# Backlight Unit Excessive Dimming Based on Perceptual Image Analysis
## 3 Methods
### Optimal Excessive Dimming
That is, for any two pixels \(b_{m}\) and \(b_{n}\) in the pixel saturation area, the average of the pixel value difference \(b_{m}-b_{n}\) (\(b_{m}>b_{n}\)) divided by the pixel distance \((b_{m},b_{n})\), which is the physical distance between pixels, is called the image slope, and the contrast can be evaluated from this. That is, the contrast response function can be evaluated with these values. The larger the contrast and the larger the pixel population \(\rm P(bed^{\prime},Max)\) from bed' to Max pixel, the narrower the range of excessive dimming becomes, so the degree of allowed excessive dimming can be expressed in terms of the saturated pixel slope (\(\rm SPS_{overall}\)) defined in (4), which identifies the location of the contrast in the contrast response curve. As in (3), constants \(d\), \(e\), and \(f\) are added to enable optimization according to the contrast response function by tests. \[\rm SPS_{overall}=d\cdot CR\left(avg\left(\frac{b_{m}-b_{n}}{pixel\ distance(b_{m},b_{n})}\right)\right)^{e}\cdot P(bed^{\prime},Max)^{f}, \tag{4}\]  
where CR is the contrast response function, \(d\), \(e\) and \(f\) are constants, and \(b_{m}\) and \(b_{n}\) are arbitrary pixels satisfying \(0\leq b_{n},\ b_{m}\leq Max,\ b_{n}\leq b_{m}\). As described in cases 4-9 of Figure 4b, since the contrast of the saturated pixel region becomes completely zero, the smaller the original pixel contrast, the less the change of the contrast is perceived enabling more excessive dimming. In addition to the \(\rm SPS_{overall}\) of (4), since the contrast decreases completely to zero by excessive dimming from the original value of the input image pixel contrast, the amount of perceived decrease of the input image contrast based on the contrast response function is determined by the image slope (\(\text{SPS}_{\text{sat}}\)) of the saturated pixel area. Based on these, the degree of possible excessive dimming can be expressed as (5). Constants \(g\), \(h\), and \(i\) are also added to optimize (5). \[\text{SPS}_{\text{sat}}=g\text{-CR}\bigg{(}\text{avg}\bigg{(}\frac{b_{m}-b_{n}}{ \text{pixel distance}(b_{m},\ b_{n})}\bigg{)}\bigg{)}^{h}\text{-P}(\text{ bed}^{\prime},\text{Max})^{i}, \tag{5}\]  
where \(\text{bed}^{\prime}\leq b_{m},\ \text{sat}_{\text{min}}\leq\frac{b_{n}-\text{ bed}^{\prime}}{b_{m}-b_{n}}\), and \(g\), \(h\) and \(i\) are constants, \(b_{m}\) and \(b_{n}\) are arbitrary pixels satisfying \(b_{n}\leq b_{m}\). As described in Figure 4b, since the contrast change is negligible if the saturation is less than a certain amount, we consider only the cases where the saturation is greater than or equal to a certain amount \(\text{sat}_{\text{min}}\), which is set by noticeable image quality degradation that is tolerable considering power budget. Optimal excessive global dimming (Opt.EGD) can be modeled as (6) by considering (3)-(5) in accordance with power budget and the tolerance of image quality degradation based on different application areas. \[\text{Opt.\ EGD}\approx\frac{\delta}{\left(\text{SPBSS}\right)^{\alpha}\text {-}\left(\text{SPS}_{\text{overall}}\right)^{\beta}\text{-}\left(\text{SPS}_{ \text{sat}}\right)^{\gamma}} \tag{6}\]  
where \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\) are constants. The weights of each of (3)-(5) can be adjusted with the constants \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\). While reducing bed', evaluating the image quality by the structural similarity index measure (SSIM) or by eye test, the values of \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\) can be determined enabling excessive dimming as much as possible, which is optimized for display panel characteristics and applications using several sample images. For local dimming, each block can be regarded as an independent image frame. Therefore, to optimize the amount of dimming according to the characteristics of the local block image by obtaining the SPBSS and \(\text{SPS}_{\text{sat}}\), \(\text{SPS}_{\text{overall}}\) of the local block, optimal excessive local dimming (Opt.ELD) can be modeled as (7) based on (6).