## 2 Deep Learning Based Underground Pipeline Target Recognition Using 3-Dimensional GPR Data
### Improved 3D-CNN Model  
When using the 3D-CNN model to directly process 3D data, if a 3D voxel image is taken as the input of the deep learning model, the spatial characteristics of 3D data can be completely retained. However, the subsequent problem is that the training cost is very expensive in terms of calculation, and the model size is also large, so it is not suitable for final deployment to platforms with limited computing resources. The depth-wise separable convolution block includes the depth-wise part and the point-wise part. The depth-wise convolution block is mostly used in the lightweight improvement of two-dimensional neural networks. Similarly, the 3D convolution kernel will significantly increase the amount of calculation, which requires an effective method to reduce the amount of calculation. Therefore, this paper extends the depth-separable convolution block to the lightweight improvement of the 3D neural network. For the 3D-CNN, \(W\), \(H\), \(L\), and \(C\) are used to represent the three-dimensional dimensions and the channel number of the input feature tensor, respectively, and \(K\) represents the size of the convolution kernel. Then, for a 3D convolution operation, the input feature is \(W\times H\times L\times C_{in}\) and the output feature is \(W\times H\times L\times C_{out}\). The traditional convolution operation can be divided into \(C_{in}\) depth-wise processes of \(K\times K\times K\times 1\) and \(C_{out}\) point-wise processes of \(1\times 1\times 1\times C_{in}\) by using a depth-wise separable convolution block. The number of network parameters is used to represent the amount of calculation, so the amount of calculation of traditional convolution is \(C_{out}\times K\times K\times K\times Cin\times W\times H\times L\), that of the depth-wise part is \(K\times K\times K\times C_{in}\times W\times H\times L\), and that of the point-wise part is \(1\times 1\times 1\times C_{in}\times C_{out}\times W\times H\times L\). The relationship between the amount of calculation is as follows:  
\[\frac{(K\times K\times K\times C_{in}\times W\times H\times L)+(C_{in}\times C _{out}\times W\times H\times L)}{K\times K\times K\times C_{in}\times C_{out} \times W\times H\times L}=\frac{1}{C_{out}}+\frac{1}{K\times K\times K}, \tag{10}\]  
Therefore, with the help of the 3D depth-separable convolution block, the parameters and calculation of 3D convolution operation are reduced. However, the depth-wise separable convolution block separates the traditional convolution operation from the channel dimension and the space dimension. While reducing the number of parameters, it also reduces the connection of the dimension information, which will lead to a decline in classification accuracy. Therefore, by integrating dimension information, we can increase the interaction between the channel dimension and the space dimension to improve the accuracy of performance. This paper proposes an improved depth-wise separable convolution block whose structure is shown in Figure 19, shows the number of channels before @ and the size of the convolution kernel after @. First, on the original basis, a dimension fusion module is added before Batch Normalization. Second, in the dimension fusion module, the pooling layer is used to average the corresponding positions of data for different channels, and then using SoftMax to process the data, it maps the data in the interval of (0, 1) and multiplies the data from different channels to obtain the data after dimension fusion. Finally, the steps following the original depth-wise separable convolution block are performed successively. \[\mathrm{U}_{DF}=\alpha*U_{i}, \tag{11}\]  
\[\alpha=Softmax\Bigg{(}\frac{1}{C_{in}}\sum_{i=1}^{C_{in}}f_{WHL}(i)\Bigg{)}, \tag{12}\]  
where \(C_{in}\) is the number of channels and \(f_{WHL}\) (\(i\)) and \(U_{i}\) are the data of the \(i^{th}\) channel. The paper refers to and adjusts AlexNet's multi-layer network structure [12], which is widely used in image classification and recognition.