## 3 Methods
### Channel Attention Module  
Similar attention networks used for segmentation, such as [25; 30], have bigger regions of interest and are more suitable for pathological segmentation. Our channel attention network can allocate the  
Figure 3: Left is the overall structure of the Attentionblock, right is the structure of the channel attention module SCA. weight after each convolution and enhance the useful features, which is suitable for the segmentation of small blood vessels. Generally, the output of the convolutional layer does not consider the channel dependence. We adopt the structure in SEblock [19], which is called Se calculation. It can enhance the effective features and suppress ineffective features between channels. We combine it with the channel attention module and propose a new channel attention module called SCA (Figure 3). Then add the SCA module to the second residual block of u-net and call it an Attentionblock (Figure 3). The following is the detailed calculation process of the channel attention module. We assume that the original feature is \(\text{F}\in R^{\text{C}\times\text{H}\times\text{W}}\), and the original feature goes through three pipelines 2, 3, and 4 as shown in Figure 3. After passing through these three pipelines, the original feature first undergoes Squeeze-and-Excitation calculation (Hereinafter referred to as Se). In Se calculation, the first step is the Squeeze operation \(\text{F}_{sq}\), which is the operation of global average pooling:  
\[Z_{\text{c}}=F_{sq}\left(f_{c}\right)=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j =1}^{W}f_{c}(i,j) \tag{3}\]  
Among them, \(f_{c}\) represents the initial feature (i.e., the three-dimensional matrix \(\text{F}\in R^{\text{C}\times\text{H}\times\text{W}}\)), and the subscript c represents the c-th two-dimensional matrix in F, i.e., the channel. Equation (3) converts the input of \(\text{C}\times\text{H}\times\text{W}\) into \(1\times 1\times\text{C}\), which indicates the numerical distribution of the c feature maps of the layer, i.e., the global information. The Squeeze operation in Equation (3) operated in the feature map of a channel, and the operation in Equation (4) is to fuse the weight of the feature map of each channel, i.e., the Excitation operation \(F_{ex}\):  
\[s=F_{ex}(z,W)=\sigma(g(z,W))=\sigma\left(W_{2}\delta\left(W_{1}z\right)\right) \tag{4}\]  
where \(z\) is the result of Equation (3), \(W_{1}\) multiplied by z is the first fully connected layer operation, and the dimension of \(W_{1}\) is \(\frac{\text{C}}{r}\times\text{C}\), where r is a scaling parameter, to reduce the number of channels and thus reduce the amount of calculation. In this paper, r sets to 2. The dimension of z is \(1\times 1\times\text{C}\), then the dimension of \(W_{12}\) is \(1\times 1\times\frac{\text{C}}{r}\). Then it goes through a RELU layer with the same dimensions, multiply it with \(W_{2}\), which is the operation of the second fully connected layer. The dimension of \(W_{2}\) is \(c\times\frac{\text{C}}{r}\), and the dimension of output is \(1\times 1\times\text{C}\). Finally, the dimension is unchanged after passing the sigmoid function. The obtained s (Equation (4)) is the feature map weight of the channel learned through the previous fully connected and non-linear layers. It is the result of pipeline 2, 3, 4 after Se operation. In pipeline 4, we transform the initial characteristics \(\text{F}\in R^{\text{C}\times\text{H}\times\text{W}}\) to \(\text{F}\in R^{\text{C}\times\text{N}}\), where \(\text{N}=\text{H}\times W\) represents the pixels of the picture. Pipeline 3 was reshaped after SE processed the original features. Then perform matrix multiplication on the reshaped F and the transpose of F passing through pipeline 4, and finally use a SoftMax layer to get the channel attention map \(\text{X}\in R^{\alpha}\):  
\[x_{ij}=softmax(F_{i}\cdot F_{j})=\frac{exp(F_{i}\cdot F_{j})}{\sum_{i=1}^{ \text{C}}exp(F_{i}\cdot F_{j})} \tag{5}\]  
where \(x_{ij}\) represents the influence of the i-th channel on the j-th channel.