# Improved Color Attenuation Prior for Single-Image Haze Removal
## 4 Evaluations
### Quantitative Evaluation
#### 4.1.3 Real Datasets  
The IVC [37], O-HAZE [39], and I-HAZE [40] image datasets are used in this section to assess the dehazing performance on hazy images of the real scene. The IVC dataset contains 25 hazy images of people, animals, landscape, indoor, and outdoor real images and does not contain their corresponding ground-truth haze-free images. Conversely, the O-HAZE dataset consists of 45 pairs of hazy and haze-free images of outdoor scenes, and the I-HAZE dataset comprises 30 pairs of hazy and haze-free images of indoor scenes. The haze in the hazy scenes of O-HAZE and I-HAZE datasets is created by the vapor generator. Due to the lack of reference images in the IVC dataset, the rate of new visible edges (\(e\)), the quality of the contrast restoration (\(r\)), proposed by [PERSON] et al. [45], and FADE are used to evaluate the performance of dehazing approaches. Since O-HAZE and I-HAZE possess reference images, SSIM, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Haze Type** & **SSIM** & **TMQI** & **FSIMc** & **FADE** \\ \hline \multirow{4}{*}{DCP} & Homogeneous & 0.6653 & 0.7639 & 0.8168 & 1.0177 \\  & Heterogeneous & 0.5374 & 0.6894 & 0.7251 & 1.2793 \\  & Cloudy homogeneous & 0.5349 & 0.6849 & 0.7222 & 1.2587 \\  & Cloudy heterogeneous & 0.6500 & 0.7781 & 0.8343 & 1.0792 \\ \cline{2-6}  & Overall average & 0.5969 & 0.7291 & 0.7746 & 1.1587 \\ \hline \multirow{4}{*}{FFD} & Homogeneous & 0.7096 & 0.7259 & 0.7833 & 0.9307 \\  & Heterogeneous & 0.6970 & 0.7310 & 0.7725 & 1.4961 \\  & Cloudy homogeneous & 0.6719 & 0.7312 & 0.7567 & 1.3583 \\  & Cloudy heterogeneous & 0.7431 & 0.7373 & 0.8104 & 1.1021 \\ \cline{2-6}  & Overall average & 0.7054 & 0.7314 & 0.7807 & 1.2218 \\ \hline \multirow{4}{*}{CAP} & Homogeneous & 0.5651 & 0.7533 & 0.7947 & 0.5527 \\  & Heterogeneous & 0.5519 & 0.7254 & 0.7845 & 0.9599 \\  & Cloudy homogeneous & 0.5310 & 0.7080 & 0.7764 & 0.8267 \\  & Cloudy heterogeneous & 0.5412 & 0.7674 & 0.8117 & 0.6752 \\ \cline{2-6}  & Overall average & 0.5473 & 0.7385 & 0.7918 & **0.7536** \\ \hline \multirow{4}{*}{HPM} & Homogeneous & 0.5949 & 0.7320 & 0.8048 & 0.9675 \\  & Heterogeneous & 0.6245 & 0.7037 & 0.7805 & 1.6836 \\  & Cloudy homogeneous & 0.6124 & 0.7015 & 0.7751 & 1.5741 \\  & Cloudy heterogeneous & 0.6078 & 0.7343 & 0.8135 & 1.0774 \\ \cline{2-6}  & Overall average & 0.6099 & 0.7179 & 0.7935 & 1.3256 \\ \hline \multirow{4}{*}{ICAP} & Homogeneous & 0.7022 & 0.7475 & 0.8013 & 0.7825 \\  & Heterogeneous & 0.7089 & 0.7318 & 0.7919 & 1.1610 \\ \cline{1-1}  & Cloudy homogeneous & 0.6918 & 0.7268 & 0.7854 & 1.0711 \\ \cline{1-1}  & Cloudy heterogeneous & 0.7253 & 0.7539 & 0.8152 & 0.8895 \\ \cline{1-1} \cline{2-6}  & Overall average & **0.7070** & **0.7400** & **0.7984** & 0.9761 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average Structural Similarity (SSIM), Tone-Mapped image Quality Index (TMQI), Feature Similarity extended to color image (FSIMc), and Fog Aware Density Evaluator (FADE) results on Foggy Road Image Database 2 (FRIDA2) dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **SSIM** & **TMQI** & **FSIMc** & **FADE** \\ \hline DCP & **0.8348** & 0.8631 & **0.9002** & 0.7422 \\ FFD & 0.7475 & 0.8000 & 0.8703 & 0.9504 \\ CAP & 0.7984 & 0.8206 & 0.8880 & 0.9745 \\ HPM & 0.7520 & **0.8702** & 0.8590 & 0.8556 \\ ICAP & 0.7691 & 0.8165 & 0.8787 & **0.7420** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average SSIM, TMQI, FSIMc, and FADE results on the D-HAZY dataset. TMQI, FSIMc, and FADE are used as in the preceding section. The values of \(e\) and \(r\) are determined by the following equations:  
\[e=\frac{n_{r}-n_{o}}{n_{o}}, \tag{33}\]  
\[r=exp\Bigg{[}\frac{1}{n_{r}}\sum_{i\in\Psi}log(r_{i})\Bigg{]}, \tag{34}\]  
where \(n_{r}\) and \(n_{o}\) denote the numbers of the set of visible edges in the restored image and the original image, respectively. Thus, \(e\) assesses the ability of an algorithm to restore edges that are visible in the restored image, but are not in the original one [45].