## 1 Introduction
In filter-based point-cloud denoising methods for tunnel structures, filtering techniques such as cloth simulation filtering (CSF) [22] and wavelet transform [23] have achieved promising results. Optimization-based point-cloud denoising methods formulate the denoising process as an optimization problem. By defining objective functions based on geometric properties and noise distributions, these methods seek a denoised point cloud that best fits the objective function derived from the input noisy point cloud. Fitting methods, represented by the least-squares method [24], have achieved notable results in point-cloud denoising. This approach introduces locally approximated surface polynomials to adjust point set density, enabling the smooth reconstruction of complex surfaces while minimizing geometric errors. The least-squares method and its improved variants have also been widely applied in the denoising of point-cloud data [25; 26; 27; 28]. Meanwhile, the least-squares method, combined with other denoising techniques such as outlier filtering [29] and local kernel regression (LKR) [30], has also been applied to point-cloud data denoising. In addition to the least-squares method, other fitting optimization techniques, such as local optimal projection (LOP) [31], weighted local optimal projection (WLOP) [32], and moving robust principal component analysis (MRPCA) [33], have also been widely applied. Some of the aforementioned point-cloud denoising techniques have also been applied to the processing of tunnel-structure point-cloud data. [PERSON], [PERSON] et al. [34] conducted research on denoising tunnel cross-sectional point clouds by leveraging the geometric features and intensity information of the point-cloud data. Their method effectively removes most noise points in the tunnel point cloud, thereby improving data quality and accuracy. However, because this method requires manually transforming the coordinate system and extracting the cross-section based on the point cloud's geometric and intensity features, the denoising accuracy is significantly affected by factors such as equipment, environment, and the precision of manual data preprocessing. Consequently, its robustness under complex tunnel conditions is relatively poor. Since the tunnel cross-sectional structure exhibits minimal variation along the tunnel's mileage, some scholars have extracted tunnel cross-sections along the mileage direction based on this structural characteristic [35] and performed denoising on individual cross-section point clouds. Moreover, [PERSON] et al. [36] projected the three-dimensional point cloud onto a two-dimensional plane and extracted the tunnel axis by obtaining the planar skeleton, thereby achieving tunnel cross-section extraction. In addition, some researchers employ ellipse-fitting methods to model the boundary lines of tunnel point clouds and, based on the fitting results, remove outliers to complete both the denoising of tunnel cross-sectional point clouds and the extraction of the cross-section. Among various ellipse-fitting methods, the least-squares method [37; 38; 39; 40] is widely used. The least-squares method can effectively fit and denoise tunnel point clouds that contain relatively few noise points and where the noise causes only minimal dispersion of the fitted curve. However, some tunnel point clouds contain a significant amount of discrete noise, such as those generated by tunnel pipelines, making it difficult for the least-squares method to perform effective fitting and denoising. In order to improve the robustness of the fitting method against noise, some researchers have employed RANSAC [41; 42; 43] to fit tunnel cross-sectional curves. RANSAC is highly robust method capable of extracting valid data even in the presence of a large amount of noise and outliers, making it suitable for complex point-cloud distributions with unevenly distributed noise or numerous outliers.