## 4 Conclusions  
In this paper, we propose an efficient framework to extract tunnel cross sections from the Terrestrial Laser Scanning point clouds. Our framework starts with the extraction of the tunnel axis using a robust slice-based method. To get an accurate position of the tunnel profiles, we further divide the initial axis into linear and nonlinear segments via an enhanced RANSAC algorithm. In contrast with the traditional RANSAC algorithm, our algorithm has been implemented in the tangent space rather than the data space. By this way, the simultaneous linear and nonlinear axis segmentation problem is thus translated into sole linear element segmentation. It does not only reduce the complex of segmentation but also increases the credibility of segmented results. Based on the segmented axis segments, we can fit the linear and nonlinear segments via the linear regression model and the polynomial regression model, respectively. The extracted attitude of the three-dimensional tunnel axis lays a solid foundation for accurate extraction of tunnel cross sections. The initial cross-sectional points are generated by intersecting a sequence of straight lines that rotate orthogonally around the tunnel axis with the corresponding local quadric surfaces. It should be noted that the size of the quadric surface is not a constant but progressive adjustment according to the density of the local point clouds. This advantage helps the algorithm to adapt to the variations of point clouds and makes the algorithm insensitive to the point density. The initial cross-sectional points are further refined and densified via a \"fitting-and-resampling\" strategy. That is, the coarse cross-section points are first fitted by an assumption of circular tunnel, i.e., using the circular shape/model to fit the cross-sectional points, followed by resampling of the circular shapes. This process significantly enhances the completeness of cross-sectional points, and more importantly makes the proposed algorithm resistant to missing data. The results on Nanjing dataset show that the RMSE of the fitting accuracy of the cross sections is 1.687 mm. Compared with the design value of 2.75 m, the RMSE of the radii of extracted cross sections is only 1.60 mm. In addition, by trial-and-error experiments, we find that reconstructing the entire metro tunnel model via cross sections evenly spaced at a distance of around 4 m can get the relatively minimum geometric errors. It should be aware that the extracted tunnel profiles have explicit topology information not only existing within each profile but also among multiple profiles. This is beneficial to geometric processing oriented applications such as metro tunnel reconstruction, model editing and retargeting. We also compare our results with the state-of-the-art method proposed by [PERSON] [1] based upon the same dataset, i.e., Shanghai metro tunnel point clouds. It is to be proved that our methodology can cope with large-area missing data and successfully extract the profiles from very  
Figure 15: Tunnel profile extraction from one scan of Shanghai metro tunnel dataset. The raw tunnel point clouds are shown in (**a**), where large-area of missing data and severe variations of point density are shown in the enlarged view of (**b,c**). The extracted 260 metro tunnel profiles, denoted by the black points, are overlaid onto the raw data. From the zoomed views (**d–f**), we can vividly see that the missing data areas are filled by the extracted profiles, and meanwhile the profiles are successfully derived from extremely sparse point clouds. sparse and unevenly distributed point clouds. Meanwhile, based on the Shanghai dataset, the RMSEs of extracted cross sections' radii with regard to the design radius of 2.75 m are only 4.6 mm, which is superior to [PERSON]'s method of 6 mm. Although our algorithm achieves promising results on Nanjing and Shanghai datasets, there are some drawbacks and interesting ideas which can be further explored to extend the research reported in this paper.