# Dark-Center Based Insulator Detection Method in Foggy Environment
## 4 Experimental Results and Analysis
### Defogging Experiments  
Generally, peak signal-to-noise ratio (_PSNR_), structural similarity (_SSIM_), and information entropy (\(S\)) are adopted to evaluate the performance of the defogging algorithm. _PSNR_ is evaluated by calculating the mean squared error (_MSE_) of the fogged and unfogged images to assess the model. The smaller the _MSE_, the larger the _PSNR_, representing the greater similarity between images. For an \(H\times W\) image, the _MSE_ and _PSNR_ are obtained using Equation (12) and Equation (13), respectively. \[MSE=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}(X(i,j)-Y(i,j))^{2} \tag{12}\]  
\[PSNR=10\lg\frac{(2^{n}-1)^{2}}{MSE} \tag{13}\]  
_SSIM_ indicates the similarity of the two images and evaluates the similarity between the images in three aspects: brightness, contrast, and structure, respectively. The closer the result is to 1 means the more similar the graphics are and the less distorted the images are. The expressions are expressed as follows:  
\[SSIM(X,Y)=l(X,Y)\cdot c(X,Y)\cdot s(X,Y) \tag{14}\]  
\[l(X,Y)=\frac{2u_{X}u_{Y}+C_{1}}{u_{X}^{2}+u_{Y}^{2}+C_{1}} \tag{15}\]  
Figure 9: E-ASPP feature pyramid module. \[c(X,Y)=\frac{2\partial_{X}\partial_{Y}+C_{2}}{\partial_{X}^{2}+\partial_{Y}^{2}+C_{ 2}} \tag{16}\]  
\[s(X,Y)=\frac{\partial_{XY}+C_{3}}{\partial_{X}\partial_{Y}+C_{3}} \tag{17}\]  
where \(\partial_{X}\) and \(\partial_{Y}\) denote the variance of image \(X\) and image \(Y\); \(u_{X}\) and \(u_{Y}\) denote the mean of image \(X\) and \(Y\); \(C_{1}\), \(C_{2}\), and \(C_{3}\) are constant terms; \(\partial_{XY}\) denotes the covariance of image \(X\) and \(Y\). Calculating the magnitude of the information entropy evaluation value is in finding the total expectation of the image grayscale value. The amount of detailed information in an image can be characterized by the result of the information entropy evaluation. The more information the image contains, the larger the value of information entropy is. Its calculation formula is expressed as follows:  
\[S=\sum_{i=0}^{255}\frac{f(i,j)}{\left(M\times N\right)^{2}}\log\frac{f(i,j)}{ \left(M\times N\right)^{2}} \tag{18}\]  
where \(I\) is the gray value of a pixel, \(j\) is the average of the grayness of a small region centered on that pixel value, \(f(i,j)\) is the number of occurrences of the binary, and \(M\) and \(N\) denote the length and width of the image, respectively. To verify the effectiveness of the improved dark channel prior algorithm, this paper compares the effects of the three improvement strategies on the model performance with experimental results derived from the CPILD test set, as shown in Table 1. As seen in the table, each improvement strategy on the model does not make SSIM values change greatly. However, the PSNR is significantly improved over the original model with a value of 16.27 dB after fitting the transmittance estimation using the dual dark channel; meanwhile, after optimizing the atmospheric light value estimation, the PSNR model is improved by 0.36 dB, and the PSNR metric is slightly improved when CLAHE is used as the restoration module. Combining these three improvements, the PSNR improves by 0.55 dB compared to the original model. These experiments show that the improved model has improved both the defogging effect and the image quality. Since there are several variants of the method based on physical and non-physical models, and most of the image evaluation results are evaluated using the full reference method on a synthetic dataset containing pairs of clear and haze images, the haze images with different concentrations are not necessarily consistent with the results of different method variants. The best defogging method on thin haze images does not have the best defogging effect on thick haze images, and the best method in the full-reference image quality evaluation does not necessarily perform consistently in the no-reference image quality evaluation.