## 2 Methods
### Reconstruction of 3D Pavement Macro Texture Evaluation
#### 2.4.2 Effectiveness Evaluation  
Fourteen different types of asphalt mixture test plates were used as research objects. Four scanning positions were randomly selected for each test plate for the calculation of MTD and \(f_{8}\). 56 sets of experimental data were obtained for the validity analysis of the reconstructed asphalt macro-texture. If the reconstructed texture features have a significant correlation with the measured features, this indicates that the reconstructed macro-texture structure is consistent with the actual pavement macro-structure [23].  
The evaluation metrics for the effectiveness of pavement macro-texture include arithmetic average height, root mean square height, kurtosis, skewness, and average texture depth. [PERSON] et al. [24] studied 14 feature indexes of the Grey Level Co-occurrence Matrix (GLCM) and demonstrated that the \(f_{8}\) (Sum Entropy) feature index has a strong correlation with MTD. Therefore, this paper uses MTD and \(f_{8}\) to evaluate the effectiveness of the reconstructed asphalt macro-texture. The Grey Level Co-occurrence Matrix refers to the probability that the gray level of a pixel at a distance of (\(d_{x}\), \(d_{y}\)) from a pixel with a gray level of \(i\) is \(j\), as shown in Formula (19). The calculation formulas for \(f_{8}\) are provided in Formulas (20) and (21):  
\[P(i,j|d,\theta)=\#\{(x,y)|f(x,y)\}=i,f(x+dx,y+dy)=j,x,y=0,1,2\ldots,N-1 \tag{19}\]  
where \(d\) is the spatial distance between two pixels; this paper takes 1; \(\theta\) is the direction considered when sampling the image; this paper takes 90\({}^{\circ}\); \(\#\) is a collection; \(i,j=0\), 1, 2\(\ldots\), \(L-1\):  
\[f_{8}=-\sum\limits_{k=2}^{2N_{g}}P_{x+y}(k)\log\{p_{x+y}(k)\} \tag{20}\]  
\[P_{x+y}(k)=\sum\limits_{\begin{subarray}{c}i=1\\ i+j=k\end{subarray}}^{N_{g}}\sum\limits_{j=1}^{N_{g}}P_{d}^{\theta}(i,j) \tag{21}\]  
where \(P_{d}^{\theta}\) (\(i,j\)) is the probability of the occurrence of the pixel pair (\(i,j\)); \(N_{g}\) is the maximum gray level of gray image.  
The average structural depth is measured using the sanding method. As shown in Figure 9, a measuring cylinder with a capacity of 40 cm\({}^{3}\) is filled with dry sand. Four scanning positions are randomly selected, and the dry sand is evenly spread over a rectangular area of the paving plate. The remaining volume of dry sand, \(V^{\prime}\), in the measuring cylinder is recorded after covering the unmeasured area. The ratio of the volume of sand used to cover the rectangular area to the coverage area gives the average structural depth of the area. The calculation formula is shown in Equation (22):  
\[MTD=\frac{(40-V^{\prime})\times 1000}{L\times W} \tag{22}\]  
where MTD represents the average texture depth of asphalt pavement; \(V^{\prime}\) represents the remaining amount of sand in the sand barrel; \(L\), \(W\) denotes the length and width of the dry sand coverage area.  
Figure 9: Sanding method.  
Through the proposed CNN model, the 3D model of asphalt macro-texture can be reconstructed, and the average texture depth of asphalt macro-texture can be directly calculated by using the pavement elevation data in the 3D model. The calculation formula is shown in Equation (23):  
\[MTD^{\prime}=\frac{\sum_{j=1}^{M}\sum_{i=1}^{N}\left(Z_{\max}-\varepsilon-Z_{ij} \right)\times s}{S} \tag{23}\]  
where \(MTD^{\prime}\) is the average construction depth of macro texture calculated by using 3D model; 5 is the area of the reconstructed texture corresponding to the dry sand coverage area; \(s\) is the area of each scanning point; \(i\) is the number of pixels of a texture contour; \(j\) is the number of texture contours; \(Z_{\max}\) is the maximum depth value of the reconstructed texture; \(z_{ij}\) is the depth value of the \(i\) th pixel in the \(j\) th texture contour; \(\varepsilon\) is the correction parameter of \(Z_{\max}\), and the value in this paper is 0.8.