*4.4. Experiment of Simulated Images*

#### 4.4.1. Subjective Experiment

The simulated comparisons of the proposed local dimming method with LUT method, CDF method, and the method based on Otsu [10] are shown in Figure 11.

For Figure 11a, the dark areas in red rectangles of CDF and LUT algorithms are brighter, leading to a lower CR than the other two methods. In contrast, the method in [10] missed details caused by reducing luminance. The proposed method is a balance between improving CR and preserving details.

For Figure 11b, the clouds in the red circles of CDF and LUT methods are brighter than Figure 10b, which should be darker. For the clouds in the red rectangle by the method in [10], the image distortion is caused by overcompensation. For the image by the proposed method, the image contents in both the red circle and the red rectangle are well-compensated to improve CR and preserve details.

For Figure 11c, CDF and LUT methods simply improve the overall image luminance but without improvement of CR and image quality. The method in [10] improved the luminance of bright areas and decreased that of dark areas, which shows a preferable image. The image of the proposed method shows a higher CR with a higher saturation. However, the mountain part is slightly unsatisfactory compared with the image obtained by the method in [10]. This may be because the low luminance is mapped to smaller by histogram equalization.

**Figure 11.** Simulation results. From left to right: Images (**a**–**d**).

For Figure 11d, the images of CDF and LUT methods are bright to show rich details. In contrast, the image obtained by the method in [10] is distorted. Note that the red rectangle, seen as a high spatial-frequency part, retains more details by the proposed method compared with the image obtained by the method in [10].

### 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 *CRSI* and obtained by Equation (19).

$$
\mathbb{C}R\_{SI} = P\_{\mathbb{90}} / P\_{\mathbb{10}} \tag{19}
$$

where *P*<sup>10</sup> and *P*<sup>90</sup> 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).

$$\begin{cases} PSNR\left(\mathcal{C}\_1, \mathcal{C}\_2\right) = 10 \times \log\left(\frac{255^2}{MSE\left(\mathcal{C}\_1, \mathcal{C}\_2\right)}\right) \\\\ MSE\left(\mathcal{C}\_1, \mathcal{C}\_2\right) = \frac{1}{w \times h} \sum\_{i=1}^{w} \sum\_{j=1}^{h} \left(\mathcal{C}\_1\left(i, j\right) - \mathcal{C}\_2\left(i, j\right)\right)^2 \end{cases} \tag{20}$$

where *C*<sup>1</sup> and *C*<sup>2</sup> 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)

$$SSIM\left(\mathbb{C}\_1, \mathbb{C}\_2\right) = \frac{\left(2\mu\_{\mathbb{C}\_1}\mu\_{\mathbb{C}\_2} + \epsilon\_1\right)\left(2\sigma\_{\mathbb{C}\_1\mathbb{C}\_2} + \epsilon\_2\right)}{\left(\mu\_{\mathbb{C}\_1}^2 + \mu\_{\mathbb{C}\_2}^2 + \epsilon\_1\right)\left(\sigma\_{\mathbb{C}\_1}^2 + \sigma\_{\mathbb{C}\_2}^2 + \epsilon\_2\right)}\tag{21}$$

where *μC*<sup>1</sup> and *μC*<sup>2</sup> are the mean values of *C*<sup>1</sup> and *C*<sup>2</sup> respectively; *σC*<sup>1</sup> and *σC*<sup>2</sup> are the variance of *C*<sup>1</sup> and *C*2, respectively; *σC*1*C*<sup>2</sup> is the covariance of *C*<sup>1</sup> and *C*2; and <sup>1</sup> and <sup>2</sup> 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).

$$\begin{cases} \Delta \mathcal{C} = \sqrt{\left(2 + \frac{\overline{r}}{256}\right) \times \Delta R^2 + 4 \times \Delta G^2 + \left(2 + \frac{255 - \overline{r}}{256}\right) \times \Delta B^2} \\\\ \mathcal{C}D = \frac{\Delta \mathcal{C}}{w \times h} \end{cases} \tag{22}$$

where *r* = (*C*1,*<sup>R</sup>* + *C*2,*R*) /2, Δ*R* = *C*1,*<sup>R</sup>* − *C*2,*R*, Δ*G* = *C*1,*<sup>G</sup>* − *C*2,*G*, and Δ*B* = *C*1,*<sup>B</sup>* − *C*2,*B*; *C*1,*R*, *C*1,*G*, and *C*1,*<sup>B</sup>* represent the normalized components of original image, respectively; and *C*2,*R*, *C*2,*G*, and *C*2,*<sup>B</sup>* represent the normalized components of simulated image; respectively. The comparisons of the above four metrics are shown in Table 2.


**Table 2.** Comparisons of algorithmic processing. The best performance is marked in bold.

In Table 2, *CRSI* 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. In other words, the objective evaluation values are consistent with the subjective quality of the simulated images.

#### **5. Conclusions**

In this paper, a stronger adaptive local dimming method with details preservation is proposed to alleviate the disadvantage of a single algorithm. A three-step backlight extraction method is applied to determine the optimal backlight to improve display quality. In the pixel compensation, we compensate the luminance of the input image according to the smoothed backlight information. In addition, IBHE is proposed to enhance the luminance of an image and realize details preservation. Both the objective and subjective evaluation results demonstrate the effectiveness of the proposed local dimming method in keeping chroma information, and improving CR as well as PSNR, SSIM.

**Author Contributions:** Conceptualization, T.Z., W.D., and H.W.; methodology, T.Z., W.D., and H.W.; software, W.D.; validation, W.D., Q.Z., and L.F.; formal analysis, W.D.; investigation, H.W., W.D., Q.Z., and L.F.; resources, T.Z.; data curation, H.W.; writing—original draft preparation, T.Z. and W.D.; writing—review and editing, H.W., Q.Z., and L.F.; visualization, W.D.; supervision, T.Z.; project administration, T.Z.; and funding acquisition, T.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Research on HDR Backlight Liquid Crystal Processing Technology Based on Depth Neural Network under Contract HO2018085418.

**Conflicts of Interest:** The authors declare no conflict of interest.
