## 3 Experimental Results and Analysis
The colors of the columns and chairs are more uniform and similar to the original image. In group (d), the concentration of the fog in the picture is not uniform. There is more fog in the upper middle of the picture. Additionally, this group of pictures has the richest texture details. The picture of DCP is still dull, and there are more black blocks in the grass, such as where the red box shows. The result of FDCP has been improved to a certain extent. However, the texture details in the grass are still insufficient. The result of GDCP has been completely degraded, and no valid information can be obtained. MDCP improves the darkening of the image, but the green and yellow parts of the bushes are missing, and the overall color is lost. In the result of FFA, the fog removal is incomplete, but the texture details are relatively complete. The result of HDCP is more in accord with the real situation. The fog removal is more complete. The texture details are rich. Additionally, there are fewer black blocks as interference. It can be seen that the method proposed in this paper has a wide range of applicability, and it can also play a good role in defogging in the case of complex environments and uneven fog concentration. In order to further verify the performance of the proposed algorithm and objectively evaluate the enhanced image enhancement quality, this paper adopts the mean squared error (_MSE_), peak signal-to-noise ratio (_PSNR_), structural similarity (_SSIM_), and information entropy (_E_) of the image as evaluation criteria. (1) Mean squared error (_MSE_):  
\[MSE=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[I(i,j)-J(i,j)]^{2} \tag{12}\]  
where \(I(i,j)\) and \(J(i,j)\) are the original and restored images with sizes of \(m\) by \(n\). (2) Peak signal-to-noise ratio (_PSNR_):  
\[PSNR=10\cdot\log_{10}\left(\frac{MAX_{I}^{2}}{MSE}\right) \tag{13}\]  
where \(MAX_{I}\) is the maximum possible pixel value of the picture. Generally, for uint8 data, the maximum pixel value is 255. (3) Structural similarity index (_SSIM_):  
\[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+c_{1}\right)\left(2\sigma_{xy}+c_{2} \right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{1}\right)\left(\sigma_{x}^{2}+\sigma _{y}^{2}+c_{2}\right)} \tag{14}\]  
where \(x\), \(y\) are the two images. \(\mu_{x}\) and \(\mu_{y}\) are the pixel means of \(x\) and \(y\). \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variances of \(x\) and \(y\). \(\sigma_{xy}\) is the covariance of \(x\) and \(y\). \(c_{1}\) and \(c_{2}\) are two constants used to maintain stability and avoid division by zero. (4) Information entropy (_E_):  
\[E=-\sum_{i=0}^{255}\sum_{j=0}^{255}\sum_{k=1}^{3}p_{ijk}\cdot\log_{2}p_{ijk} \tag{15}\]  
where \(i,j,\) and \(k\) are the sizes of the image. \(p_{ijk}\) means the probability of occurrence of \(p_{\bar{y}}\) in channel \(k\). The comparison of different algorithms is compared as follows. The best-performing indexes are shown in bold. In Table 1, the proposed method in this paper has the smallest _MSE_, indicating that the method does not alter the images much. In Table 2, there is no significant difference in the statistical sense as well as in numeral values for DCP, FDCP, and GDCP. The results show that the normal DCP and the other two improved DCP algorithms have almost the same _PSNR_s. The _PSNR_s of MDCP and FFA are relatively close. The proposed HDCP has the biggest _PSNR_. This indicates that the image distortion degree of the processing result in this paper is the least. As shown in Table 3, in terms of _SSIM_, FFA has the best processing results, and the gap between HDCP and FFA is not significant, indicating that the processed images are more similar to the original images. For the _entropy_ in Table 4, the method in this paper still has an absolute advantage. The larger the value is, the richer the information contained in the restored image. For generality, this paper processed all the images in the O-Haze dataset, containing 45 groups of foggy and fog-free photos.