## Normalized CCFL Power

(b)

(c)

1

(e)

(f)

(a)

### 0.6

0.5

0.4

0.3

0.2

0.1

Fig. 6: (a) Histogram of the example image (b) Optimal gl (left) and gl+dr (right) as functions of dynamic range dr in the y axis (c) Global contrast fidelity F_{c as a function of dynamic range dr }for b=1 (upper) and b=0.5 (lower) (d) Optimal solutions <F_{c,Pbacklight> (e) CBCS policy (f) Brightness-invariant policy. }

0

0

0.2

0.4

0.6

0.8

## Overall Contrast Fidelity

(d)

# B. Contrast fidelity Optimization Problem

To simplify the optimal CBCS policy problem, our approach is first to find the optimal linear transmissivity function for each given backlight factor, called the contrast fidelity optimization problem. Then we sweep the backlight factor domain to find the globally optimal solutions.

Our goal is to find the optimal gl and gu that maximize the overall contrast fidelity F_{c. After that, the optimal }coefficients c and d can be calculated from (10). The optimal transmissivity function t(x), which should be applied to the LCD as Fig. 4a, can then be determined by

0 , ( ) c x d b t x 1,

0xgl

, glxgu

gux1

,

(14)

and the backlight should be dimmed to b concurrently.

The optimal solution to the contrast fidelity optimization problem for an arbitrary histogram can be found by the following procedures.

Let dr=gu-gl be the size of the required dynamic range [gl,gu] and the backlight factor b be the size of the available dynamic range [0,b]. For each dr, we can find the required dynamic range [gl,gl+dr] that maximizes

gldr

∑

The optimal gl is found by scanning gl=0*256/k , . () px

## gl

1*256/k,…(k-1)*256/k, where k represents the resolution of the PLRD in (7). Based on the histogram shown in Fig. 6a, Fig. 6b shows the optimal gl and gl+dr in the x axis as functions of dr in the y axis. The left and right curves are the optimal gl and gl+dr, respectively, for different dr values. This means when the backlight is dimmed to dr, using the available dynamic range [0,dr] from the backlit

LCD to display the required dynamic range [gl,gl+dr] by the image will generate a backlight-scaled image that minimizes the number of undershot or overshot pixels.

Now consider the contrast fidelity c in (10). If the available dynamic range is larger or equal to the required dynamic range (dr≤b), the optimal contrast fidelity c=1 can be obtained with d≤0 and the overall contrast fidelity

# F_{c is simply }

gu

∑

( ) p x

.

O t h e r w i s e , i f d r > b , t h e h i g h e s t

## gl

possible contrast fidelity is c=b/dr with t=1 and d=0.

# Thus, F_{c becomes }

b dr

## gl dr

∑ ^{p(x). }

gl

(15)

Fig. 6c shows F_{c as a function of dr for b=1 (upper) and }b=0.5 (lower). The F_{c increases as dr increases from dr=0 }to dr=0.5. For the b=1 curve, the example image needs no more than 70% of available dynamic range to represent the whole histogram with the best contrast fidelity c=1. For the b=0.5 curve, the F_{c decreases from dr=0.5 to dr=1 }

because in (15) the

gldr

∑ ^{p(x) }

increases slower than dr. The

gl

optimal F_{c happens at dr=0.5 and the contrast fidelity c=1 }in the region [gl,gl+dr]. Notice that c=1 is not always the optimal solution when dr>b. If the distribution in the histogram is not normal (e.g. has two peaks) the optimal

dr

can

be

greater

than

b,

such

that

gldr

∑

p(x)

can

be

gl

increased. For each backlight factor b, the complexity of f i n d i n g t h e o p t i m a l F c , g l a n d g u i s O ( k 2 ) w i t h k a s m a l number (<12). l

C. Fidelity-Power Optimization

Given the solution to the contrast fidelity optimization problem for any backlight factor b, the optimal CBCS policy problem can be solved by sweeping the backlight factor range between b_{min and bmax, where bmin and bmax are }user-specified minimum and maximum backlight factors, respectively. All of the optimal solutions are recorded along with their power consumptions. The inferior solutions, i.e., same fidelity but higher power or same power but lower fidelity, are discarded. The remaining solutions are stored for the CBCS policy to select the most suitable solution according to the user preferences. Fig. 6d shows the 7 optimal solutions for b=0.8, 0.7,…0.2 from top-right to bottom-left. The x and y coordinates of each solution indicate the global contrast fidelity and backlight power, respectively. The two inferior solutions for b=1.0 and 0.9 are discarded because they have the same fidelity, F_{c=1, as that of b=0.8. The results show that more than }50% power savings can be achieved by the CBCS policy while maintaining almost 100% of contrast fidelity at a backlight factor of 70%. The visual effect is shown in Fig.