## 1 Introduction
[14] demonstrated that ICP and its variants could achieve high alignment accuracy, particularly in structured environments like tunnels, by minimizing the error between points of consecutive scans. Moreover, methods such as Coherent Point Drift (CPD) and probabilistic approaches have been proposed to address alignment challenges posed by complex, large-scale point cloud data. Studies such as that by [PERSON] et al. [15] have demonstrated their applicability in environments with high variability. Quantifying displacements from point cloud data is fundamental for assessing structural changes. Several studies have applied displacement analysis to MLS data for tunnel monitoring, focusing on identifying shifts in tunnel surfaces between successive scans. [PERSON] et al. [16] proposed a method that combines segmentation and spatial alignment to isolate deformed regions and quantify displacements. Such methods use metrics like the mean square error and centroid shifts to map surface changes effectively. Likewise, [PERSON] et al. [17] developed a point-to-plane analysis framework, which aligns point cloud segments to evaluate the distribution and magnitude of displacements, highlighting subtle yet critical shifts that indicate potential structural risks. Deformation analysis using point clouds has become an essential tool in tunnel engineering, especially for evaluating the structural stability of aging infrastructure [18]. Ovality and axis-based metrics have been extensively used to detect distortions in tunnel cross-sections. For instance, [PERSON] et al. [19] utilized Principal Component Analysis (PCA) for fitting ellipses to tunnel cross-sections, enabling the calculation of deformation indicators such as major and minor axis variations. Additionally, research by [PERSON] et al. [20] employed 3D model fitting techniques to monitor the evolution of cross-sectional deformations, successfully applying these metrics in practical tunnel safety assessments. [PERSON] et al. [21] utilized point cloud data to automate deformation detection in shield tunnels, enhancing accuracy and efficiency compared to traditional methods. While these advancements significantly enhance tunnel deformation monitoring, challenges remain in ensuring the robustness of algorithms across diverse environments and conditions, such as 3D point cloud displacement for circular shield tunnels. Building on these advancements, this study aims to develop a comprehensive three-dimensional point cloud displacement analysis framework for detecting tunnel deformation using MLS data. The proposed approach involves aligning sequential point clouds from consecutive scans, measuring displacements, and analyzing deformation patterns through metrics such as the average of the tunnel cross-section displacement, centerline shifts, and ovality based on MLS shield ring point clouds. The experimental study used the methodology by comparing MLS point cloud data collected in different periods via the Self-Mobile Intelligent Laser Scanning System (SILSS). The accuracy of the proposed method was assessed by comparing the SILSS with the Leica Pegasus Two Ultimate scanner, using metrics like average point cloud displacement and ovality.