## 3 Semantic Segmentation of 3D Point Clouds
### Feature Extraction Network
#### 3.2.2 The Local-Global Feature Extraction Module  
The local-global feature extraction module is embedded in the encoder module. As shown in Figure 2, the input of the module includes the spatial information, color information and feature information \(F_{e}\) learned previously. After feature learning by the local-global feature extraction module, the extracted features \(F_{o}\) is outputted. The local information is extracted by using the dual distance feature extraction module, while the global information is extracted using by the global feature extraction module. **The dual distance feature extraction module** From a 3D perspective, distance is an important indicator of the correlation between points. The smaller the distance between points, the higher their correlation. Distance includes not only the spatial distance between two points but also the feature distance between two points. Therefore, we propose the dual distance feature extraction module based on the spatial and feature distances between two points, which can automatically learn the effective local information features. Its specific structure is shown in Figure 2.  
The input of the dual distance feature extraction module is the spatial information, feature information, and color information of the point \(\mathbf{p_{i}}\) and its \(k\) neighboring points. The dimension of spatial information and color vector information is \((k,3)\), and the dimension of input feature is \((k,8)\). In this module, we calculate the spatial distance \(d^{j}_{ig}\) and feature distance \(d^{j}_{if}\) between the point \(\mathbf{p_{i}}\) and its \(j\)-th neighboring point \(\mathbf{p_{i}^{j}}\) as  
\[ \begin{split} d^{j}_{ig}=&\left|\mathbf{p_{i}}-\mathbf{p_{i }^{j}}\right|\ \ j=1,\cdots,k\\ d^{j}_{if}=&\left|f(\mathbf{p_{i}})-f\left(\mathbf{p_{i}^{j }}\right)\right|\ \ j=1,\cdots,k\end{split}  \tag{1}\]  
where \(\left|\cdot\right|\) is the L\({}_{1}\) norm. \(f(\mathbf{p_{i}})\) is the \(i\)-th point feature and \(f\left(\mathbf{p_{i}^{j}}\right)\) is its \(j\)-th neighboring point feature. Since the features are automatically learned by the network, we use the negative exponent of both distances to learn two attention concentration weights and use \(\lambda\) to adjust \(d^{j}_{if}\) to address instability to obtain the dual distance \(\mathbf{d^{j}_{i}}\). \[\mathbf{d^{j}_{i}}=exp\left(-d^{j}_{ig}\right)\oplus\lambda exp\left(-d^{j}_{if}\right) \tag{2}\]  
where \(\oplus\) is the concatenation operator. Then, the dual distance \(\mathbf{d^{j}_{i}}\) and the feature \(\mathbf{f^{j}_{i}}\) are concatenated as  
\[\mathbf{d^{j+}_{i}}=\mathbf{d^{j}_{i}}\oplus\mathbf{f^{j}_{i}} \tag{3}\]  
Figure 2: The local-global feature extraction module (LGFE). where \(\mathbf{f}_{i}^{j}\) is obtained by concatenating the color information and the feature information of the \(k\) neighboring points of the point \(\mathbf{p}_{i}\). And a shared MLP and softmax are applied to \(\mathbf{d}_{i}^{j+}\) to obtain \(\mathbf{a}_{i}^{j}\)  
\[\mathbf{a}_{i}^{j}=\text{softmax}\Big{(}\text{MLP}\Big{(}\mathbf{d}_{i}^{j+}\Big{)} \Big{)}. \tag{4}\]  
Finally, the output feature of the dual distance feature extraction module is obtained by  
\[\mathbf{f}_{i}=\text{MLP}\Big{(}\sum_{j=1}^{k}\Big{(}\mathbf{a}_{i}^{j}\odot\mathbf{f}_{i} ^{j}\Big{)}\Big{)} \tag{5}\]  
**Global Feature Extraction Module** The dual distance feature extraction module can extract the semantic features between two points within the neighborhood, but its power to judge the semantic segmentation of the overall 3D point clouds is insufficient. Since the semantic segmentation of the entire 3D point clouds requires integration and global information, we propose a global feature extraction module to learn global features from the 3D point cloud \(P\). As shown in Figure 3, we use 2D point clouds to express the relationship between the local region and the global region in the 3D point clouds.