# An Improved Crack Identification Method for Asphalt Concrete Pavement
## 2 Methodology
### Segmentation Processing of Crack Image Based on Watershed Algorithm  
The idea of watershed segmentation originates from the surface model in topography, and the segmented asphalt concrete pavement crack image is regarded as a topological surface [15; 16; 17]. In the gray image, each pixel's gray value corresponds to the height in the terrain, and each local minimum value and its influence area become a catchment basin. It is envisaged that a hole will be pierced in each bottom valley area, and the water will flow upward from the hole, gradually immersing the whole terrain in the water. Then, the water from different bottom valleys will build dams one by one, forming the watershed of the included area. These watersheds also correspond to the boundary outline of the topology and surface image. The watershed is the maximum point of the image. In practical applications, in order to obtain the edge contour of the image, the input image is a gradient grayscale image \(I(x,y)\), where \(x\) and \(y\) comprise the image pixel, and its gradient image expression equation is:  
\[F(I)=I\oplus SE-I\Theta SE \tag{15}\]  
In Equation (15), \(\oplus\) is the expansion operator, \(\Theta\) is the corrosion operator and \(SE\) is a morphological structural element. Watershed division steps are as follows:  
Step 1: Scan the crack image of gradient asphalt concrete pavement \(F(I)\), and find the minimum value. \((x,y)\in F(I)\), where neighborhood set \(N(x^{\prime},y^{\prime})\), \(x^{\prime}=\{x-1,x,x+1\}\), \(y^{\prime}=\{y-1,y,y+1\}\). If \(F(x,y)>F(x^{\prime},y^{\prime})\), \(x^{\prime},y^{\prime}\in N(x,y)\), then \(F(x,y)\) is marked as non-minimum, first-in, first-out queue \(Q\); when \(Q\) is not empty, its first element will be queued. Set \(F(x^{\prime},y^{\prime})\) as the first queue element of \(Q\); if \(F(x^{\prime\prime},y^{\prime\prime})\) marks as empty, \(x^{\prime\prime},y^{\prime\prime}\in N(x,y)\) and \(F(x^{\prime},y^{\prime})=F(x^{\prime\prime},y^{\prime\prime})\), then \(G(x^{\prime\prime},y^{\prime\prime})\) is marked as minimum and queued \(Q\). Step 2: Place the found minimum adjacent pixels in an orderly queue \(Q^{\prime}\). Scanning gradient asphalt concrete pavement crack image \(F(I)\), set, if \(F(x,y)\) marks as empty, then \(F(x,y)\in CB_{i}\), \(F(x,y)\) in queue \(Q\). If \(Q\) is non-empty, the first element is out of the column. Set \(F(x^{\prime},y^{\prime})\) as the first queue element of \(Q\); if \(F(x^{\prime\prime},y^{\prime\prime})\) marks as empty, \(x^{\prime\prime},y^{\prime\prime}\in N(x,y)\), then \(F(x^{\prime\prime},y^{\prime\prime})\) in queue \(Q\); otherwise \(G(x^{\prime\prime},y^{\prime\prime})\) is marked and placed in \(Q^{\prime}\). Step 3: Queue \(Q^{\prime}\), where the pixel containing the smallest gray value, is listed. Set \(F(x,y)\) as the first queue element of \(Q^{\prime}\), if \(F(x^{\prime},y^{\prime})\) marks as empty, \(x^{\prime\prime},y^{\prime\prime}\in N(x,y)\) and \(F(x^{\prime},y^{\prime})\in CB_{k}(k=1,2,\cdots,i)\), then \(F(x,y)\in CB_{k}\). Because of the subtle gradient change in the image's gray level and the influence of noise, the problem of oversegmentation can occur very easily [18]. Eliminating oversegmentation is mainly performed to limit the number of regions. Merging similar regions can solve the problem of oversegmentation. The region-merging algorithm often uses the gray difference between a point and its surrounding neighborhood as the merging criterion. This method is more suitable for images with large gray changes. For the crack image, the crack information is weak, accounting for a small proportion in the whole image, and the image gray level changes relatively gently, which is not suitable for use. To solve this problem, this paper proposes an improved similar-region-merging algorithm. The steps are as follows:  
Step 1: Set \(\varsigma_{i}\), \(\sigma_{i}(i=1,2,\cdot\cdot\cdot,m)\) to represent the mean value and standard deviation of pixels in the region, respectively.