# Research on Multi-Scale Point Cloud Completion Method Based on Local Neighborhood Dynamic Fusion
## 3 Method
### Multi-Scale Feature Extractor  
Multi-scale Feature Extractor \(E\). It aimed to extract and fuse features from the sparse and incomplete point cloud features of different input scales, thereby obtaining a global feature vector \(V\) containing more detailed features and semantic information. The incomplete point clouds of different scales input into the network were 2048, 512, and 256, respectively, where 2048 was the original point cloud, and the point clouds of 512 and 256 different scales were obtained by performing farthest point sampling (FPS) on the input sparse point cloud. Then, the three-point clouds with different resolutions performed feature extraction at the current scale through the serial design of the local neighborhood dynamic fusion layer (LNDFL) and the attention layer to obtain the attention vector with rich detailed features at the current scale. Finally, the final feature vector V extracted by the multi-scale feature was output through Multilayer Perception (MLP). The LNDFL first constructed the local neighborhood. For the point cloud data of each scale, let the point cloud be \(p\) and one point in it be \(p\). The local neighborhood _N_(_p_\({}_{i}\)) was determined by the farthest point sampling method. For _p_\({}_{i}\), the \(K\) nearest points were found as the neighborhood points, that is  
\[N(p_{i})=\{p_{i}|i\in[1,K]\} \tag{1}\]  
Secondly, the difference feature calculation was carried out to calculate the feature difference and position difference between the neighborhood points and the central point. Let _f_\({}_{i}\) and _f_\({}_{j}\) be the feature vectors of the central point _p_\({}_{i}\) and the neighborhood point _p_\({}_{j}\) respectively. The feature difference _Af_\({}_{ij}\) and the position difference _D_\({}_{ij}\) are as follows:  
\[ \begin{array}{l}\Delta f_{ij}=f_{j}-f_{i}\\ \Delta p_{ij}=p_{j}-p_{i}\end{array}  \tag{2}\]  
Finally, an aggregation function was used to aggregate the difference features of all neighborhood points and the central point to obtain the aggregated neighborhood feature _f_\({}_{agg}\). Through max pooling and average pooling to ensure the integrity of the  
Figure 1: A framework of the multi-scale point cloud completion network based on local neighborhood dynamic fusion. overall structure, the maximum value \(f_{max}\) and the average value \(f_{avg}\) among all the feature differences between the neighborhood points and the central point were obtained and concatenated to form the aggregated feature as the aggregated neighborhood feature \(f_{agg}\). Here, the weights \(w\) of max pooling and average pooling were dynamically adjusted, and \(w_{1}+w_{2}=1\), so as to improve our ability to extract local detailed features, and its calculation formula is expressed as  
\[f_{agg}=w_{1}f_{max}+w_{2}f_{avg} \tag{3}\]  
The multiple local features were obtained through the local neighborhood dynamic fusion. We implemented the model with the PyTorch 1.8.2 deep learning framework and nonlinearly connected it using a multilayer perceptron (MLP), with each layer incorporating batch normalization (BN) and a ReLU activation function. This process resulted in feature representations with six dimensions: 64, 64, 128, 256, 512, and 2048. Following this, the features were subjected to dynamic adjustment via max pooling (MP) and average pooling (AP), after which they were concatenated and aggregated to produce the final global feature vector. The schematic representation of this aggregation process is shown in Figure 2, and the corresponding calculation formula is expressed as  
\[LNDFL=MP\left(\sum_{i=0}f_{i}\right)\oplus AP\left(\sum_{i=0}f_{i}\right),i\in[ 0,5] \tag{4}\]  
The LNDFL performed global-to-local feature extraction on three different low-resolution point clouds sequentially. The goal was to capture both comprehensive and detailed feature information from each point cloud scale.