# Adaptive Tolerance Dehazing Algorithm Based on Dark Channel Prior
## 4 Comparison and Analysis of Experiential Results
### Quantitative Comparison
#### 4.3.1 Blind Contrast Enhancement Assessment  
In studying the dehazing effect, [PERSON]'s blind evaluation method based on the visible edge contrast is well known [33; 34]. This method evaluates the contrast enhancement of each image detail  
Figure 8: Qualitative comparison of different dehazing algorithms for synthetic depth images. (**a**) The hazy images. (**b**) [PERSON]’s results. (**c**) [PERSON]’s results. (**d**) [PERSON]’s results. (**e**) Results of used fixed tolerance. (**f**) Our results. (**g**) Ground truth.  
before and after dehazing. It uses three indicators to objectively describe the quality of the images (new visible edge ratio \(e\), visible edge normalized gradient \(r\), saturated black or white percentage pixels \(\sigma\)):  
\[e=\frac{n_{r}-n_{0}}{n_{0}}, \tag{16}\]  
\[r=\exp(\frac{1}{n_{r}}\sum_{p_{i}\in\psi_{r}}\log r_{i}), \tag{17}\]  
\[\sigma=\frac{n_{s}}{\dim_{x}\times\dim_{y}}, \tag{18}\]  
where \(n_{0}\) and \(n_{r}\) are the numbers of visible edges of the image before and after the dehazing, respectively, \(\Psi_{r}\) is the set of visible edges for the dehazed image, \(P_{i}\) is the pixels on the visible edge, \(r_{i}\) is the ratio of the Sobel gradient at \(P_{i}\) and the corresponding point of the original image, \(n_{s}\) is the number of saturated black and white pixels, \(dim_{x}\) and \(dim_{y}\) represent the width and height of the image, respectively. The comparative data are shown in Table 1.  
Table 1 shows the results of the three objective indicators \(e\), \(r\) and \(\sigma\) of the image in Figure 6. A lower \(\sigma\) value represents better performance. Table 1 shows that the \(\sigma\) value of the algorithm in this paper is the smallest. Even if the \(\sigma\) value of the fifth picture is higher than that of [PERSON]'s method, the difference is small. The two indicators \(e\) and \(r\) focus on edge recovery and usually larger values indicate better performance. However, the increase in the visible edge may also result from a false edge caused by severe color distortion (as shown in Figure 6b). Figure 9 shows it more concretely, where [PERSON]'s result shows evident false edges in the local enlarged regions. Our method suppresses the color distortion effectively, which is further manifested as a decrease in false fake edges. Thus, our results often have a lower value than the results of [PERSON] and in those two indicators. However, our method is actually better than most other methods in most images (as shown in Table 1).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**IndexesMethods** & **[PERSON]’s Method** & **[PERSON]’s Method** & **[PERSON]’s Method** & **Introducing Fixed Tolerance** & **Our Method** \\ \hline \multirow{3}{*}{Image 1} & \(e\) & 0.3163 & 0.1873 & 0.1116 & 0.1447 & 0.1918 \\ \cline{2-7}  & \(\sigma\) & 0 & 0 & 0.002 & 0 & 0 \\ \cline{2-7}  & \(r\) & 1.7532 & 0.9660 & 0.1023 & 1.2540 & 1.3576 \\ \hline \multirow{3}{*}{Image 2} & \(e\) & 2.2372 & 0.2567 & 0.3605 & 0.2518 & 0.6276 \\ \cline{2-7}  & \(\sigma\) & 0 & 0 & 0.0126 & 0 & 0 \\ \cline{2-7}  & \(r\) & 2.3742 & 0.7349 & 1.1263 & 1.0557 & 1.2857 \\ \hline \multirow{3}{*}{Image 3} & \(e\) & 0.3086 & 0.0723 & 0.1417 & 0.1174 & 0.1654 \\ \cline{2-7}  & \(\sigma\) & 0 & 0 & 0.0038 & 0 & 0 \\ \cline{2-7}  & \(r\) & 1.5427 & 1.0296 & 1.0957 & 1.1384 & 1.4328 \\ \hline \multirow{3}{*}{Image 4} & \(e\) & 0.1752 & 0.0894 & 0.0060 & 0.0920 & 0.1103 \\ \cline{2-7}  & \(\sigma\) & 0 & 0 & 0.0092 & 0 & 0 \\ \cline{2-7}  & \(r\) & 1.3786 & 1.0870 & 1.0894 & 1.2175 & 1.7019 \\ \hline \multirow{3}{*}{Image 5} & \(e\) & 1.3827 & 0.6887 & 0.5149 & 0.5483 & 0.8144 \\ \cline{2-7}  & \(\sigma\) & 0 & 0.0052 & 0.0052 & 0.0018 \\ \cline{1-1} \cline{2-7}  & \(r\) & 1.8337 & 1.4929 & 1.4040 & 1.5380 & 1.7013 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Indicator \(e\), \(r\) and \(\sigma\) of the images in Figure 6.