## 4 Experimental Results and Analysis
### Feasibility Verification of the Feature-Enhanced Point Transformer  
The research model's pre-training phase utilized the S3 DIS [57] three-dimensional point cloud dataset. This dataset covered an area of over 6000 square meters and contained more than two-hundred-million labeled points. The study divided the S3 DIS dataset into six regions based on the building areas and employed a cross-validation approach. In this paper, common metrics, such as the IoU (intersection over union), mIoU (mean intersection over union), and OA (overall accuracy), were employed as accuracy evaluation metrics for the segmentation results. The comparative results are presented in Table 1.  
From the results, it can be seen that the improved network model proposed in this paper has a relatively higher semantic segmentation accuracy at r = 0.2. Specifically, the IoU improved by 1.0% compared to the original point transformer (k = 16) network, and the OA improved by 1.1%. This indicates that the improvement based on the ball tree algorithm can effectively enhance the accuracy of the point cloud semantic segmentation, providing strong support for practical applications. This is because, in some unevenly distributed point sets, the original network's KNN-based queries can lead to a decrease in the network model's generalization ability. Additionally, this experiment also found that increasing the value of K for the KNN and the query radius, r, for the ball tree algorithm improved the network's performance to some extent. For example, point transformer (k = 64) relative to point transformer (k = 16) and feature-enhanced point transformer (r = 0.2) relative to feature-enhanced point transformer (r = 0.1) both showed improved network performances, but at the cost of longer computation times. The intersection over union (IoU) values for each category were also calculated, and their averages were determined. The S3 DIS dataset contained 13 semantic categories and the specific statistical results are shown in Table 2. From the table, it can be observed that the improved network model generally exhibits a higher segmentation accuracy compared to the original model in most categories. For example, in the office area, the improved model shows a 2.2% increase in the segmentation accuracy for the \"chair\" category compared to the original model, and an 0.8% increase in the accuracy for the \"wall\" category. Generally, in semantic segmentation and local sampling processes, there are often more stringent requirements for categories such as \"desk\", \"chair\", and \"sofa\" compared to architectural components, like \"wall\" and \"door\". Categories like \"desk\" and \"chair\" have more local details, requiring more precise segmentation and sampling activities. These details include chair armrests, chair legs, table edges, table legs, and other structural elements. These local \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Extraction Model** & **mIoU (\%)** & **OA (\%)** \\ \hline Point Net & 42.70 & 79.1 \\ Point Net++ & 49.39 & 81.1 \\ Point Transformer (k = 16) & 70.3 & 90.8 \\ Point Transformer (k = 64) & 70.8 & 91.2 \\ Feature-Enhanced Point Transformer (r = 0.1) & 70.6 & 91.1 \\ Feature-Enhanced Point Transformer (r = 0.2) & 71.3 & 91.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overall intersection over union (mIoU) and segmentation accuracy (OA) values. details are crucial for the overall structure and functionality of desks and chairs, hence the higher demands for semantic segmentation and local sampling. In contrast, categories, like \"wall\" and \"door\", typically have simpler geometric shapes and structures, resulting in fewer local details and less requirements for segmentation and sampling. Therefore, in the point cloud semantic segmentation process, the semantic segmentation of categories, like \"desk\" and \"chair\", places higher demands on the network's ability to perform local segmentations. It is evident that the improved network significantly enhances its capability for performing local segmentations.