# A Single Image Enhancement Technique Using Dark Channel Prior
## 4 Experimental Results And Analysis
### Quantitative Comparisons  
In order to fully evaluate the defogging effect, PSNR and SSIM are used to quantify the defogged results of different algorithms. Taking Figures 6 and 7 as examples, the evaluation results are shown in Tables 1 and 2, respectively. Moreover, we also report the evaluation results on the test set in Table 3.  
PSNR value, the smaller the distortion between the image to be evaluated and the reference image, and the better the image quality. The definition of PSNR can be formulated as:  
\[PSNR=10*log_{10}\frac{MAX_{T}^{2}}{MSE}, \tag{22}\]  
where \(MAX\) denotes the maximum pixel value of the image \(I\), \(MSE\) represents the mean square error between two images. Structural SIMilarity (SSIM) is an objective criterion for image quality that meets the characteristics of the human visual system. The larger the value of SSIM, the better it can reflect people's subjective feelings. The formulation of SSIM can be defined as:  
\[SSIM(x,y)=\frac{(2u_{x}u_{y}+c_{1})(2\delta_{xy}+c_{2})}{(u_{x}^{2}+u_{y}^{2}+ c_{1})(\delta_{x}^{2}+\delta_{y}^{2}+c_{2})}, \tag{23}\]  
where (x,y) denotes two samples, \(u_{x}\) denotes the mean value of \(x\), \(u_{y}\) denotes the mean value of \(y\), \(\delta_{x}\) denotes the variance of \(x\), \(\delta_{y}\) denotes the variance of \(y\), \(\delta_{xy}\) denotes the co-variance of \(x\) and \(y\), and \(c_{1}\) and \(c_{2}\) are constants. As can be seen from Table 1, in scene 1, the SSIM value obtained by using the algorithm of this paper is 0.19 larger than that obtained by [PERSON]'s defogging algorithm, which means that the defogged image obtained by using the algorithm of this paper can better reflect people's subjective feelings. The PSNR value obtained by using the algorithm of this paper is 4.50 larger than that obtained by [PERSON]'s defogging algorithm. That is, the defogging effect obtained by using the improved algorithm of this paper has smaller pixel error and better image quality than the first image of Figure 6a. The time obtained by the algorithm of this paper is 0.3s less than the time obtained by [PERSON]'s defogging algorithm. In [PERSON]'s defogging algorithm, he used the soft matting to refine the transmittance. Although this matting algorithm can be used to repair the obtained transmittance and achieve satisfactory results, the algorithm involves the reversible operation of large matrices, resulting in high time complexity. In this paper, guided filtering instead of soft matting can not only refine the transmittance, but also shorten the image processing time. A similar improvement can be found in scene 2. In summary, no matter from the SSIM, PSNR, or time, we can objectively verify that the proposed method can improve the edge effect and shorten the image processing time. As can be seen from Table 2, the algorithm in this paper is quantitatively compared with three classic sky defogging algorithms. For scene 1, the improved algorithm we proposed is 5.45 larger in PSNR than the defogging algorithm [16] based on cost function, 5.72 larger than the PSNR of the defogging algorithm based on tolerance [12], and 3.58 larger than the PSNR of the defogging algorithm [15] based on the sky segmentation. Therefore, whether it is from the previous subjective analysis or objective index analysis, it can explain that the defogged images obtained by our improved method have less distortion and better image quality. For scene 2, the improved algorithm we proposed is 0.28 larger in SSIM than the defogging algorithm [16] based on cost function, 0.28 larger than the SSIM of defogging algorithm [12] based on the tolerance mechanism, and 0.11 larger than the SSIM of defogging algorithm [15] based on the sky segmentation. Therefore, it is verified again from objective indicators that the defogged image obtained by our improved algorithm can better reflect human subjective feelings.