# Image Dehazing Algorithm Based on Deep Learning Coupled Local and Global Features
## 4 Experimental Results and Analysis
### Experimental Results of Synthesizing Uniform Haze Images  
In the experiment of synthesizing uniform haze images, 500 randomly selected outdoor synthetic haze images from the target test dataset (SOTS) were used for testing, and some of the experimental results are shown in Figure 4. The figure shows that the method in [5] effectively removed the fog, but because the dark channel a priori theory is only suitable for the non-sky area, resulting in overexposure of the sky area and low overall brightness of the non-sky area after the fog removal (such as the first, second and fifth pictures in Figure 4b), the visual effect is poor. The defogged images of the method in [6] solve the problem of dark channel theory overexposure in the sky region, but the color deviation of the sky region after defogging is larger than that of the sky region of the standard fog-free images (e.g., the first, second, and fifth images in Figure 4c), while the overall brightness of the non-sky region is still lower compared to the standard fog-free images. After the method in [11] for the test image defogging, individual images still had the problem of more residual haze with incomplete defogging (e.g., the first and second images in Figure 4d), and the recovered images did not show color distortion. The method of fog removal in [12] had a good effect without obvious fog, but the fogged images showed local color deviations such as the ships and city buildings in the first panel of Figure 4e and the yellowish color of the ground in the fourth panel and the road in the fifth panel, which differed greatly from the standard fog-free images. Comparing the above-mentioned various defogging algorithms with the algorithm in this paper, it is obvious that the algorithm in this paper effectively removed the fog from the image without color distortion, and the image was recovered more naturally, which was closer to the real fog-free image compared with the other methods. Comparing the resulting images in [15] and the algorithm of this paper together, we found that there was no fog residue in the visual effect, and both could accomplish the task of haze removal well on the same dataset. However, the haze situation in this dataset was lighter, and when faced with complex haze situations, the algorithm in this paper was better able to highlight the advantages. The effectiveness of the method in this paper cannot be fully explained by subjective judgment alone, so two indices, peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [20] were selected for the data analysis of the experimental results in this paper. PSNR is an important indicator of image quality, and the larger the value, the closer the defogged image is to a standard fog-free image. PSNR is calculated as follows:  
\[MSE=\frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[I(i,j)-K(i,j)]^{2} \tag{8}\]  
\[PSNR=10\cdot\log_{10}\left(MAX_{I}^{2}/MSE\right) \tag{9}\]  
where \(I\) is the original fogged image; \(K\) is the defogged image; \(i,j\) are the horizontal and vertical coordinates of the pixel values, respectively; and \(MAX\) was set to 255 for an image with a bit depth of 8. SSIM is also a fully referenced image quality evaluation metric that mainly describes image similarity and consists of three contrast modules: brightness, contrast, and structure [21]. Comparing the defogged image with the real standard fog-free image, SSIM takes the value range of \([0,1]\), and a larger value means less image distortion, which is calculated as follows:  
\[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+c_{1}\right)\left(\sigma_{xy}+c_{2} \right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{1}\right)\left(\sigma_{x}^{2}+ \sigma_{y}^{2}+c_{2}\right)} \tag{10}\]  
where \(\mu_{x}\mu_{y}\) are the means of images x and y, respectively; \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the standard deviations of images x and y, respectively; \(\sigma_{xy}\) is the x and y covariances of the images; \(c_{1}\), \(c_{2}\) are constants to avoid denominators of 0.