## 3 Methodology
### Spatiotemporal Data Collection and Processing  
Following the preliminary processing of bridge point cloud data with CloudCompare, this paper employs a conditionally repeated sparse processing method for the point cloud, which simplifies and reduces the volume and storage requirements of the data while preserving the relative density values among different features. This strategy is crucial for maintaining the reliability of the subsequent analysis phases [39]. Figure 2 clearly illustrates the comparison between the processed point cloud data and the original data following the aforementioned steps. Figure 1: Vision map of research methods in articles. Due to factors such as sensor errors, environmental interference, vibrations, or movements during data collection, outliers and noise points may occur in the bridge point cloud data [40]. Figure 3 highlights and enlarges the outliers and noise points present in the bridge point cloud data. These points can negatively impact subsequent modeling, detection, and structural analysis, and therefore need to be removed to enhance data quality and accuracy. This processing ensures that the subsequent analysis and handling are more reliable and effective. Therefore, this paper selects the gradient filtering algorithm and the Bilateral filtering algorithm for point cloud filtering, completing the cleaning preprocessing of the point cloud data. The gradient filtering algorithm is a commonly used filtering method that removes noise points and outliers from point cloud data. This algorithm identifies and filters out the points that do not conform to the gradient change pattern based on the gradient information of the point cloud data, achieving the purpose of denoising and removing outliers. The authors adjusted the relevant parameters in CloudCompare, including the gradient threshold T (gradient threshold), search radius R (search radius), neighborhood size S (neighborhood size), and kernel size. Through manual debugging, it was found that the applicable numerical ranges for the four parameters in the bridge point cloud data processing are \(0\leq\) T \(\leq\) 1; \(0.1\leq\) R \(\leq\) 1; \(5\leq\) S \(\leq\) 20; \(10\leq\) kernel size \(\leq\) 20. Finally, filtering was performed using gradient-based techniques. The Bilateral filtering algorithm is based on two kernel functions: one for measuring the spatial distance between points and the other for measuring the difference in attribute values between points. First, the spatial distance and similarity of attribute values between points are calculated to determine the filtering coefficients. Then, these coefficients are used to perform a weighted average of the point cloud, selectively removing some adjacent sampling points that are too different from the current sampling point, thus achieving  
Figure 3: Schematic diagram of noise and outliers in bridge point cloud data. Figure 2: Point cloud secondary thinning process and effect diagram. noise removal and smoothing. For parameter selection, the study found through manual debugging that the spatial standard deviation (spatial standard deviation) should be chosen to be smaller, with a range of values between 0.1 and 0.5; the range standard deviation (range standard deviation) should be selected according to the size of the bridge point cloud data, with a range of values between 0.1 and 1.0. After consulting with several experienced bridge engineers, the authors have made the informed decision to utilize the three-dimensional point cloud model of Hedong Bridge, along with its corresponding parameters, for the analysis. This choice reflects a careful consideration of the bridge's structural significance and the suitability of its data for the proposed research objectives. So, taking the point cloud data of Hedong Bridge in 2018 as an example, the authors applied the two gradient filtering algorithms for data cleaning, effectively eliminating outliers, scattered points, and noise points in the bridge point cloud data, thereby improving the data quality.