# Content-Adaptive Light Field Contrast Enhancement Using Focal Stack and Hierarchical Network
## 4 Experimental Results and Discussion
### Objective Assessment  
An effective enhancement algorithm should improve the perceived quality without affecting the naturalness of the image or adding any artifacts [49]. Nonetheless, relying on a subjective judgment of image quality is not sufficiently accurate, since the judgment of each individual varies greatly. Table 2 shows the data results, and we made the following objective assessments of the images. Ideally, the contrast enhancement method should not change the hole brightness. The Absolute Mean Brightness Error (AMBE) calculates the brightness change, which is defined as the difference between the mean intensity of the original image \(I_{o}\) and that of the enhanced image \(I_{e}\). \[AMBE=|E(I_{o})-E(I_{e})| \tag{15}\]  
where \(E(. )\) is the mean intensity of the underlying image. A lower AMBE indicates better corresponding brightness preservation. The results show that this evaluation criterion is consistent with the subjective assessment. The HE method has poor brightness preservation, while our method and CLAHE have better expression. The average brightness is effectively maintained, and the enhanced image can better restore the overall brightness characteristics of the original image, and has better adaptability to the human eye. The most obvious metric by which to access a contrast enhancement architecture is contrast improvement. [PERSON] et al. [50] proposed a method to evaluate the contrast of complex images called the Measure of Enhancement by Entropy (EMEE), and defined it for the enhanced image \(I_{e}\) as  
\[EMEE=\frac{1}{M\times N}\sum_{i=1}^{M}\sum_{j=1}^{N}\alpha\left(\frac{I_{e}^{ max}(i,j)}{I_{e}^{min}(i,j)+C}\right)^{\alpha}log_{2}\frac{I_{e}^{max}(i,j)}{I_{e}^{ min}(i,j)+C} \tag{16}\]  
where the symbols max and min correspond to the maximum and minimum intensity values, \(M\) and \(N\) are the width and height, \(C\) is a constant to avoid division by zero, and \(\alpha\) is an exponent to control for the enhancement effect [50]. Using this evaluation criterion, HE achieves the best presentation, although it may produce unreal appearances and may not produce visually pleasing images. This finding is understandable, because HE does not consider whether the image is natural and real, and only aims to improve the contrast. The results show that our method improves the image contrast and does not produce an unnatural appearance. This result can be seen in Figure 7; although the contrast of the LF image is greatly improved, the detailed information in the LF image is lost due to the excessive contrast enhancement of the LF image after the HE method, and the texture of the cars, stones, and other objects disappears. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **AMBE** & **EMEE** & **SMO** & **LOM** \\ \hline CLAHE & 10.1256 & 4.4620 & 2.8811 & 143.5008 \\ HE & 12.6343 & 10.5646 & 6.8140 & 511.9235 \\ Imadjust & 17.0528 & 6.5435 & 1.0178 & 403.5677 \\ Ours & 5.2129 & 4.3252 & 2.4648 & 197.9581 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Image quality evaluation of the proposed algorithms compared with CLAHE, HE, and Imadjust. [PERSON] et al. [51] devised an objective criterion with which to detect over-enhancement, which is called the Structure Measure Operator (SMO) and is defined as  
\[SMO=\frac{1}{M\times N}\sum_{i=1}^{M}\ \sum_{j=1}^{N}\frac{\left|HO_{ij}^{o}- HO_{ij}^{e}\right|}{HO_{ij}^{o}} \tag{17}\]  
where \(HO_{ij}\) is the product of three values: the entropy, edge value, and standard deviation around a pixel in a \(d\times d\) window. The SMO is insensitive to changes in contrast, but sensitive to changes in structure. Ideally, the SMO is zero if the enhancement does not change the structure. The results show that over-enhancement occurs with the HE method, and the other methods show a high performance, which is consistent with our subjective analysis. To evaluate the preservation of image naturalness, [PERSON] et al. [52] presented the Lightness Order Measure (LOM) from a local inversion of the lightness order.