## 2 Digital Image Processing
### Crack Extraction
#### 2.2.2 Strength Image Acquisition Based on Non-Negative Characteristics of Cracks  
After filtering out most of the non-crack images, the intensity image is obtained based on the non-negative characteristics of the crack. In the process of road image achievement, due to the illumination angle of the incident light, cracks appear as darker areas on the image, whose pixel gray values are generally lower than the background pixels nearby and generally have a substantial difference. This feature is defined as the non-negative feature of cracks.  
In some complex road sections, some crack areas with large widths will be filled or covered by the dust on the road, resulting in a higher gray value of its pixels than the nearby background pixels. At this time, the gray value of the pixel at the edge of the crack is lower than that of the pixel filled with dust in the middle, which also has a significant difference, so the non-negative feature is also applicable in this case. Non-negative features mainly describe the gray value characteristics of a single crack point in the region. As the most basic and main feature of crack pixels, they can be used to extract the most basic crack information. The schematic diagram of non-negative characteristics is shown in Figure 1:  
Figure 1 is a schematic diagram of an image containing a crack area, the size of which is \(a\times b\); the crack area is marked with a circle and a diamond. \(f(x,y)\) is the current point to be processed; other points in the area can be represented as \(f(x+w,y+h)\), where: \(w\in[-(a+1)/2,(a+1)/2]\), \(h\in[-(b+1)/2,(b+1)/2]\).  
\(f(x+w,y+h)\) includes both cracked pixels and non-cracked pixels. Based on the non-negative characteristics, design-related algorithms are used to obtain the intensity map of the crack image. Considering that cracks are linearly distributed, the width is small, and the closer the point is to the current point, the greater the influence factor on the determination of crack points is, so a distance weight function is introduced. The calculation formula for strength \(\zeta_{i}\) is shown in Formula (12):  
\[\zeta_{i}=[f(x,y)-f(x+w,y+h)]e^{\frac{w^{2}+h^{2}}{K}} \tag{12}\]  
When \(\zeta_{i}<0\), we count the quantity \(n\), \(e^{\frac{w^{2}+h^{2}}{K}}\) as the distance influence factor, which is taken according to the size of the selected window \(K=64\). Calculated in this way, the influence of edge pixels \(\zeta_{i}\) is weakened, which can highlight the characteristics of the crack area more. Then, we calculate the strength value \(O\) of the current point, as shown in Formula (13):  
\[O=|(\sum_{i=0}^{n}\zeta_{i})/N| \tag{13}\]  
Among them, \(N\) is the total number of pixels in the region. In actual processing, using a 21 \(\times\) 21 size window scans the acquired image and calculates the intensity value of each point according to Formulas (12) and (13) as \(O\) and the quantity influence factor \(n\). According to the prior knowledge obtained from a large number of experiments, the best threshold suitable for fracture extraction is \(O<30\), \(n>0.8N\). When the calculated  
Figure 1: Schematic diagram of non-negative characteristics.  
and \(n\) meet the requirements, the value of \(O\) can be assigned to the current point \(f(x,y)\). Otherwise, the value is assigned to 0.  
Non-negative features mainly calculate and screen the differences shown by single crack pixels and then obtain basic candidate crack information, including background noise, non-crack edge signals, and other interference factors. The image obtained after non-negative feature calculation mainly describes the strength information of the original crack image, which is called the crack strength map for short.