## 3 Methodology
### Feature-Enhanced Point Transformer  
Point transformer is a deep learning model for point cloud data, with the core of the point transformer layer, which uses a \"Vector Self-Attention Mechanism\" and combines a position encoder to extract local and global features from point clouds. In comparison to other point cloud feature extraction algorithms, the point transformer is better suited for use concerning large and complex 3D scenes, thereby advancing the technological capabilities of understanding extensive point clouds [21]. This study builds upon the point transformer to perform the semantic segmentation of indoor point cloud data. The inputs of the point transformer layer was the point coordinates and corresponding feature vectors. The position encoder obtained the position encoding vector, which was then concatenated with the feature vectors to obtain the original feature representation of the point. By using the \"Vector Self-Attention Mechanism\" to weighted average the features of the points, the attention vector, \(\gamma\), of each point was obtained, and then concatenated with the original feature vectors, obtaining new feature representations of points \(\alpha\) through MLPs (multi-layer perceptrons). Finally, we concatenated the position encoding vector with the new feature representation to obtain the final point feature representation, as shown in Formula (1):  
Figure 1: Research flowchart. \[y_{i}=\sum_{x_{j}\in X(i)}\rho(\gamma(\varphi(x_{i})-\psi(x_{j})+\delta))\odot( \alpha(x_{i})+\delta) \tag{1}\]  
Subset \(X(i)\subseteq X\) is the local neighborhood of \(x_{i}\). The mapping function for point transformer \(\gamma\) is an MLP containing two linear layers and an ReLU nonlinear function. In this way, the point transformer layer is able to perform a local feature transformation and self-attention calculation on each data point and its neighborhood to better capture the correlation between the data points. Figure 2 shows the structure of the point transformer layer. Based on this, the point transformer constructs a residual point transformer block with a point transformer layer as the core, as shown in Figure 3.  
The transformer block integrates a self-attention layer, with the input consisting of a set of feature vectors, x, and associated three-dimensional coordinates, p. Point transformer blocks can facilitate information exchange between local feature vectors and apply the generated new feature vectors as outputs to all data points, adapting to the content of feature vectors and their layout in a three-dimensional space. A point transformer is the main feature aggregation function in a complete 3D point cloud-understanding network,  
Figure 3: Residual of point transformer block. Figure 2: The structure of the point transformer layer. without using a convolution for preprocessing or auxiliary branching. The complete network architecture for the semantic segmentation is shown in Figure 4.  
From the perspective of the entire network, the feature encoder of the point transformer for semantic segmentation and classification purposes had five stages, which operated on gradually downsampled point sets. The downsampling rates for these stages were [1; 4; 4; 4; 4]. Therefore, the cardinality values of each short point set are [N, N/4, N/16, N/64, N/256], where N is the number of input points. The number of stages and downsampling rates can vary depending on the application. For example, lightweight networks of components can be rapidly processed, with continuous stages connected by conversion modules: downward conversion for feature encoding and upward conversion for feature encoding. In the output stage, for semantic segmentation tasks, the final decoder generates feature vectors for each point in the input point set. The network application MLP maps this function to the final logic. For classification tasks, this network performs global AVG pooling on point-by-point features to obtain the global feature vectors corresponding to the entire point set.