# A Stronger Adaptive Local Dimming Method with Details Preservation
## 4 Experiment
### Experiment of Simulated Images
#### 4.4.2 Objective Experiment  
In our experiments, in addition to for CR [10], Peak Signal-to-Noise Ratio (PSNR) [27], Structural Similarity Index (SSIM) [14], and Color Difference (CD) [28] were further applied to evaluate the simulated image comprehensively. CR, used to evaluate the dynamic range of luminance, is an important metrics in image processing. Generally, an image with a high CR presents vivid and rich colors. Note that the CR used to evaluate the simulated images is calculated differently compared with the CR in Section 4.3.2. To distinguish them, the CR calculated by the simulated image is defined as \(CR_{SI}\) and obtained by Equation (19). \[CR_{SI}=P_{90}/P_{10} \tag{19}\]  
where \(P_{10}\) and \(P_{90}\) are the luminance of which the cumulative numbers account for 10% and 90% of the total number of pixels in simulated image, respectively. PSNR was employed to evaluate the distortion between signal and noise. A higher PSNR indicates a lower distortion. The definition of PSNR is described in Equation (20). \[\left\{ \begin{aligned} & PSNR\left(C_{1},C_{2}\right)=10\times log \left(\frac{255^{2}}{MSE\left(C_{1},C_{2}\right)}\right)\\ & MSE\left(C_{1},C_{2}\right)=\frac{1}{w\times h}\sum_{i=1}^{w} \sum_{j=1}^{h}\left(C_{1}\left(i,j\right)-C_{2}\left(i,j\right)\right)^{2} \end{aligned} \right. \tag{20}\]  
where \(C_{1}\) and \(C_{2}\) are the original image and the simulated image, respectively, while \(w\) and \(h\) mean the width and the height of the simulated image. SSIM is widely used in realizing structural similarity theory. SSIM ranges from 0 to 1 and a better image quality leads to a higher SSIM. The definition of SSIM is described in Equation (21)  
\[SSIM\left(C_{1},C_{2}\right)=\frac{\left(2\mu_{C_{1}}\mu_{C_{2}}+\epsilon_{1} \right)\left(2\sigma_{C_{1}C_{2}}+\epsilon_{2}\right)}{\left(\mu_{C_{1}}^{2}+ \mu_{C_{2}}^{2}+\epsilon_{1}\right)\left(\sigma_{C_{1}}^{2}+\sigma_{C_{2}}^{2 }+\epsilon_{2}\right)} \tag{21}\]  
Figure 11: Simulation results. From left to right: Images (**a**–**d**). where \(\mu_{C_{1}}\) and \(\mu_{C_{2}}\) are the mean values of \(C_{1}\) and \(C_{2}\) respectively; \(\sigma_{C_{1}}\) and \(\sigma_{C_{2}}\) are the variance of \(C_{1}\) and \(C_{2}\), respectively; \(\sigma_{C_{1}C_{2}}\) is the covariance of \(C_{1}\) and \(C_{2}\); and \(\epsilon_{1}\) and \(\epsilon_{2}\) are two constants to avoid invalid division. Besides, from the perspective of color information, we adopted CD to evaluate the color distortion by applying weighted Euclidean distance in RGB color space. The process to obtain the CD is expressed in Equation (22). \[ \begin{cases}\Delta C=\sqrt{\left(2+\frac{\overline{r}}{256}\right)\times \Delta R^{2}+4\times\Delta G^{2}+\left(2+\frac{255-\overline{r}}{256}\right) \times\Delta B^{2}}\\ CD=\frac{\Delta C}{w\times h}\end{cases}  \tag{22}\]  
where \(\overline{r}=\left(C_{1,R}+C_{2,R}\right)/2\), \(\Delta R=C_{1,R}-C_{2,R}\), \(\Delta G=C_{1,G}-C_{2,G}\), and \(\Delta B=C_{1,B}-C_{2,B}\); \(C_{1,R}\), \(C_{1,G}\), and \(C_{1,B}\) represent the normalized components of original image, respectively; and \(C_{2,R}\), \(C_{2,G}\), and \(C_{2,B}\) represent the normalized components of simulated image; respectively. The comparisons of the above four metrics are shown in Table 2.  
In Table 2, \(CR_{SI}\) obtained by the proposed method is higher than that of the three other top algorithms by 7.0%, 10.0%, 26.8%, and 23.1%, respectively. PSNR is improved by 33.9%, 11.4%, 4.1%, and \(-\)4.1%, respectively. PSNR of high contrast ratio image by the proposed method follows the highest one by the method in [10] closely. For SSIM, the performance of the proposed method is slightly inferior for low contrast ratio image. However, it is still competitive to other algorithms, especially for low luminance image. For CD, images processed by the proposed method reduce the distortion of chroma information effectively, especially for the low luminance image and the high contrast ratio image.