## 2 Morphological Characteristic Evaluation
### Texture
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Texture Indexes** & **Equations \({}^{*}\)** & **Characteristics** & **Literatures** \\ \hline Texture factor (TF) & \(\sum_{\text{P}=1}^{N}\sum_{\text{q}=1}^{N}\left[\left(\frac{a(p,q)}{a_{0}} \right)^{2}+\left(\frac{b(p,q)}{a_{0}}\right)^{2}\right]-AF\) & Fast measurement of aggregated morphological features based on 2D fast Fourier transform. & [55] \\ Texture index (TI) & \(\frac{1}{3N}\sum_{i=1}^{3}\sum_{j=1}^{N}\left(D_{ij,i}(x,y)\right)^{2}\) & Quantization of textures using wavelet methods. & [55] \\ Erosion dilation area ratio (EDR) & \(\frac{A_{1}-A_{2}}{A_{1}}\times 100\%\) & Changes in area after erosion and dilatation cycles are directly related to aggregate texture. & [56] \\ Comprehensive erosion dilation area ratio (CEDR) & \(\frac{\sum_{i}^{n}(a_{i}\times EDR_{i})}{\sum_{i}^{n}a_{i}}\) & Aggregate gradation is considered. & [57] \\ Surface texture & \(\sum_{m=n_{2}+1}^{m=n_{3}}\sqrt{a_{m}^{2}+b_{m}{}^{2}}\) & The shape, angularity and texture of the aggregates are considered separately. & [38] \\ Fourier series analysis method & \(\frac{1}{2}\sum\limits_{m=n_{2}+1}^{m=\infty}\left[\left(\frac{a_{0}}{a_{0}} \right)^{2}+\left(\frac{b_{m}}{a_{0}}\right)^{2}\right]\) & Calculation of the surface fabric of aggregates used in PIAS. & [23] \\ Direct measurement of aggregate dimensions & \(\left(\frac{p}{P_{\text{source}}}\right)^{2}\) & For evaluating textures, the texture parameters are related to the perimeter. & [44] \\ Three-dimensional Texture (MT\({}_{3D}\)SHF) & MT\({}_{3D}=\sum\limits_{n=26}^{n_{\text{max}}}\sum\limits_{m=-1}^{n}|a_{nm}|\) & 3D textures can be calculated.Can differentiate between aggregates with similar sizes.Used to compare aggregates of different sizes and volumes. & [58] \\ Texture (MT\({}_{3D}\)SHF) & MT\({}_{3 DN}=\frac{MT_{3D}}{a_{0}}\) & & \\ \hline \hline \end{tabular}  
* \(N\)—the level of decomposition; \(i\)—a value of 1, 2, or 3 for the three detailed images of texture; \(j\)—the wavelet coefficient index. \(A_{1}\)—the 2D profile area of the aggregate; \(A_{2}\)—the 2D profile area of the aggregate after the erosion and expansion. \(a_{i}\)—the proportion of the \(i\)th grade aggregate in the gradation; \(EDR_{i}\)—erosion expansion area ratio of the \(i\)th grade of aggregate in the sample. \(P\)—the perimeter of a particle measured on a black and white image; \(P_{\text{source}}\)—the perimeter of a bounding polygon. \(MT_{3D}\)—3D microstructure.  
\end{table} 
Table 3: Texture index of aggregate with calculation equations and main characteristics. it is difficult for the researchers to control the aggregate morphological characteristics variables [63]. [PERSON] et al. [64] mixed aggregates from different sources and tested them using AIMS to obtain aggregates with different angles and textures; nevertheless, it was impossible to distinguish which morphological characteristics were responsible for the effect. [PERSON] et al. [65] employed a modified Los Angeles (LA) wear test to obtain aggregates with different angles, calculated the fractal dimension and changed the size and surface texture of the aggregates. [PERSON] et al. [66] proposed a 3D model evaluation method for pavement texture based on digital image processing techniques, which used photographs to generate a Digital Surface Model (DSM) to calculate the digital Mean Texture Depth (MTD) and calculate and analyze other texture parameters for contour extraction. [PERSON] [55] evaluated the effect of aggregate morphology variation on the performance of asphalt pavements and investigated the asphalt coverage ratio and the mechanical properties of the mixture for different types of aggregates to quantify the aggregate morphological characteristics by AIMS. An accurate definition of the aggregate morphological characteristics is important for the initial design phase of pavements, extending the service life of roads and reducing the use of natural aggregates and the generation of solid waste.