# Image Dehazing and Enhancement Using Principal Component Analysis and Modified Haze Features
## 4 Experimental Results
### Application to Low-Light Image Enhancement  
In this subsection, we demonstrate that the proposed method can improve the quality of a low-light image by using the degradation model of an inverted haze image. [PERSON] et al. assumed that inverted low-light images are similar to hazy images by analyzing a histogram [24]. [PERSON] et al. showed that an inverted low-light image can be regarded as a haze image in terms of visual similarity [25]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{[1]} & \multicolumn{3}{c}{[9]} & \multicolumn{3}{c}{[8]} & \multicolumn{3}{c}{[2]} & \multicolumn{3}{c}{[6]} & \multicolumn{3}{c}{**Proposed**} \\ \cline{2-13}  & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) & \(\mathbf{\Sigma}\) & \(\mathbf{\bar{r}}\) \\ \hline Figure 8a & 0.0000 & 1.0870 & 0.1848 & 1.5752 & 1.8338 & 1.7643 & 0.0011 & 1.4817 & 0.0335 & 1.2680 & 0.0095 & 1.1960 \\ Figure 8b & 0.1664 & 1.6934 & 1.1730 & 2.1021 & 0.2565 & 2.4137 & 0.1468 & 1.7906 & 0.1694 & 1.5785 & 0.2161 & 1.4357 \\ Figure 8c & 0.0451 & 1.3218 & 0.2335 & 2.1207 & 6.8876 & 2.3389 & 0.4164 & 1.5604 & 0.7551 & 1.2884 & 0.3001 & 1.2475 \\ Figure 8d & 0.0000 & 1.1548 & 0.0000 & 1.5989 & 0.1561 & 2.1856 & 0.0000 & 1.3821 & 0.0000 & 1.3001 & 0.0000 & 1.2380 \\ Figure 8e & 0.0168 & 1.6015 & 0.1468 & 2.1761 & 0.2651 & 2.1589 & 0.0485 & 1.7905 & 0.1226 & 1.7027 & 0.1152 & 1.4676 \\ Figure 8f & 0.1256 & 2.2194 & 0.0487 & 2.6322 & 0.0563 & 2.3590 & 0.8070 & 1.9389 & 0.0019 & 1.8372 & 0.4088 & 1.6709 \\ Figure 8g & 0.0285 & 1.0251 & 0.5099 & 1.3173 & 2.0646 & 1.9343 & 0.0801 & 1.2948 & 0.5049 & 1.1967 & 0.2038 & 1.1557 \\ Figure 8h & 0.0003 & 2.6491 & 0.0366 & 3.6266 & 0.1915 & 5.0999 & 0.0000 & 1.7928 & 0.0000 & 1.7705 & 0.0000 & 1.5342 \\ Figure 8i & 0.0000 & 1.2353 & 0.0293 & 2.3817 & 0.3793 & 2.0831 & 0.1233 & 1.3019 & 0.1233 & 1.3019 & 0.0459 & 1.2112 \\ Figure 8j & 0.3083 & 1.1934 & 0.2971 & 1.5665 & 4.7788 & 2.8473 & 54.6675 & 1.6899 & 0.2363 & 1.1427 & 0.2992 & 1.3260 \\ \hline
**Avg.** & 0.0691 & 1.5181 & 0.1660 & 2.1097 & 1.6870 & 2.5185 & 0.7291 & 1.6112 & 0.1947 & 1.4387 & 0.1599 & 1.3469 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of objective assessments using [PERSON]’s method [21]. Figure 12: The test images used for the objective assessments of the performance of transmission estimation [23]: (**a**)-(**e**) are the real outdoor haze-free images of size 3873 \(\times\) 2516. The haze image can be synthesized using corresponding depth map of the haze-free image. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{[4]} & \multicolumn{2}{c}{**Proposed**} \\ \cline{2-5}  & \(\mathbf{\#\text{of Trees}}\) & \(\mathbf{200}\) & \(\mathbf{200}\) & \(\mathbf{100}\) & \(\mathbf{50}\) \\ \hline Figure 12a & MSE & 0.0600 & 0.0313 & 0.0316 & 0.0324 \\ Figure 12b & MSE & 0.0500 & 0.0428 & 0.0428 & 0.0430 \\ Figure 12c & MSE & 0.0780 & 0.0314 & 0.0316 & 0.0320 \\ Figure 12d & MSE & 0.0693 & 0.0245 & 0.0241 & 0.0252 \\ Figure 12e & MSE & 0.0612 & 0.0384 & 0.0390 & 0.0390 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the objective assessments of the transmission estimation using random forest. Based on this observation, they improved the quality of low-light images by solving the degradation model of a haze image with an inverted low-light image. The conventional haze model in (1) can be rewritten by respectively substituting \(g(x)\) and \(f(x)\) with their inverted versions:  
\[g_{inv}(x)=f_{inv}(x)t(x)+A(1-t(x)), \tag{10}\]  
where \(g_{inv}(x)\) and \(f_{inv}(x)\) respectively represent the inverted versions of the input low-light and the latent images. To enhance the brightness of an input low-light image, [PERSON] et al.