## 3 3D Burden Surface Feature Extraction
### Voxel Feature Extraction by BNVGG  
The traditional convolutional neural network (CNN) is very mature in 2D images, but due to the out-of-order nature of the point cloud data, it is difficult for CNNs to be directly applied to point clouds. We transform the 3D models into Euclidean spaces such as image regions, voxel regions, or primitive regions to accommodate traditional deep learning methods.  
The term voxel is a combination of pixel, volume, and element, being equivalent to pixels in 3D space. Through standard meshing, the \((x,y)\) coordinates of the burden surfaces are aligned, and each \((x,y)\) corresponds to a different \(z\). The 3D burden surface data are converted into a 2D array, and their voxel features are extracted. The results of this meshing are shown in Figure 4.  
VGGNet is a deep convolutional network structure proposed by the Visual Geometry Group (VGG) of the University of Oxford [19]. In VGG, three 3 \(\times\) 3 convolution kernels are used instead of 7 \(\times\) 7 convolution kernels, and two 3 \(\times\) 3 convolution kernels are used instead of 5 \(\times\) 5 convolution kernels. The main purpose of this is to increase the depth of the network, reduce the parameters, and improve the effectiveness of the neural network to a certain extent under the condition of ensuring that it has the same sensing field. The network structure of VGGNet is shown in Figure 5.  
Figure 4: The burden surface meshing.  
Following the concept of the convolution kernel in VGGNet, the network structure is optimized, and a BN layer is added after each convolutional layer [20]. We call the optimized network structure BNVGG. The BN layer normalizes the features of the output of the convolutional layer; that is, it converts the input data into a normal distribution with zero as the mean and one as the variance.  
\[\tilde{x}^{(k)}=\frac{x^{(k)}-E\Big{[}x^{(k)}\Big{]}}{\sqrt{\text{Var}\big{[}x^ {(k)}\big{]}}} \tag{11}\]  
where \(\tilde{x}^{(k)}=wu+b\), \(w\) is the weight of the layer, and \(u\) is the output of the previous layer. This operation increases the derivative value of the activation function and makes convergence occur faster:  
\[y^{(k)}=\gamma^{(k)}\hat{x}^{(k)}+\beta^{(k)} \tag{12}\]  
where the \(\gamma\) and \(\beta\) parameters can be learned through backpropagation, through which the data are expanded and translated to restore the distribution of some features.  
The optimized network structure is shown in Figure 6, which includes nine convolutional layers, three maximum pooling layers, and four fully connected layers. Among them, the activation functions of the convolutional layer and the fully connected layer are both ReLU functions.  
We set the neural network parameters of BNVGG. The batch size was set to 30, the momentum was 0.9, and the learning rate was set to 0.01. Training was regularized by  
Figure 5: The network structure of VGGNet.  
Figure 6: The network structure of improved BNVGG.  
weight decay (L2 penalty multiplier set to \(5\times 10^{-4}\)), and the first two fully connected layers took dropout regularization (dropout ratio set to 0.5). Then, 128 features were extracted from the third fully connected layer (FC-128) and transformed into dimensions to obtain a voxel feature matrix of the 3D burden surface, which was saved and used for subsequent research.