## 1 Introduction
However, the selection of parameters for this method (such as the inlier threshold and the number of iterations) relies on experience, and the tuning process is quite cumbersome. Moreover, because this method is based on random sampling, the ellipse-fitting results obtained with RANSAC tend to be unstable and lack repeatability. In addition, B-spline curves [44] have also been applied to the curve fitting of tunnel cross-sectional point clouds. This method can generate smooth, continuous curves with excellent local control, making it suitable for describing complex tunnel cross-sectional shapes. However, it is sensitive to the selection of initial control points and parameter settings, and inappropriate settings may lead to fitting bias. Machine learning-based point-cloud denoising does not rely on manually defined filters or objective functions. Instead, it denoises through a data-driven approach, leveraging the powerful computational capabilities of computers to uncover the inherent patterns and features within the data. Machine learning primarily includes two types: supervised learning and unsupervised learning. In the field of point-cloud denoising, unsupervised learning denoising methods are often based on clustering techniques. These methods group similar data points into clusters and identify and remove outliers or noise points to achieve denoising. Density-based clustering algorithms such as DBSCAN [45]; PCA-based adaptive clustering [46]; the DTSCAN clustering method based on Delaunay triangulation and the DBSCAN mechanism [47]; clustering based on spatial distance, normal similarity, and logarithmic Euclidean Riemannian metrics [48]; and K-means clustering based on local statistical features of point clouds [49] have been applied to point-cloud denoising. These methods have achieved good denoising results for point-cloud data with distinct geometric distribution features. These unsupervised learning models typically do not require explicit labels. Instead, they learn the inherent features of the data by identifying structures, patterns, or correlations within the data. In contrast, supervised learning involves learning from labeled training data to predict outcomes for new, unseen data. In the field of point-cloud denoising, supervised learning-based denoising is often achieved using neural networks. Network architectures such as PointNet and convolutional neural networks (CNNs) have been applied to point-cloud denoising. The PointNet [50] and PointNet++ [51] architectures, which can directly process point-cloud data, have opened new directions in the field of 3D data processing and have driven the development of point-cloud processing networks. Improved versions of the PointNet network, such as PointCleanNet [52], which focuses on the fusion of local and global features of point clouds, and PCPNet [53], which emphasizes the estimation of local geometric features like normal vectors and curvature, have demonstrated good performance in point-cloud denoising tasks. PointNet has relatively weak local feature extraction capabilities and lacks spatial structure awareness of point-cloud data. To address this, some researchers have employed improved convolutional neural networks (CNNs) for point-cloud denoising tasks [54; 55; 56; 57]. For existing convolutional neural networks (CNNs), the unstructured and sparse nature of point-cloud data does not perfectly match the input data requirements of CNNs. Therefore, the use of CNNs for point-cloud denoising still has room for improvement. In machine learning-based point-cloud denoising, DBSCAN clustering [58] has been applied to tunnel point-cloud denoising. In the aforementioned research on point-cloud denoising, various models of laser scanning devices have been applied for point-cloud acquisition.