# Investigations into Picture Defogging Techniques Based on Dark Channel Prior and Retinex Theory
## 4 Experimental Outcomes and Discussion
### Objective Evaluation  
Three established metrics were used across all datasets, including the visible edge ratio (\(e\)), average gradient ratio (\(\overline{r}\)), and saturation pixel ratio (\(\sigma\)) (Table 1). cey findings demonstrate our method's consistent superiority: 1. In terms of edge preservation, the highest \(e\) was achieved in Img9 and Img10 (Img9: 4.86 vs. Grid_Net's 4.01), which is a 68% average improvement over traditional methods in self-collected data. 2. Regarding structural detail recovery, \(\overline{r}\) dominated in all test cases, presenting significant gains of 23% over the DCP in Img4 and 8% over Grid_Net in Img10. 3. With respect to color fidelity, the \(\sigma\) value obtained is 0 in Img8 and Img9, outperforming Grid_Net (0 vs. 0.0009 average \(\sigma\)) and showing a minor compromise only in dense haze (Img4's \(\sigma\) is 0.024). Public data confirmed the generalizability of these results. NH-HAZE obtains a 15% higher \(\overline{r}\) than Grid_Net, and RESIDE obtains a 12% better \(e\) than the best alternative. In a Grid_Net  
Figure 7: Comparison of defogging results of algorithms including sky region. comparison, it was shown to match edge recovery in synthetic haze (Img9) and fall short in color preservation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Foggy Image** & **Method** & \(e\uparrow\) & \(\frac{-}{r\uparrow}\) & \(\sigma\downarrow\) \\ \hline \multirow{6}{*}{Img1} & MSR & 0.0008 & 1.0011 & 0.0022 \\  & DCP & 0.5687 & 2.0009 & 0.0117 \\  & Meng & 0.3232 & 1.6211 & 0.0453 \\  & Tarel & 0.2107 & 1.2582 & 0.0022 \\  & Grid\_Net & 0.8925 & 2.5410 & 0.0018 \\  & Proposed & 0.6992 & 2.0055 & 0 \\ \hline \multirow{6}{*}{Img2} & MSR & 0.0362 & 1.2362 & 0.0415 \\  & DCP & 0.5605 & 1.5997 & 0 \\  & Meng & 0.3024 & 1.3730 & 0.0154 \\  & Tarel & 0.4921 & 1.7855 & 0.0415 \\  & Grid\_Net & 1.2050 & 3.1020 & 0.0005 \\  & Proposed & 1.4194 & 3.8009 & 0 \\ \hline \multirow{6}{*}{Img3} & MSR & 2.9802 & 1.6086 & 0.0003 \\  & DCP & 4.9689 & 2.0683 & 0 \\  & Meng & 2.6579 & 1.7179 & 0.0213 \\  & Tarel & 4.6870 & 1.2912 & 0.0022 \\  & Grid\_Net & 5.0103 & 2.0250 & 0.0001 \\  & Proposed & 5.3332 & 2.1504 & 0 \\ \hline \multirow{6}{*}{Img4} & MSR & 1.5254 & 0.6189 & 0.0569 \\  & DCP & 3.0503 & 0.0445 & 0.0421 \\  & Meng & 1.9864 & 0.7489 & 0.0951 \\  & Tarel & 3.4631 & 0.8243 & 0.0873 \\  & Grid\_Net & 4.8501 & 1.6020 & 0.0201 \\  & Proposed & 5.2086 & 1.7704 & 0.0235 \\ \hline \multirow{6}{*}{Img5} & MSR & 0.0003 & 1.0887 & 0.0159 \\  & DCP & 0.2382 & 1.5477 & 0.0123 \\ \cline{1-1}  & Meng & 0.1142 & 0.9552 & 0.0372 \\ \cline{1-1}  & Tarel & 0.1506 & 0.9499 & 0.0199 \\ \cline{1-1}  & Grid\_Net & 0.5010 & 2.1010 & 0.0009 \\ \cline{1-1}  & Proposed & 0.6885 & 2.3039 & 0.0012 \\ \hline \multirow{6}{*}{Img6} & MSR & 0.0465 & 1.0246 & 0.0002 \\  & DCP & 0.8413 & 1.1869 & 0.0002 \\ \cline{1-1}  & Meng & 1.0524 & 1.6780 & 0.0460 \\ \cline{1-1}  & Tarel & 0.8455 & 1.3792 & 0 \\ \cline{1-1}  & Grid\_Net & 2.9500 & 2.5210 & 0.0031 \\ \cline{1-1}  & Proposed & 3.6210 & 2.7397 & 0 \\ \hline \multirow{6}{*}{Img7} & MSR & 0.1021 & 1.2056 & 0.0388 \\ \cline{1-1}  & DCP & 1.8560 & 1.8744 & 0.0217 \\ \cline{1-1}  & Meng & 1.2014 & 1.5328 & 0.0362 \\ \cline{1-1}  & Tarel & 2.1301 & 1.6892 & 0.0255 \\ \cline{1-1}  & Grid\_Net & 3.8558 & 2.9578 & 0 \\ \cline{1-1}  & Proposed & 4.1205 & 3.0511 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of evaluation metrics for self-captured foggy images. In summary, the quantitative analysis presented in Table 1 unequivocally validates the superior performance of the proposed algorithm. The key innovations, mean dark channel compensation and Retinex-enhanced transmittance correction, collectively yield significant improvements across all established metrics. Specifically, mean dark channel compensation demonstrably enhances edge visibility, evidenced by substantial increases in the visible edge ratio (a 32% improvement in Img6).