## 1 Introduction
To obtain the accurate direction of the cross-sectional planes, the authors in [14] optimize the initial cross sections by means of twice adjustments using the total least squares method and Rodrigues' rotation formula, respectively. The critical step for profile-based methods is to obtain the real cross-sectional points. To this end, some methods focus on how to eliminate non-lining points (accessories) from the raw point clouds. Generally, two types of methods are used to remove non-lining points. The first method is based on the geometric characteristics of the tunnel. More specifically, it is assumed that the tunnel can be fitted by the circular model [1; 11; 12; 14; 15] and then uses the circular filtering to filter cables and other equipment in the tunnel. The second method separates liner and accessories by combining TLS geometric and radiometric information. For example, the results in [16] demonstrate that the corrected intensity information is an effective physical criterion and a complementary data source to removeaccessories that cannot be eliminated by sole geometric information. In another method, [PERSON] et al. (2018) use the radiometric characteristics for Mobile Laser Scanning (MLS) data to filter the accessories from the tunnel raw data, which cannot be directly used for processing the TLS point clouds because not only the scattering property of an object but also other variables, especially distance and incidence angle effects will influence backscattered energy in TLS data ([PERSON] et al., 2016). To address this deficiency, [PERSON] et al. (2017) further investigate the effect of distance on the intensity of TLS data and propose a new correction method for different TLS scanners to overcome the deficiency of directly using the original intensity. Although the acquisition of actual geometric parameters for inspection of tunnel is efficient, accurate and has flexible implementation from TLS point clouds, the profile-based works are more restricted regarding pointwise and piecewise description of the profiles. That is, the profile-based method has some potential risks between the areas of adjacent cross sections, where the slight deformations might not be tracked. To address this issue, the profile-based method has been expanded to an overall evaluation of tunnel models. For example, [PERSON] et al. (2019) reconstruct the models by means of triangulating tunnel point clouds to detect the underbreak and overbreak areas. [PERSON] and [PERSON] (2018) use the non-uniform rational B-spine (NURBS) fitting technique to achieve parametric representation of arbitrary 3D geometries from point clouds. [PERSON] and [PERSON] (2019) present an algorithm for automated quantification of discrepancies for components of assemblies by using skeletonized 3D models and TLS laser scans. [PERSON] and [PERSON] (2018) propose a novel clearance inspection technique to generate the high-resolution digital surface model of a railway tunnel surface (bare lining) from TLS point clouds. By introducing a high-accuracy interpolation and filtering algorithm, this method can generate bare-lining models without limitation of tunnel cross section shapes. In Ref. (2019), the scanned surface of a bored tunnel is approximated with a cylindrical model, and the point-wise deformation analysis is performed by comparing surface patches. Although the tunnel model-based method can detect the minor differences by comparison with the tunnel models generated at different times, this type of method is sensitive to non-lining point clouds, which means the real deformation and displacement can be hidden behind the artifacts of the created tunnel models. In addition, the generation of tunnel models ranging from geometric primitives, e.g., planes, cylinder or spheres, to more complex ones, such as parametric patches and NURBS is time-consuming, which does not meet the requirement of real-time interaction for processing large-scale TLS point clouds.