# Backlight Unit Excessive Dimming Based on Perceptual Image Analysis
## 3 Methods  
### Optimal Excessive Dimming  
In this section, by mathematically analyzing and modeling the image quality deterioration that a human perceives caused by excessive dimming, we seek a way to maximize it while preserving the perceived image quality according to all the theories described before. The image quality degradation caused by pixel saturation due to the excessive dimming described in the previous section depends on how many the input image pixels exist in the saturation region, brightness sensitivity considering the perceived brightness change shown in Figure 3, the contrast response function for humans' sensitivity of perceived contrast change caused by contrast magnitude difference shown in Figure 4a, and the contrast deterioration due to excessive dimming at pixel saturation region shown in Figure 4b. Let an arbitrary pixel value in an image to be \(\mathsf{b}_{i}\), \(\mathsf{f}(\mathsf{b}_{i})\) to be the relative frequency of pixels with pixel value \(\mathsf{b}_{i}\) in the entire image, the lowest input pixel value saturated by excessive dimming to be bed' as shown in Figure 1 and the maximum pixel value to be Max. Then, the ratio of the number of saturated pixels to the total number of pixels, \(\mathsf{P}(\mathsf{bed}^{\prime},\text{Max})\), can be expressed as (1). \[\mathsf{P}(\mathsf{bed}^{\prime},\text{Max})=\sum_{\mathsf{b}_{i}=\mathsf{ bed}^{\prime}}^{\text{Max}}\mathsf{f}(\mathsf{b}_{i}) \tag{1}\]  
For excessive dimming, since additional dimming is performed beyond the Max, \(\mathsf{P}(\mathsf{bed}^{\prime},\text{Max})\) cannot be equal to zero. As described in Figure 3, the lower the brightness sensitivity is, the lower the image quality degradation caused by pixel saturation is. For any pixel value \(\rm b_{i}\), if we let humans' perceived brightness to be \(\rm PB(b_{i})\), the slope on the brightness sensitivity slope (BSS) shown in Figure 3b is modeled as humans' perceived brightness difference by input pixel luminance value after saturation:  
\[\rm BSS(bed^{\prime})=\frac{\rm PB(Max)-PB(bed^{\prime})}{Max-bed^{\prime}} \tag{2}\]  
Therefore, the smaller the BSS of (2) is, the smaller the change in brightness that people perceive by excessive dimming, making it less to recognize the saturation of brightness due to pixel saturation, enabling more excessive dimming. As described before, as the number of pixels in the saturation region increases, the number of pixels affected by the dimming increases, and allowable excessive dimming decreases. To take this into account, the Saturated Pixel Brightness Sensitivity Slope (SPBSS) is defined as (3). In addition, fitting parameters \(a\), \(b\), and \(c\) are added to enable optimization according to the characteristics of the display panel and application fields. In other words, the larger the \(\rm BSS(bed^{\prime})\) from bed' to Max pixel, the larger the SPBSS of (3), and the image quality deterioration due to dimming is severe, limiting the excessive dimming. \[\rm SPBSS=a\cdot BSS(bed^{\prime})^{b}\cdot P(bed^{\prime},Max)^{c}, \tag{3}\]  
where \(a\), \(b\), and \(c\) are constants. Excessive dimming causes a decrease in contrast by pixel saturation. According to the contrast response function described in Figure 4a, within the range of contrast that a general image can usually have, the smaller the contrast is, the less noticeable the change of the contrast becomes, allowing more excessive dimming. The larger the number of pixels within saturation region, the less excessive dimming possible. Since the contrast between pixels increases as the difference in pixel brightness per unit distance increases, the difference between the pixel values of two arbitrary pixels, \(b_{m}\) and \(b_{n}\), and the distance between them are used.