## 2 Digital Image Processing  
### Image Enhancement Processing of Expressway Asphalt Pavement  
The detection method of expressway asphalt pavement crack damage based on digital image processing technology uses the non-subsampled contourlet transform (NSCT) to enhance the image of expressway asphalt pavement. NSCT can be divided into two translation invariant parts: a non-down sampling pyramid and a non-down sampling directional filter bank. The combination of these two parts ensures the multi-directional and multi-scale analysis characteristics of NSCT. Moreover, the filter banks of these two parts avoid sampling, making NSCT translation invariant. This feature ensures that the NSCT transformed image information is preserved and the frequency domain characteristics of different subbands in the image are clear. In the actual pavement crack damage detection process, the pavement image that needed to be enhanced not only contains weak signal crack information but also contains different noise levels. Therefore, the road image enhancement algorithm must keep the crack edge information as far as possible, suppress noise, and enhance the contrast between the road background image and the crack [7; 8]. The idea of the NSCT image denoising and enhancement algorithm is first to select an appropriate threshold to distinguish noise from weak edge information. Secondly, a suitable threshold function is selected to enhance the contrast of pavement background and crack information [9; 10]. Because the frequency domain characteristics of noise are unstable, there is no fixed shape. The frequency distribution of weak edges is relatively stable, and the shape presents a certain geometric structure, so this morphological difference can be used to distinguish the noise and weak edge information in a road image. By incorporating the translation invariance of the NSCT transform, the crack information in the road image can be enhanced and noise minimized. A pavement image is transformed by NSCT to obtain the subband coefficients of the image. According to these coefficients, the pixels in the image are divided into three categories: strong edge, weak edge, and noise. The classification of strong edges, weak edges, and noise can be determined by the threshold \(T\). This article uses principal component analysis to determine the threshold \(T\). There are many approaches to select the method, and the proposed approach uses the principal component analysis method. In the field of image processing, a standard denoising criterion considers that the information with large changes is the target, the information with small changes is noise, and the size of changes is described by variance. The idea of the PCA method is to project high-dimensional data into a low-dimensional subspace, use new variables with fewer dimensions and mutual independence to reflect most of the information provided by the original variables, and then solve the problem by analyzing the new variables [11; 12]. PCA has many different calculation methods. The proposed method calculates the data matrix \(X\) covariance matrix of \(COV\) the eigenvalues and eigenvectors of \(W\) for solving. First, the pavement image of order \(M\times N\) is represented by a matrix as \(X=[x_{1},x_{2},\cdots,\)\(x_{n}]\), using the \(X\) standardization process to obtain \(X^{\prime}\). As shown in Formula (1):  
\[X^{\prime}=X-\overline{X} \tag{1}\]  
where \(\overline{X}=X^{T}I/M\), \(I\) by \(m\times 1\) dimensional vector; \(M\) is the number of observation indicators of \(X\). Furthermore, each element in the covariance matrix \(X^{\prime}\) of the standardized matrix \(COV\) can be calculated, as shown in Formula (2):  
\[COV(i,j)=\left(\sum_{k=1}x_{ki}\cdot x_{kj}\right)/\left(m-1\right) \tag{2}\]  
where \(x_{ki}\), \(x_{kj}\) standardize matrix \(X^{\prime}\) elements.