## 3 Methodology
### Structure Deterioration Identification
#### 3.2.3 Bridge Structure Deformation Detection Based on Point Cloud Data  
For detecting spatial morphological changes in bridges, it is crucial to consider both the structural characteristics of individual components and the overall form of the bridge. Therefore, the detection process should be divided into two categories: the deformation detection of bridge components and the overall displacement detection of the bridge. The detection tasks are completed through steps including feature recognition, point cloud segmentation, point cloud registration, and deformation parameter comparison, ensuring the safety and reliability of bridge engineering. The detailed framework of the deformation detection process model proposed in this paper is shown in Figure 9.  
Figure 8: Particle swarm optimization algorithm flowchart. Feature Extraction  
Before performing point cloud segmentation, it is necessary to select the appropriate feature descriptors to characterize the point cloud data, thereby refining the classification criteria for more accurate and detailed grouping. Commonly used features include surface normal, curvature, and normal histograms. During this process, feature descriptors can be employed to identify the characteristic points of the main beam and bridge piers. For the main beam, linear features can be extracted, while for piers, planar features are considered. When extracting features to distinguish between the beams and piers of bridges, the following types of features are typically considered:  
1. Surface Normal: These are vectors perpendicular to the surface of point cloud data, characterizing the direction and shape of the point cloud surface. Main beams often exhibit large flat surfaces with relatively consistent normal directions, tending to be orthogonal to the curvature direction with minimal variations in normal direction. Piers, on the other hand, typically have curved surfaces, showing larger variations and dispersion in normal directions. 2. Curvature: This feature describes the local curvature variation in the point cloud data and is useful for distinguishing between flat and curved sections. Main beams generally have smaller curvature values compared to piers, which exhibit larger curvature values. 3. Normal Histograms: These histograms depict the distribution of normals in different directions, reflecting the geometric shape of the point cloud surface. Histograms for main beams tend to show a more uniform distribution of normals, whereas histograms for piers may exhibit pronounced directionality. 4. Density: This metric reflects the number of points in different areas of the point cloud. Main beams typically have higher density, while the density of piers may be relatively lower. Figure 9: Framework diagram of deformation detection process model. Component Segmentation  
Due to the spatial morphological changes in bridges, which include the overall bridge deformation and component-level deformation, the former reflects the relationship between the overall bridge structure and its environment, such as the total settlement of the bridge, and also indicates changes in component boundary conditions. The latter needs to be further divided into the rigid body displacement of components and internal deformation considerations, which can reflect the internal forces and damage experienced by components. The analysis of internal deformation can provide insights into the structural performance of components, such as bending moments and torsion. Internal deformation and overall deformation mutually influence each other; internal deformation may reduce component stiffness and lead to the redistribution of internal stresses, potentially causing component failure. Therefore, it is necessary to first obtain spatial changes at the component level of the bridge in order to further analyze its mechanical properties. Based on extracted feature data, the effective segmentation of bridge components can be achieved. Figure 10 shows the segmentation results using bridge piers as an example.