## 5 Conclusions  
LiDAR is widely used in tunnel and other construction structure measurement and inspection due to its advantages such as non-contact measurement, fast data acquisition speed, and high automation. However, the presence of non-structural facilities, such as pipelines, within tunnel structures can interfere with the detection of tunnel lining structures. To address the noise point clouds, this study proposes a tunnel cross-section fitting and projection denoising method based on the Huber loss function, as well as a point-cloud coordinate system transformation method. The research has achieved the following outcomes:  
1. A tunnel cross-section point-cloud ellipse-fitting and denoising method based on the Huber loss function and the shortest radial distance projection is proposed. This method can denoise raw tunnel point-cloud data without preprocessing, effectively removing noise points while preserving the geometric features of the tunnel lining, and it has good computational efficiency.  
2. A method based on PCA and Huber loss function for tunnel point-cloud coordinate transformation was proposed. This method effectively transforms the tunnel point-cloud coordinate system, aligning the tunnel point-cloud data with the Cartesian coordinate system axes (orthogonally), reducing the errors caused by manually rotating the point cloud during the denoising process.  
3. When evaluating the denoising effect, in addition to calculating the entire point-cloud section, the top point cloud with fewer non-structural facility point clouds on the top of the tunnel was also selected for calculation, which more comprehensively reflects the denoising effect of the tunnel point cloud.  
In the next phase of this work, we will continue to improve the algorithm and optimize the denoising effect of the method on the bottom point cloud (tunnel-track point cloud). At the same time, the method will be adjusted to effectively denoise point-cloud data for more complex tunnel structures, such as non-circular tunnels and curved tunnels.  
Conceptualization, S.L.; methodology, S.L.; software, S.L.; validation, Y.B. and S.L.; formal analysis, Y.B.; investigation, S.L.; resources, C.T.; data curation, C.T. and Y.W.; writing--original draft preparation, S.L.; writing--review and editing, S.L. and K.Y.; visualization, S.L.; supervision, Y.B. and Z.S.; project administration, Y.B.; funding acquisition, Y.B. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fitting Denoising Method** & **Huber Loss-Based Method** & **Least-Squares Method** & **RANSAC Method** \\ \hline Algorithm Running Time & 1 min 33 s & 20 s & 11 h 48 min 43 s \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of algorithm running time.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant numbers 52378385 and 51829801.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** The first author would like to thank [PERSON], [PERSON] and [PERSON] for providing some suggestions to improve the paper.  
**Conflicts of Interest:** The authors [PERSON] and [PERSON] are employed by Beijing Urban Construction Survey and Design Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.