# Enhanced Atrous Extractor and Self-Dynamic Gate Network for Superpixel Segmentation
## 3 Methods
### Enhanced Atrous Extractor  
To extract the multi-scale superpixel feature with contextual information, we design an enhanced atrous extractor (EAE). As shown in Figure 3, our proposed EAE consists of an Enhanced Atrous Module and an MLP head. The EAE Module introduces the Atrous convolution and _SiLU_ function to produce the weight and sum the features to add the multi-scale superpixel feature with contextual information. And the MLP can add the non-linear complexity. The input feeds to the Enhanced Atrous Module and an MLP to extract the multi-scale superpixel feature and add the contextual information under the specific receptive field.  
For the Enhanced Atrous Module, as shown in Figure 4, we introduce five atrous convolutions with different dilation rates on the input to produce five superpixel features with contextual information under the specific receptive field. Then, we introduce the _SiLU_ function on it to produce weights and multiply these by weighted features. Finally, we sum them up to obtain the final output. Formally, the whole process can be written as:  
\[f_{i}=AConv_{r=i}(p_{m}),\{i=1,2,3,4,5\} \tag{15}\]  
Figure 3: The overall architecture of EAE. The EAE consists of the Enhanced Atrous Module and MLP head. The Enhanced Atrous Module can extract the different superpixel features under different receptive fields.  
Figure 2: The overall architecture of EAGNet. The EAGNet consists of a CNN backbone, an enhanced atrous extractor, and a self-dynamic gate. The CNN backbone and the enhanced atrous extractor can extract the pixel feature and multi-scale superpixel feature. The self-dynamic gate can filter the pixel feature and superpixel feature and fuse them to obtain the pixel–superpixel relationship information for the final prediction.  
where \(AConv_{r=1}\) means the atrous convolution with a dilation rate equal to \(i\), and \(i\) is the dilation rate. The \(f_{i}\) means the superpixel feature of dilation rate \(i\). The \(P_{m}\) is the multi-scale pixel feature, which is the input of the Enhanced Atrous Module.  
\[f_{i}=f_{i}\times sigmoid(f_{i}),\{i=1,2,3,4,5\} \tag{16}\]  
where \(sigmoid(.)\) is the sigmoid non-linear activation function. And Equation (16) is also the process of the \(SiLU\) activation function.  
\[Output=SUM(f_{i}),\{i=1,2,3,4,5\} \tag{17}\]  
where \(Output\) is the output of the Enhanced Atrous Module. The \(SUM(.)\) is the sum operation.  
The Atrous convolution can extract the contextual information under the specific receptive field. The \(SiLU\) function can weight the feature to strengthen the representation ability of the feature. And we can add all the features to obtain the multi-scale superpixel feature with contextual information under different receptive fields with a powerful representation ability. And we also conduct experiments to show that contextual information can improve compactness.  
For the MLP part, as shown in Figure 5, it consists of two fully connected layers and a \(3\times 3\) depth-wise convolution. And every fully connected layer consists of a \(1\times 1\) convolution, a batchnorm, and a \(LeakReLU\) layer. We set the expand ratio of the MLP to 2. The whole process of the MLP can be written as:  
\[f_{1}=fullyconnectedlayer(x)f_{2}=DWConv(f_{1}) \tag{18}\]  
\[f_{2}=DWConv(f_{1}) \tag{19}\]  
\[output=fullyconnectedlayer(f_{2}) \tag{20}\]  
where \(fullyconnectedlayer(.)\) is the fully connected layer. The DWConv is the \(3\times 3\) depth-wise convolution layer.  
Figure 4: The overall architecture of the Enhanced Atrous Module. The Enhanced Atrous Module introduces the atrous convolution and silu function to extract the superpixel feature and strengthen them.