## 3 3D Burden Surface Feature Extraction
### Point Cloud Feature Extraction
#### 3.2.2 PointCNN
Neighbor sampling: The KNN algorithm is used to find \(K\times D\) nearest neighbors for each representative point in \(q\), and the interval \(D\) sampling is decimated to obtain the \(P\times K\) nearest neighbor point set matrix. 2. Decentralization: Subtract the corresponding representative point coordinates from each set of neighbor coordinates to obtain the relative coordinate matrix of the near neighbor points. 3. Feature splicing: The relative coordinate matrix boosts the dimensions through two fully connected layers and is spliced with the input feature vector set \(F\) to obtain a new set of features. 4. Calculation transformation \(\Xi\)-matrix: The relative coordinate obtained by step 2 is processed, and the coordinate-related features are extracted to obtain a set of a \(K\times K\) transformation \(\Xi\)-matrix. 5. Conduct transformation \(\Xi\)-matrix: The features extracted in step 3 are combined with the transformation \(\Xi\)-matrix to obtain a new feature matrix. 6. Feature transformation: New features are extracted and elevated to the \(C\) dimension. The process in step 4 is shown in Figure 9.  
The calculation of the transformation \(\Xi\)-matrix first performs a conventional convolution operation through \(K\times K\) convolution kernels, which promotes the feature dimension to the \(K\) dimension. Then, two depth-wise convolutions are conducted while keeping the feature dimension unchanged. The use of a deep convolutional layer here to increase the influence of each channel individually, on the one hand, is conducive to feature extraction, and on the other hand, it also reduces the parameters in the calculation. For a sampling of the nearest neighbor points in step 1, the expansion rate \(D\) is introduced into the \(\Xi\)-Conv. It acts as a perforated convolution to improve the information contained in the extracted features. We built a PointCNN based on \(\Xi\)-Conv, and the structure is shown in Figure 10.  
In the first layer of \(\Xi\)-Conv, the point set \(p\) is processed as representative points, and the feature of each point is extracted, where \(p_{0}=q_{0}\). The subsequent \(\Xi\)-Conv layer takes the previous representative point as the point set of the feature processing; that is, \(q_{n-1}=p_{n}\), and it randomly extracts a certain number of points as the representative point \(q_{n}\) of this \(\Xi\)-Conv. The network structure is such that with the increase in the number of layers, the number of extracted representative points \(P\) decreases, and the feature dimension \(C\) increases, which is similar to a CNN, increasing the depth of the feature channels and reducing the number of input points. The number of neighboring points \(K\) increases correspondingly with the expansion rate \(D\), and the point set \(p\) used to sample the near neighbors is sparser, which will make each feature fuse more point cloud information. This means that the previous layer integrates the local information of the point cloud and gradually increases the scale of integration until the deeper layer has more macroscopic information for data extraction and reflects the global structure information of all of the point cloud data. In the PointCNN network structure, the last three layers are fully connected layers that aim to fuse and classify the features of the extracted data. The last fully connected layer also plays a simple classification role, realizing four classifications of compressed features. In the penultimate fully connected layer, this experiment also adds a dropout layer, which sets the probability of discarding at 0.3 so that each feature value output by FC-192 discards 30% of each training time to prevent data overfitting. The Adam optimizer is still selected  
Figure 10: The PointCNN based on \(\Xi\)-Conv. Figure 9: Transformation \(\Xi\)-matrix. to optimize the gradient of the output results of the network model, which increases the adaptability of the learning rate. As in PointNet, the learning rate decay strategy is set to reduce the learning rate to 0.85 every thousand iterations.