [38], this mechanism captures global contextual information across both spatial and channel dimensions. Consequently, it enables the model to prioritize task-relevant features, thus enhancing the efficiency of information transmission and contributing to a more comprehensive representation of semantic and structural details in medical images, ultimately improving segmentation accuracy.  
The three-branch attention mechanism processes spatial and channel dimensional information concurrently by capturing their interplay within the input tensor. This method not only boosts feature extraction efficiency but also reduces the risk of information loss. The output from the encoder feeds into this attention mechanism, whose architecture is illustrated in Figure 4. The input feature maps are processed through three distinct branches: the first branch captures interactions between channel \(C\) and the spatial dimension \(W\); the second branch focuses on interactions between channel \(C\) and the spatial dimension \(H\); and the third branch concentrates on establishing spatial attention. The outputs from these branches are then combined using a basic averaging technique, and the aggregated outputs are merged with the up-sampled feature data to integrate low-level semantic features.  
Mathematically, the three-branch attention mechanism can be defined as:  
\[y_{1}=\sigma(BN(Conv(Z-Pool(x_{1}))))\odot x_{1} \tag{8}\]  
\[y_{2}=\sigma(BN(Conv(Z-Pool(x_{2}))))\odot x_{2} \tag{9}\]  
\[y_{3}=\sigma(BN(Conv(Z-Pool(x))))\odot x \tag{10}\]  
\[\textit{at\_out}=\text{AVG}(y_{1}+y_{2}+y_{3}) \tag{11}\]  
Figure 4: Structure of the three-branch attention mechanism module. The topmost branch is primarily responsible for computing the attentional weights across the channel dimension \(C\) and the spatial dimension \(W\). Similarly, the middle branch is responsible for the attentional weights across the channel dimension \(C\) and the spatial dimension \(H\). The bottom branch is utilized to capture spatial dependencies. In the first two branches, a rotation operation is used to establish the link between the channel dimension and the spatial dimension. Finally, the weights are clustered through an averaging operation.  
Among them, the input feature map \(x\in R^{\text{C}\times H\times W}\), the first two branches convert the feature map tensors into \(x_{1}\in R^{H\times\text{C}\times W}\) and \(x_{2}\in R^{W\times H\times\text{C}}\) through a rotation operation. \(\sigma\) represents the sigmoid activation function for calculating attention weights, \(BN\) represents the Batch Normalization layer, and \(\odot\) represents element-wise multiplication. \(at\_out\) represents the final output of the attention mechanism.  
The Z-Pool layer in the three-branch attention mechanism reduces the 0 th dimension of the feature graph to 2. It extracts the average pooled features and maximum pooled features in this dimension for the splicing process. This operation not only reduces the computational load but also preserves the rich information of the tensor. Mathematically, the Z-Pool layer can be represented as:  
\[Z-pool(x)=\ [MaxPool_{0d}(x),\ AvgPool_{0d}(x)] \tag{12}\]  
where \(0d\) is the 0 th dimension for maximum pooling and average pooling operations.