# Semantic Segmentation Method for Road Intersection Point Clouds Based on Lightweight LiDAR
## 2 Materials and Methods
### Point Cloud Semantic Segmentation Model
#### 2.3.2 Improved Feature Aggregation Module
Then, concatenate the coordinates of the central point \(\text{s}_{i}\), the coordinates of the neighborhood points \(\text{s}_{i}^{k}\), and their Euclidean distances \(||\text{f}_{i}-\text{f}_{i}^{k}||\) to obtain the relative position feature. This process can be represented as follows: \[\text{r}_{i}^{k}=\text{MLP}\Big{(}\text{s}_{i}\oplus\text{s}_{i}^{k}\oplus( \text{s}_{i}-\text{s}_{i}^{k})\oplus||\text{s}_{i}-\text{s}_{i}^{k}||\Big{)}\] (6) where \(\oplus\) denotes the concatenation of feature matrices of the same dimension. * Step 4: Neighborhood Feature Enhancement For each neighborhood point \(\text{p}_{i}^{k}\) of the central points, concatenate its corresponding feature with the relative position feature \(\text{r}_{i}^{k}\) to obtain the enhanced feature vector \(\text{f}_{i}^{k}\). Then, the output via the multi-layer perceptron (MLP) is the relative position feature enhanced feature \(\Phi_{i}=\big{\{}\varphi_{i}^{1},\cdots,\varphi_{i}^{k},\cdots,\varphi_{i}^{K \text{new}}\big{\}}\): \[\varphi_{i}^{k}=\text{MLP}(\text{f}_{i}^{k}).\] (7) The output of the spatial information encoding unit is the neighborhood feature of each central sampling point. This information is encoded in a matrix that captures the local semantic structure of each central point, effectively enhancing the neighborhood spatial features of the input point cloud. (2) Aggregation Pooling Layer: This layer retains the attention mechanism of the original network and enhances the point cloud features based on multi-pooling fusion. Firstly, the maximum pooling function Hmax and the average pooling function Hmean are used, respectively, to obtain global features of each point and local features within their neighborhood. Secondly, a shared function, g(0), consisting of an MLP with shared weights W and a Softmax activation function, is established to learn individual attention scores \(\alpha_{i}^{k}\) for each point:  
\[\alpha_{i}^{k}=\text{g}(\varphi_{i}^{k},\text{ W}). \tag{8}\]  
Weighted summation is employed to aggregate the neighborhood features, as follows:  
\[\text{H}_{i}^{\text{w}}=\text{MLP}\Big{(}\sum\big{(}\varphi_{i}^{k}\cdot \alpha_{i}^{k}\big{)}\Big{)}. \tag{9}\]  
Finally, the results of the maximum pooling, average pooling, and high-dimensional features output by attention pooling are concatenated:  
Figure 4.0  
This result encompasses both local and global information in the point cloud, enabling the model to more accurately capture the input point cloud's spatial structure. (3) Dilated Residual Layer: To balance model computational efficiency and information richness when downsampling large-scale input point clouds, it is necessary to progressively expand the receptive field of each central sampling point to cover the key semantic features of the original point cloud. The network's dilated residual layer stacks the spatial information encoding layer and aggregation pooling layer twice to increase the effective spatial range of central points in the neighborhood.