## 2 Methods
### Data Set
#### 2.1.2 Point Cloud Data Preprocessing  
Due to the irregularity in the texture of the asphalt surface, the light intensity in certain depressed areas falls below that of the threshold that can be recognized by the laser texture scanner. These regions fail to provide accurate depth information, leading to the loss of some data in the acquired point cloud. This data gap affects the precise representation of the macro texture of the asphalt pavement. Compared to other methods, linear interpolation offers advantages, such as fast computation, broad applicability, and simplicity, making it an effective approach for filling in missing point cloud data. Therefore, to mitigate the impact of missing points on the reconstruction results, this paper employs the linear interpolation method for data imputation, as shown in Equation (1):  
\[Z_{i,j}=\frac{Z_{nj}-Z_{mj}}{n-m}(i-m)+Z_{mj} \tag{1}\]  
where \(i\) represents the number of missing points, \(j\) represents the \(j\)th texture contour, \(m\) represents the number of the nearest effective point before \(i\), \(n\) represents the number of the effective value point closest to \(I\), \(z_{ij}\) represents the value of the interpolation of the point \(i\) in the extracted texture contour, \(z_{mj}\) represents the value of \(n\) in the sample of texture contour \(j\), and \(z_{mj}\) represents the value of sample m in the texture contour \(j\). In addition, the spikes observed in the 3D point cloud data of the road surface are abnormal points with significant amplitude, which can introduce errors in the calculation results and negatively affect the computation, such as texture characterization of asphalt pavement. Therefore, this paper adopts the bilateral filtering algorithm to remove the noise. The bilateral filtering algorithm constructs a surface using noisy points and their local neighborhood points, shifts the noisy points along the normal direction, and achieves a smoothing and denoising effect by iteratively adjusting the positions of the noisy points. Figure 2: Establishment of macroscopic texture data set of asphalt pavement: (**a**) Acquisition of asphalt pavement texture image; (**b**) Uncut 2D images; (**c**) 2D image after cutting; (**d**) Scanning point cloud depth image. Compared with other methods, this approach offers advantages such as strong adaptability, broad applicability, and reduced artifacts. The results before and after denoising are shown in Figure 3, and the bilateral filtering formula is shown in Equation (2)  
\[B_{j}^{\prime}=B_{j}+\alpha\cdot n_{j} \tag{2}\]  
where \(B_{j}\) represents the 3D coordinates of the point before filtering; \(\alpha\) represents the filtering factor of bilateral filtering; \(n_{j}\) denotes the normal vector of \(B_{j}\); and \(b_{j}\) represents the three-dimensional coordinates of the point after bilateral filtering. In the process of collecting point cloud data for asphalt surface texture, it is challenging for the laser texture scanner to be perfectly parallel to the surface of the specimen, leading to a tilt in the overall texture data. This tilt causes significant deviations between the calculated results and the actual values, which in turn affects the accurate evaluation of the surface texture. To address this, this paper proposes a planar model that accounts for the inclination of the pavement texture. By calculating the deviation between the projection of each point on the plane model and its original position, the model corrects the inclined texture data. Commonly used plane fitting methods include the least squares method and the eigenvalue method [17]. The least squares method, however, only considers errors in the elevation (\(z\)-direction) and results in unstable corrections across different coordinate systems [18]. Therefore, this paper adopt the eigenvalue method to fit the plane that reflects the inclination of a pavement texture.