## 2 Materials and Methods
### Data Acquisition System  
The MLS system used in this study enables high-precision data acquisition for tunnel deformation analysis. Mounted on a rail-borne platform, the system continuously emits laser beams to scan the surrounding tunnel surfaces, while sensors record the reflected signals to capture the spatial coordinates of millions of points. This results in a dense 3D point cloud representation of the tunnel's geometry. This study employed an independently designed SILSS, specifically developed for high-density point cloud acquisition in tunnel environments. It was independently designed and developed by the China Railway Design Group Co. Ltd., located in Tianjin, China The SILSS comprises key components, including a high-precision laser scanner capable of capturing 360-degree profiles, a control unit that synchronizes scanning with the movement of the railcar, an integrated positioning system for tracking the railcar's location and orientation, and a data storage unit for recording the acquired point cloud data. The system achieves geolocation through a combination of an odometer and an inertial navigation system (INS). The odometer measures the distance traveled by the railcar along the track, while the INS provides precise data on the orientation of the railcar and movement in three-dimensional space. This dual-system integration ensures sub-centimeter accuracy in determining the railcar's position along the tunnel, minimizing potential measurement errors with respect to an external reference point through continuous monitoring of both position and orientation during scanning. The SILSS operates at 100 profiles per second, achieving a profile interval of 5.6 mm and a laser point spacing of 1.6 mm, while moving at a controlled speed of 2 km/h (0.56 m/s). The system achieves a precision of \(\pm\)1 mm for its distance meter, ensuring high accuracy in point cloud data collection. These specifications ensure dense and accurate data collection during tunnel inspections.  
In this study, the SILSS was deployed in the shield tunnel section of Guangzhou Metro Line 1, which is 15.85 km in length underground, successfully capturing point cloud data from 102 shield rings, which constituted the experimental area (122 m), over two measurement sessions. The precise synchronization of scanning and positioning allowed for the determination of track chainage with sub-centimeter accuracy. As illustrated in Figure 2, the high-resolution data captured by the SILSS proved instrumental for 3D deformation analysis, ensuring reliable monitoring of structural integrity. [PERSON] et al. [2] provided further insight into the SILSS system's capabilities, emphasizing its mobility, accuracy, and adaptability for on-site measurements, particularly in complex tunnel environments. This  
Figure 1: Flowchart of the proposed method.  
system is highly effective for infrastructure monitoring, delivering consistent 3D models and deformation metrics crucial for assessing tunnel stability over time.  
The experimental dataset focused on a tunnel cross-section containing multiple adjacent shield rings connected by circumferential joints (or seams). The displacement analysis was based on the same cross-section at two different epochs (\(P_{0}\) and \(P_{i}\)). The first dataset represented \(P_{0}\) compared to \(P_{i}\). Therefore, based on the point cloud of the shield tunnel from the processing step, displacement analysis was executed on the shield level. Then, the 3D deformation magnitude was executed at the cross-section level to identify displacement regions. It was necessary to apply point cloud processing to both cross-section datasets to achieve this goal.