## 1 Introduction  
The growth in transportation demand and the expanded utilization of underground space have driven the rapid development of tunnel engineering, leading to the continuous expansion of tunnel scale worldwide [1]. Shield tunnels have become the predominant form in most urban subway systems due to their advantages, such as construction convenience [2]. However, the growth in tunnel scale has also brought about a series of issues. Due to factors such as the aging of tunnel structures and the mechanical effects of the surrounding soil on the tunnel, structural deformation and damage inevitably occur. RThese issues ultimately affect the load-bearing capacity of the tunnel structure and pose safety hazards. At the same time, defects such as cracks, spalling, and lining water leakage are widely present in operational tunnels [3, 4], which also impact the load-bearing performance of tunnel structures. Therefore, structural inspections of tunnels play a crucial role in tunnel operations [5]. Traditional tunnel inspections primarily rely on manual methods, using tools such as measuring tapes, rangefinders, ground-penetrating radars, and total stations to collect data [6; 7; 8]. However, these measurement methods require significant time, manpower, and material resources during preparation and measurement. Additionally, the measurement accuracy for tunnel deformation is greatly affected by factors such as human intervention and the arrangement of measurement points [9]. Therefore, there is a significant demand for rapid and high-accuracy detection methods for structural deformation in the field of tunnel inspections. Light Detection And Ranging (LiDAR) has been widely applied in structural inspections due to its advantages, such as non-contact measurement and fast data acquisition. Laser scanning systems, including mobile laser scanning systems and tripod-based laser scanning systems, are also increasingly being utilized in tunnel inspections [10; 11]. However, laser scanning systems acquire surface point-cloud data of tunnels during the scanning process, and these raw point-cloud data contain a large number of non-structural facilities, such as pipelines and maintenance walkways. While these non-structural facilities have relatively little impact on the mechanical performance of the shield tunnel itself, the effectiveness of removing non-structural facility point clouds significantly affects the health inspection of the tunnel lining structure [12]. Numerous researchers have conducted extensive studies on point-cloud denoising, integrating various computer science theories into the denoising process. This has led to the development of a range of point-cloud processing techniques, including filter-based point-cloud denoising, optimization-based point-cloud denoising, and machine learning-based point-cloud denoising [13; 14; 15]. Filter-based point-cloud denoising primarily originates from the concept of filters in signal processing, where appropriately designed filters are used to remove unwanted noise components. This method typically smooths the data directly through weighted averaging or similar operations, eliminating noise while striving to preserve the characteristics of the original signal. For example, [PERSON] et al. [16]. considered the impact of three parameters--number of nearest neighbor points (N), Euclidean distance weight, and normal vector direction weight--on denoising performance and applied bilateral filtering to denoise point-cloud data in autonomous driving scenarios. Similarly, [PERSON] et al. [17]. denoised forest point-cloud data using statistical filtering, effectively segmenting ground point-cloud data and individual tree point-cloud data. In addition, filters such as statistical outlier removal (SOR) [18], geometry-based filtering [19; 20], and radius filtering [21] have also been applied to point-cloud denoising in various scenarios. Filter-based point-cloud denoising achieves good results when targeting specific point-cloud distributions.