## 3 Materials and Methods
### Multi-Scale Feature Adaptive Fusion  
As shown in Figure 3, the proposed multi-scale feature adaptive fusion (MFAF) mainly consists of two parts: multi-scale feature extract (MFE) and feature adaptive fusion (FAF). \(\otimes\) denotes the element-wise multiplication, and \(\copyright\) denotes the concatenate operator in the channel dimension. _in_ch_ and _mid_ch_ denote the number of channel of feature maps. To capture multi-scale contextual information, the MFE makes use of a cascade of different kernels and dilated convolution layers. Specifically, MFE consists of two ordinary convolution layers with \(1\times 1\) and \(3\times 3\) kernels respectively, and a \(3\times 3\) atrous  
Figure 2: Architecture of the proposed ACA-Net.  
convolution layer with the dilation rate of 3. The ordinary \(3\times 3\) convolution layer is added before the atrous convolution layer. Then, the three kinds of features, from the ordinary convolution and atrous convolution, are concatenated in the channel dimension. Mathematically, the multi-scale feature map can be obtained by a concatenation way as  
\[F=Cat(F_{1},F_{2},F_{3}) \tag{1}\]  
where \(F_{1},F_{2}\) and \(F_{3}\) are the three kinds of feature maps with different receptive fields, and \(F\) is a multi-scale feature map.  
After obtaining the multi-scale features, FAF is used for fusing features adaptively. Firstly, the channel attention weights of the three kinds of features are extracted by the  
Figure 3: The multi-scale feature adaptive fusion (MFAF). (**a**) The Architecture of MFAF. (**b**) SEWeight, (**c**) The improved SAM.  
SEWeight [17] respectively. As illustrated in Figure 3b, it uses a global average pooling and two fully-connected (FC) layers. The vector of channel attention weights can be represented as  
\[Z_{i}=SEWeight(F_{i}),i=1,2,3 \tag{2}\]  
where \(Z_{i}\) is the channel attention weights of the feature map with different scales. The multi-scale attention weight vectors can be obtained in a concatenation way as  
\[Z=Z_{1}\mathbb{O}Z_{2}\mathbb{O}Z_{3} \tag{3}\]  
where \(\mathbb{O}\) is the concatenation operator, \(Z\) is the multi-scale attention weight vectors. Then, these channel weights are re-calibrated by using the Softmax operation to establish long-range channel dependency. A soft assignment weight can be obtained as  
\[att_{i}=Softmax(Z_{i})=\frac{exp(Z_{i})}{\sum_{i=1}^{3}exp(Z_{i})} \tag{4}\]  
where \(att_{i}\) is the re-calibrated weight of the multi-scale channel. Analogously, the whole channel attention weight can be given by  
\[att=att_{1}\mathbb{O}att_{2}\mathbb{O}att_{3} \tag{5}\]  
where \(att\) denotes the final multi-scale channel weights after Softmax operation. Thus, the channel-wise features can be obtained by multiplying the re-calibrated weight attention \(att\) with the feature map \(F\). It could be defined as  
\[Y=F\otimes att \tag{6}\]  
where \(\otimes\) denotes the element-wise multiplication, and \(Y\) is channel-wise multi-scale feature map.  
Finally, these channel-wise features are operated by improved SAM. As illustrated in Figure 3b, we employ an extra added \(1\times 1\) convolution layer compared to original SAM [18]. The spatial information from average-pooling, max-pooling and \(1\times 1\) convolution layers is operated by \(7\times 7\) convolution layer with the Sigmoid function to obtain spatial attention weights. Mathematically, the final feature can be given by  
\[Out=SAM(Y) \tag{7}\]  
where \(Out\) is the channel-wise and spatial-wise feature map with multi receptive fields, and \(SAM\) denotes the improved SAM operation.