# Investigations into Picture Defogging Techniques Based on Dark Channel Prior and Retinex Theory
## 4 Experimental Outcomes and Discussion
### Computational Efficiency Analysis  
To analyze computational complexity and runtime performance issues, we measured the average processing time of all the compared algorithms on the complete RESIDE dataset (400 \(\times\) 400). The results in Table 2 show the competitive efficiency of our approach.  
As demonstrated in Table 2, the proposed algorithm achieves a favorable balance between computational efficiency and restoration quality. While MSR exhibits the fastest processing time (0.004 s) owing to its computationally lightweight multi-scale convolution, traditional restoration methods like the DCP (0.018 s) incur higher costs primarily due to the computationally intensive guided filtering step for transmission refinement. Meng (0.006 s) and Tarel (0.007 s) show moderate efficiency. The deep learning-based Grid_Net, despite its strong performance, is the slowest (0.059 s) due to the inherent complexity of its multi-scale CNN architecture. In contrast, our method processes images in 0.023 s on  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Foggy Image** & **Method** & \(e\dagger\) & \(\tau\dagger\) & \(\sigma\downarrow\) \\ \hline \multirow{6}{*}{Img8} & MSR & 0.0890 & 1.1024 & 0.0410 \\  & DCP & 1.9287 & 1.8059 & 0.0189 \\  & Meng & 1.3055 & 1.6025 & 0.0273 \\  & Tarel & 2.2545 & 1.7548 & 0.0201 \\  & Grid\_Net & 3.9278 & 2.9875 & 0.0010 \\  & Proposed & 4.3279 & 3.1053 & 0.0008 \\ \hline \multirow{6}{*}{Img9} & MSR & 0.2176 & 1.3056 & 0.0350 \\  & DCP & 2.1050 & 1.9527 & 0.0159 \\  & Meng & 1.5208 & 1.7039 & 0.0220 \\  & Tarel & 2.4012 & 1.8216 & 0.0180 \\  & Grid\_Net & 4.0137 & 3.1528 & 0.0009 \\  & Proposed & 4.8594 & 3.3051 & 0 \\ \hline \multirow{6}{*}{Img10} & MSR & 0.1980 & 1.2851 & 0.0362 \\  & DCP & 2.0010 & 1.9038 & 0.0161 \\ \cline{1-1}  & Meng & 1.4278 & 1.6852 & 0.0235 \\ \cline{1-1}  & Tarel & 2.3529 & 1.8022 & 0.0192 \\ \cline{1-1}  & Grid\_Net & 3.9548 & 3.1005 & 0.0011 \\ \cline{1-1}  & Proposed & 4.7278 & 3.2820 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(Cont.\)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **MSR** & **DCP** & **Meng** & **Tarel** & **Grid\_Net** & **Proposed** \\ \hline
**Avg. Time(s)** & 0.004 & 0.018 & 0.006 & 0.007 & 0.059 & 0.023 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average processing time on RESIDE.  
average, representing an increase of 2.6 in speed over Grid_Net. This efficiency stems from the deliberate design choices within our bi-level optimization framework: (1) The Retinex preprocessing method and subsequent parameter estimation steps (atmospheric light via Otsu/edge fusion, compensated dark channel via mean/min fusion) rely primarily on efficient filtering and thresholding operations, avoiding heavy optimization or learning. (2) The depth-guided transmission correction using the CAP leverages a simple linear model, adding minimal overhead compared to deep feature extraction. In practical applications, such as those based on a real-time constraint of less than 100 ms in the perception layer of automatic driving, the defogging algorithm proposed in this paper currently consumes an average of 23 ms, which satisfies the delay constraint of 20-100 ms. Crucially, this computational efficiency is attained without compromising the significant visual quality improvements demonstrated in Sections 4.1 and 4.2 and quantified in Table 1. The proposed method thus establishes a practical efficiency-quality trade-off, being substantially faster than state-of-the-art deep learning alternatives while maintaining competitive timing with traditional methods and delivering superior defogging results.