## 4 Object Classification Network DSDCN-ResNet
### Structure of DSDCN-ResNet  
This section discusses the depthwise separable deformable residual classification network DSDCN-ResNet, designed based on ResNet with the DSDCN module. The network structure is shown in Figure 7, including the input convolution module, the feature extraction module, and the classification module.  
Stage 1 was developing the input convolution module, which contained three convolution layers. The purpose was to downsample the input image before the residual blocks to avoid the computational explosion caused by the large input image. This operation first ensured that the improved network had the same receptive field as the original network, and then it could increase the network depth to further extract deep semantic information.  
Stage 2 was the feature extraction module, which introduced the DSDCN module in Section 3.2 into the feature extraction of ResNet. This module could adaptively adjust the size and shape of the convolution kernel according to the characteristics of the object and realize the sampling of the offsets. Then, the bilinear interpolation algorithm was used to pool the sampling points to efficiently extract the robust features at different scales and enhance the discrimination of objects. DSDCN modules were added after the third convolutional layer and the residual blocks. The first DSDCN module extracted the shallow features of the object, followed by the depth residual features using Conv Block and Short Block. The second DSDCN module represented the object jointly with deformable and  
Figure 6: Residual block in ResNet. (**a**) Short Block, (**b**) Conv Block.  
traditional depth features, to improve the robustness of the model and make it more applicable for underwater object classification [36].  
Stage 3 was the classification module, which used Softmax to achieve the classification of objects in SAS images. In addition, the ReLU nonlinear activation functions were used in each convolutional layer and residual block during the network propagation to reduce model overfitting and enhance the nonlinear representation. The batch normalization layer was added before the activation function to increase the prediction accuracy of the model [37], which was calculated as follows:  
\[\text{ReLU}(x)=\max(x,0), \tag{5}\]  
\[\left\{\begin{array}{c}\mu_{B}\leftarrow\frac{1}{m}\sum\limits_{i=1}^{m}x_{i }\\ \sigma_{B}^{2}\leftarrow\frac{1}{m}\frac{m}{i}\left(x_{i}-\mu_{B}\right)^{2}, \\ \hat{x}_{i}\leftarrow\frac{x_{i}-\mu_{B}}{\sqrt{\sigma_{B}^{2}+\epsilon}}\\ y_{i}\leftarrow\gamma\hat{x}_{i}+\beta\end{array}\right. \tag{6}\]  
Based on ResNet, the depthwise separable deformable residual classification network is DSDCN-ResNet proposed in this paper was composed of convolutional layers, depthwise separable deformable convolution, residual blocks, global average pooling, and the Softmax classification layer. The network structure and parameters are shown in Table 1, where c represents the number of output channels of the current network layer, \(n\) represents the number of repetitions of the network layer, and s is the convolution stride.  
Figure 7: Structure of DSDCN-ResNet. Every blue block represents the convolution layer and a batch normalization layer with ReLU nonlinear activation function. Every green block represents a DSDCN module and a maxpooling layer. Every dark yellow block represents the short block in the ResNet network. Every light yellow block represents the conv block in the ResNet network. The pink block represents the flatten layer and the gray block represents the dense layer and the softmax activation function.