# A Stronger Adaptive Local Dimming Method with Details Preservation
## 3 Method
### Adjustable Backlight Extraction Module
#### 3.1.2 Optimal Backlight Selection  
Optimal backlight constraint conditions are constructed by all of the base backlights extracted above. One of the base backlights is selected as the target backlight for its ability in reducing power consumption and improving the contrast ratio. The second step of our method is to adjust the selected target backlight. Specifically, we adjust it based on the segmentation method in [23] and the obtained constraint conditions. Based on our self-developed LCD-LED dual modulation display [10], the optimal backlight is selected from adjusted backlights by objective evaluation as well as subjective evaluation in the third step. * Backlight constraint conditions  
We change specific values of the target backlight to obtain several adjusted backlights as alternations of the optimal backlight. The change needs to be within the effective range of backlight to prevent the deterioration of image quality. For an image block, we go through all base backlights for its corresponding maximum and minimum values. The maximum and minimum matrices are denoted as \(\textbf{P}_{\textbf{max}}\) and \(\textbf{P}_{\textbf{min}}\). This process is defined as:  
\[ \begin{cases}\textbf{P}_{\textbf{max}}=max\left(\textbf{BL}^{t}(m,n)\right) \\ \textbf{P}_{\textbf{min}}=min\left(\textbf{BL}^{t}(m,n)\right)\end{cases}  \tag{8}\]  
where \((m,n)\) is the coordinate of each backlight value in the backlight image. Considering that limited backlight extraction algorithms are used to construct backlight constraint conditions, \(\textbf{P}_{\textbf{max}}\) is increased by 10% with an upper boundary 255 and \(\textbf{P}_{\textbf{min}}\) is decreased by 10% with a lower boundary 0. The adjusted \(\textbf{P}_{\textbf{max}}\) and \(\textbf{P}_{\textbf{min}}\) are represented as \(\textbf{PA}_{\textbf{max}}\) and \(\textbf{PA}_{\textbf{min}}\), and they form the constraint conditions for obtaining the optimal backlight. * Backlight adjustment and optimal backlight selection  
Just Noticeable Difference (JND) [24] reflects the sensitivity of human vision. As shown in Figure 4, under different background luminance, JND is different. In image quality evaluation, if the luminance of details is too close to the neighboring pixels, that is, the difference is less than JND, then the details of this image are not well-displayed. In real  
Figure 4: JND curve. display, the background luminance may be changed due to light diffusion between different backlights, leading to the change of JND. Therefore, the image quality in real display may be degraded. To this end, we adjust the target backlight to change the background luminance and select the backlight that presents the details effectively based on display quality as the optimal backlight. Assume that target backlight is the \(k_{th}\) base backlight denoted as \(\mathbf{BL_{0}}\). \[\mathbf{BL_{0}}=f^{k}(I)\qquad k\in\{1,2,\cdots,N\} \tag{9}\]  
where \(f^{k}\) is the \(k_{th}\) base backlight extraction method. Improving the dynamic range is important in local dimming. Hence, for \(\mathbf{BL_{0}}\), we strengthen the luminance in bright area and weaken it in dark area to improve its dynamic range. Specifically, the bright and the dark area are selected by mean and variance of the backlight image. The process is expressed as Equations (10) and (11). \[ \begin{cases} M=\left(\sum_{m=1}^{W}\sum_{n=1}^{H}\mathbf{BL_{0}} \left(m,n\right)\right)\div\left(W\times H\right)\\ V=\left(\sum_{m=1}^{W}\sum_{n=1}^{H}\left(\mathbf{BL_{0}}\left(m,n \right)-M\right)^{2}\right)\div\left(W\times H\right)\end{cases}  \tag{10}\]  
\[ \begin{cases}P_{1}=M-V\\ P_{2}=M+V\end{cases}  \tag{11}\]  
where \(W\), \(H\), \(M\), and \(V\) are the width, height, mean, and variance of \(\mathbf{BL_{0}}\), respectively. \(P_{1}\) and \(P_{2}\) are the breakpoints to partition areas of different luminance.