# Automated Tunnel Point Cloud Segmentation and Extraction Method
## 4 Discussion
The RANSAC algorithm can remove non-tunnel structural point clouds within the tunnel by identifying inliers; however, it requires continuous adjustment of the distance threshold, reducing the level of automation. Additionally, some discrete point clouds introduced by measurement equipment errors may still remain between the tunnel lining. In contrast, the GuSAC algorithm, which integrates normal vector computation with RANSAC, can more accurately identify and remove tunnel joint features while also eliminating some discrete points scattered within the tunnel structural point cloud. This improvement is achieved because GuSAC constrains the number of neighboring points during normal vector estimation, preventing isolated discrete points from obtaining stable normal vectors. As a result, these points are identified as non-structural points and removed. This processing effectively optimizes the boundary conditions of  
Figure 21: Visualization comparison between GuSAC and traditional algorithms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Algorithm** & **CD** & **RMSE** \\ \hline \multirow{4}{*}{Regular Local} & Least Squares Method & 0.00991 & 0.0214 \\  & RANSAC & 0.00801 & 0.0189 \\  & Surface Fitting & 0.00814 & 0.0205 \\  & GuSAC & 0.00821 & 0.0175 \\  & Least Squares Method & 2.84322 & 1.1409 \\ Irregular Local & RANSAC & 0.00753 & 0.0126 \\  & Surface Fitting & 3.03304 & 1.1538 \\  & GuSAC & 0.00744 & 0.0113 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation index statistics table. the tunnel structural point cloud, significantly enhancing the segmentation accuracy and generalization capability of the TMatch algorithm. After completing the preprocessing with the GuSAC algorithm, TMatch utilizes SVD to identify single-ring tunnel point clouds and combines it with GMM for initial ring segmentation, enabling high-precision automated tunnel point cloud processing. SVD calculates the covariance matrix of the point cloud data and extracts the eigenvector corresponding to the smallest eigenvalue as the normal vector of the fitted plane. Additionally, the plane position is determined based on the geometric centroid of the point cloud. This method ensures that the fitted plane precisely passes through the center of the tunnel ring, maintaining the geometric accuracy of the single-ring structure. As a probability density estimation algorithm, GMM leverages the periodic distribution characteristics of tunnel point clouds along the ring segments, fitting each ring as an independent Gaussian distribution. The EM algorithm is then applied to optimize the computation of the ring center position and its boundaries, achieving an initial automatic segmentation of the tunnel. Although GMM exhibits good adaptability in ring segmentation of tunnel point clouds, local noise, uneven density, or acquisition errors in the data may still lead to blurred boundaries or discontinuous segmentation in some ring segments. Therefore, after GMM processing, we introduce an additional regularization procedure to further refine the segmentation results. These regularization operations include geometry-constrained neighborhood analysis to eliminate local errors and enhance the overall segmentation stability. Through this approach, we further improve the segmentation accuracy of tunnel point clouds, ensuring clearer ring boundaries and enhancing the structural integrity of the point cloud data. Ultimately, this method achieves tunnel segmentation with accuracy comparable to image-based approaches without relying on tunnel image information. Finally, after completing the tunnel lining classification, the ring plane fitting technology utilizes the SVD algorithm to perform cross-section extraction, using the tunnel core area as the center and based on tunnel ring point cloud data. This ensures that the extracted results are perpendicular to the tunnel alignment, avoiding the influence of extraction intervals and design axis accuracy. The method is both fast and accurate.