## 4 Discussion  
From the experimental results that we have reported in the previous section, it can be seen that the point-cloud denoising method based on the Huber loss function can effectively denoise the point-cloud data of the shield-tunnel section, and the highest accuracy can reach the millimeter level. This method demonstrates good denoising performance for both individual cross-sectional point clouds and the entire-tunnel point cloud, indicating its robustness to complex noise distributions. This robustness is due to the fact that the Huber loss function uses squared error for small deviations--making it highly sensitive to minor errors--and linear error for large deviations, thereby reducing the influence of outliers or anomalous points on the overall fitting result. This characteristic ensures that noise from non-structural facilities such as pipelines does not excessively interfere with the final fitting, thus allowing for the accurate extraction and denoising of the main tunnel structure (tunnel lining structure). Moreover, the Huber loss function exhibits smoother error variations, combining the high precision of mean squared error when the data are relatively clean with the robustness of absolute error when handling noisy data, thereby enabling effective denoising even for tunnel-top point clouds that contain fewer noise points. In order to evaluate the merits and drawbacks of the denoising performance of the proposed method, this study compares the denoising effect of the elliptical-fitting denoising \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Metrics** & **MSE(m2)** & **RMSE(m)** & **MAE(m)** \\ \hline Result & 0.04337 & 0.20412 & 0.12645 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical table of denoising evaluation metrics for the entire-tunnel point cloud. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Metrics** & **MSE(m2)** & **RMSE(m)** & **MAE(m)** \\ \hline Result & 0.00034 & 0.01447 & 0.01118 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical table of denoising evaluation metrics for the tunnel-top point cloud (60\({}^{\circ}\)–120\({}^{\circ}\)). method based on the Huber loss function with that of a widely used free point-cloud processing software. Taking into account factors such as the user base and whether the software is open source, this study selected CloudCompare version 2.10 as the benchmark for the denoising performance comparison. CloudCompare is an open-source 3D point-cloud processing software that focuses on handling high-density point-cloud data and 3D meshes. Its primary functions include point-cloud alignment, registration, segmentation, denoising, resampling, and geometric feature extraction, among others. This software is widely used in point-cloud data processing tasks in fields such as engineering surveying and archaeological mapping. In this study, tunnel point-cloud data were denoised using CloudCompare software version 2.10, with the software interface shown in Figure 16. CloudCompare allows for denoising by manually selecting and removing points from the cloud. However, due to the enormous volume of tunnel point-cloud data, manually denoising the data consumes a considerable amount of time and manpower. Moreover, manual denoising often introduces human errors, which can affect the accuracy of the denoising process. In addition, CloudCompare software also includes a statistical outlier removal (SOR) filtering denoising function that can automatically denoise point clouds. The denoising effect is shown in Figure 17, where blue represents the original point cloud and red represents the denoised point cloud. As can be seen from the results, point-cloud denoising based on the SOR filter in CloudCompare is capable of removing some outlier points from tunnel point clouds; however, it is difficult to remove noise with a continuous spatial distribution, such as pipeline point clouds.