## 3 Experiment Results
### Quantitative Comparison  
Generally, good display performance means high clarity and even gray level distribution. In order to do the quantitative comparison, the Tenengrad [33], Entropy, Naturalness Image Quality Evaluator (NIQE) [34], and Perception-based Image Quality Evaluator (PIQE) [35] are introduced. They are widely used in evaluating the quality of an image. The Tenengrad is written as  
\[G_{x}= \begin{bmatrix}1&0&-1\\ 2&0&-2\\ 1&0&-1\end{bmatrix}  \tag{24}\]  
\[G_{y}= \begin{bmatrix}1&2&1\\ 0&0&0\\ -1&-2&-1\end{bmatrix}  \tag{25}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Image** & **Size** & **Min (Gray Value)** & **Max (Gray Value)** & **\% of the Total Gray Levels** \\ \hline IM1 & 480°640 & 0 & 16961 & 25,880 \\ IM2 & 480°640 & 9893 & 16339 & 9.835 \\ IM3 & 512°640 & 1411 & 3575 & 3.302 \\ IM4 & 512°640 & 5683 & 8188 & 3.822 \\ IM5 & 512°640 & 6433 & 8653 & 3.387 \\ IM6 & 512°640 & 5984 & 11322 & 8.145 \\ IM7 & 512°640 & 6010 & 10000 & 6.088 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic information of the test images. \[S(x,y)=\sqrt{G_{x}*I(x,y)+G_{x}*I(x,y)} \tag{26}\]  
\[Tenengrad=\frac{1}{n}*\sum_{x}\sum_{y}S(x,y) \tag{27}\]  
where \(I(i,j)\) denotes the gray value of the pixel \((x,y)\), \(*\) denotes convolution, and \(n\) is the number of pixels in image. The Tenengrad is utilized to reflect the clarity of the whole image. Theoretically, the larger the Tenengrad value is, the higher the contrast, and the better the visibility of the details of the image. The calculation Tenengrad results are listed in Table 2.  
The even distribution of the pixel values of the image is another goal of image enhancement. And the entropy of an image is a common approach to reflect the pixel value's distribution. Specifically and theoretically, the larger the entropy value is, the more evenly the gray levels distributed. The entropy of an 8 bit image is written as  
\[Entropy(im)=-\sum_{i=0}^{255}p_{i}\log p_{i} \tag{28}\]  
where \(p_{i}\) is the probability of gray level \(i\) in the image. The calculation Entropy results are listed in Table 3.  
NIQE measures the distance between the NSS-based features calculated from image to the features obtained from an image database used to train the model. The features are modeled as multidimensional Gaussian distributions. We calculate it by the Matlab function \(nique()\), which returns a non-negative scalar. Theoretically, the lower value of NIQE is, the better the perceptual quality of the image. The results are listed in Table 4.  
PIQE calculates the no-reference quality score for an image through block-wise distortion estimation. We calculate it by the Matlab function \(pique()\), which returns a non-negative scalar in the range [0, 100]. The PIQE score is inversely correlated to the perceptual quality of an image. A low PIQE value indicates high perceptual quality and high PIQE value indicates low perceptual quality. The results are listed in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Image** & **Linear Mapping** & **HE** & **CLAHE** & **AHPBC** & **MSR** & **Reinhard** & **LEP** & **Proposed** \\ \hline IM1 & 4.2562 & 18.8087 & 15.7123 & 10.5995 & 4.2137 & 11.1091 & 21.5385 & 22.3971 \\ IM2 & 4.9403 & 12.3800 & 7.4490 & 4.7770 & 4.8471 & 4.7601 & 11.1299 & 18.1054 \\ IM3 & 4.4459 & 8.9382 & 4.2856 & 4.7390 & 4.1821 & 4.2448 & 11.0855 & 18.5358 \\ IM4 & 3.1144 & 4.4115 & 2.0874 & 3.6231 & 3.1346 & 3.1205 & 5.9977 & 7.8913 \\ IM5 & 4.6191 & 5.1433 & 3.9676 & 4.6468 & 4.4070 & 4.6040 & 9.5314 & 14.9446 \\ IM6 & 1.4227 & 7.8863 & 2.9639 & 2.7526 & 1.4158 & 1.6008 & 8.4747 & 6.7918 \\ IM7 & 2.0778 & 8.7989 & 2.9121 & 2.9168 & 2.0738 & 2.2411 & 8.9327 & 6.8261 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The [PERSON]’s value of the images.