## 3 Methodology
### Structure Deterioration Identification  
2.1 Bridge Point Cloud Data Processing and Crack Detection Workflow (Apparent Disease Identification Method)  
Establishment of the Crack Detection Process Model  
The research objective involves projecting complex three-dimensional information onto multiple planes to construct a simplified two-dimensional set. Furthermore, by quantifying sparse regions within the data, potential crack locations are visualized. This method aids bridge engineers in selectively conducting on-site inspections for visible crack conditions. In relation to this methodology, the authors present a comprehensive process model for detecting structural cracks in bridges, as shown in the Figure 6 below. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Description** & **Suitability** \\ \hline Iterative Closest Point (ICP) & Iteratively finding the closest point pairs between two point clouds, optimizing rotation, and translation transformations. Uses features like normals, curvature, and keypoints for matching. & Suitable for small transformations between two point clouds. \\   Feature-Matching Methods & Uses features like normals, curvature, and keypoints for matching. & Suitable for larger transformations with low initial registration accuracy. \\   Surface-based Registration & Estimates a surface model for point cloud registration. & Insensitive to noise and missing data, best when surface shape changes are minimal. \\   Global Optimization Methods & Optimizes a global objective function using techniques like genetic algorithms or simulated annealing. & Best for large-scale point cloud data with complex transformations. \\   Deep Learning Methods & Utilizes CNNs or GANs to learn transformations between point clouds. & Suitable for complex or nonlinear transformations, leveraging data-driven approaches. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison table of point cloud registration methods. Figure 5: Manual registration renderings of point clouds. Code Implementation Section  
The point cloud processing workflow consists of several stages, including loading the dataset, calculating point density, establishing a sparsity threshold, and identifying sparse regions. Furthermore, this paper proposes calculating and normalizing the distances of point cloud data, and after reading the dataset, assigning corresponding three-dimensional coordinates to each point. Furthermore, the density of data points is quantified by the Euclidean distance between points within each plane. In this process, the paper defines that the distance between two adjacent points is inversely proportional to the density value of the point. Visualization tools are employed to highlight sparse regions within the 3D point cloud, with points below the defined threshold color-coded in shades such as red and blue to indicate varying levels of sparsity. In particular, the bridge crack detection code proposed in this study mainly performs the following tasks: (1) Point cloud data processing: The code first needs to load the three-dimensional point cloud data file and select the size of data points based on the actual conditions of the bridge engineering and computational power. (2) Density calculation: Calculate the distance of each point from its neighbors on different planes (xy, xz, and yz), and determine the density of the points based on the set threshold (distance_adiacent). (3) Marking sparse locations: The sparsity threshold is set by using the average point density and standard deviation, marking regions that fall below this threshold as sparse. (4) Visualization: Use the scatter3 function to visualize the dense and sparse points of the point cloud data in three-dimensional space. (5) Crack detection: Identify crack areas formed by sparse points through connectivity analysis, and calculate the attributes of these areas (including main axis length and secondary axis length).