# Differences Evaluation of Pavement Roughness Distribution Based on Light Detection and Ranging Data
## 3 Calculation of the Pavement Roughness Based on 3D LiDAR Data  
### Road Profile Extraction  
The extraction of the road centerlines and road profiles based on point cloud data is a critical step in road surveying. In order to obtain the road surface area, road centerline extraction should be performed first by extracting the centerline from the road profile, which is parallel to the road direction, followed by the extraction of the road profiles according to a specific sampling spacing. Two main approaches are commonly employed for extracting the road centerline from the point cloud data. The first approach involves the direct fitting of the road centerline through the point cloud data of the road surface. The second approach involves obtaining the road boundary area first using a certain method, and then estimating the median value as the road centerline by fitting the road linearity on both sides of the boundary. However, the accuracy of the first approach is affected by the quality of the collected data. When the detected vehicle does not drive along the road centerline but along the left or right lanes, the fitted centerline tends to be biased towards one side of the road.  
Therefore, the second approach was employed, determining the road boundary and extracting the centerline. Unlike the first approach, this approach obviates the need to employ all the point cloud data to compute the road boundary, thereby eliminating the necessity of performing a down-sampling operation on the original point cloud data. However, the problem of road alignment still requires redressal by the method of segmentation statistics. As illustrated in Figure 4a, the road boundary on both sides generally conforms to the maximum or minimum values in the X or Y direction. Based on this assumption, a straight line parallel to the X-axis or Y-axis was moved along the corresponding direction, and the maximum and minimum intersection points with the point cloud data were then recorded. The boundary equation was then derived by fitting the intersection points set of the upper and lower sections. The midline equation was then established, which is a line that is parallel to the upper and lower boundaries and at the same distance from them. As the length of the road cross-sections is generally less than that of the road profiles, the moving line is selected by comparing the length of the road point cloud data in the X and Y directions, with the shorter length deemed as the moving line. In addition, after the maximum and minimum values were extracted, the spacing between each pair and their mean values were calculated for processing the starting and ending areas. Pairs whose spacing deviated from the mean within a certain range were excluded as outliers.  
Figure 4: Extraction of the road profile. (**a**) Extraction of the road boundary. (**b**) Extracted road centerline.  
As shown in Figure 4b, this fitting method demonstrated a favorable outcome in extracting the road centerline. The extracted centerline is aligned with the road direction, effectively avoiding the impact of uneven point cloud density, which is a limitation encountered in the first method. In addition, the advantage of using this method was that the segmentation statistics method was adopted to avoid the centerline fitting problem of the non-straight road sections as much as possible. Consequently, the proposed method can be applied to straight and multiple curves, enhancing its applicability in various road alignments.