(b) 50% contrast
(c) 50% brightness
(d) 50% CBCS
Fig. 5: Luminance functions and visual effects of adjusting brightness (b), contrast (c), and both (d) when the backlight is
dimmed to 50%.
transmissivity increases. In other words, while maintaining the same luminance, the power consumption of the TFT-LCD decreases when dimming the backlight. In addition, the variation of TFT-LCD power consumption is very small. Therefore, we do not consider the TFT-LCD power consumption in the CBCS framework.
OPTIMAL CBCS POLICY PROBLEM
The term contrast describes the concept of the differences between the dark and bright pixels. Brightness and contrast are the two most important properties of any image. In the Human Visual System , which models the perception of human vision as a three-stage processing, the brightness and contrast are perceived in the first two stages. Virtually every single display permits the users to adjust the brightness and contrast settings. For backlit LCD displays, the brightness control changes the backlight illumination and the contrast control changes the LCD transmissivity function. Fig. 5 shows how the brightness and contrast controls change the luminance function and their visual effects when the maximum brightness is limited to 50%. In Fig. 5b, when the backlight is reduced to 50%, the image contrast is noticeably reduced. If we compensate for the contrast loss as shown in Fig. 5c, then the darker (<50%) pixels preserve their original brightness while the brighter (>50%) pixels overshoot completely and there is no contrast present among these pixels. Fig. 5d shows how the concurrent brightness and contrast scaling generates a better image by balancing the contrast loss and number of overshot pixels. The luminance function in Fig. 5d or Fig. 4b represents the following class of linear transformations that can be implemented by the PLRD expressed by (7):
0 , ( ) c x d b t x b,
0xgl , glxgu, where
Here (gl,0) and (gu,b) are the points where y=cx+d intersects y=0 and y=b, respectively. The luminance function consists of three regions: the undershot region [0,gl], the linear region [gl,gu], and the overshot region [gu,1]. In other words, the gl and gu are the darkest and the brightest pixel values that can be displayed without contrast distortion (overshooting or undershooting). Notice that the slope of the linear region is very close to that of the original luminance function, which is unity. The image has very few pixels in the undershot and overshot regions. Its histogram is shown in Fig. 6a.
The kernel of CBCS is to find the dissimilarity between the original and backlight-scaled image, which can be solely determined by examining the luminance function bt(x). We define the contrast fidelity function as the
derivative of bt(x):
0 , 0 , , 0 1 0 , 1 ( ) x g l c g l x g u c c g u x f x
The c is limited between 0 and 1. If c>1, the contrast increases and deviates from that of the original image and the dynamic range [gl,gu] shrinks. The overall contrast fidelity will decrease from this point, so we do not include c>1 in our solution space.
The contrast fidelity is defined without quantifying contrast itself, which has no universal definition  and cannot help solve the optimal CBCS policy problem. However, the definition of contrast fidelity does convey the concept of the classic definitions of contrast such as Weber's or Michelson's that express contrast as the ratio of the luminance difference to the maximum luminance . If the normalized image histogram providing the probability distribution of the occurrence of pixel
value x in the image is given as p(x)[0,1], x=0..255,
then the global contrast fidelity of the backlight-scaled image is defined as
( ) ( ) . c f x p x
Fc is a function of p, gl and gu. Finding the optimal solution that minimizes the Fc is called the optimal CBCS policy problem.
The global contrast fidelity captures the brightness distortion due to backlight scaling, also. When the backlight is dimmed, the dynamic range [gl,gu] is shrunk accordingly, so that more pixels have contrast fidelity of zero.