# Mini-Crack Detection of Conveyor Belt Based on Laser Excited Thermography
## 3 Principle of the Proposed Method
### Image Enhancement Based on Heat Signal  
Due to the low contrast of thermal images and the lack of detailed texture information, an improved local histogram equalization algorithm to highlight defect features is proposed. To enhance mini-crack characteristics of the mini-crack feature image \(M(x,y)\) and reduce the noise interference, a weighted template operator was defined, and a power function  
Figure 4: Process of image reconstruction. (**a**) Thermal response image \(R_{i}(x,y)\) and its gray image; (**b**) reference image \(Res(x,y)\) and its gray image; (**c**) grayscale feature images \(F_{i}\mathbf{\mathrm{\pi}}(x,y)\) and its gray image; (**d**) mini-crack feature image \(M(x,y)\) and its gray image.  
Figure 3: Mini-crack image feature extraction based on laser excited thermography (\(F_{i}^{\star}(x,y)\) is the new feature image which is obtained by removing the reference image \(Res(x,y)\) from the feature image \(F_{i}(x,y)\)).  
was used as the weighted function. The effect of the image enhancement depends on the selection of filter window and weighting function, and, the appropriate weighted function not only highlights the feature area but also avoids the noise enhancement. The steps for the image enhancement algorithm are as follows:  
1. Select a 3 \(\times\) 3 template operator.
2. Obtain the pixel point \((i,j)\) with the highest gray value. The pixel point \((i,j)\) with the highest gray value in the current line pixels of the mini-crack feature image \(M(x,y)\) is obtained, and is taken as the central reference pixel of the weighting function. The pixel in the center of the template is \((i_{0},j_{0})\). The further the pixel in the template is from the \((i,j)\), the smaller the weight should be assigned.
3. Calculate the weighted function by Equation (2). The weight coefficient of each pixel in the 3 \(\times\) 3 template is inversely proportional to the distance from the pixel to the center of the template. The weighted function \(\omega(i,j)\) is, \[\omega(i,j)=[\frac{1}{\rho}]^{\alpha}-\beta\] (2) where \(\rho\) is the inverse proportionality coefficient that can be expressed as, \[\rho=\sqrt{\left(i-i_{0}\right)^{2}+\left(j-j_{0}\right)^{2}}\] (3) and \(\alpha\) is the nonlinear factor can be determined by \(\alpha=k\times s\), where \(k\) is a constant, and \(s\) is a gray variance of image that can be determined by, \[s=\frac{\sum\limits_{i=0}^{M-1}\sum\limits_{j=0}^{N-1}\left[f(i,j)-\overline{ f}\right]^{2}}{M\times N}\] (4) where \(f\)\((i,j)\) is the grayscale value of the pixel \((i,j)\), \(\overline{f}\) is mean gray value of image, and \(M\times N\) is the size of the image. Additionally, in Equation (2), \(\beta\) is a correction factor which is used to guarantee that \(\omega(i,j)\) is greater than zero. It should be satisfied by the inequality \[\beta<\frac{1}{2}\times\left[\frac{1}{\rho_{\max}}\right]^{\alpha}\] (5) where \[\rho_{\max}=\left(\frac{\sqrt{2}}{2}\right)\times N\] (6)
4. Perform the weighted balance of the power function. The schematic of weighted template operator for image enhancement is shown in Figure 5. Based on Equation (2), the weighting coefficient of each pixel is determined by the distance between the template center and the pixel point. Then the template is moved horizontally or vertically according to a certain step size, and the weighted balance of power function is performed on all pixels in the template.