4.3.2. Objective Experiment

Tong, H. [26] defined a group of conditions to separate low/high luminance and low/high CR images with CDF curve. We selected one image from each category to evaluate the proposed method according to the conditions. The images chosen for the experiment and their corresponding CDF curves are illustrated in Figure 10.

**Figure 10.** Images used for objective experiment and corresponding Cumulative Distribution Function (CDF) curves: (**a**) low luminance image; (**b**) high luminance image; (**c**) low contrast ratio image; (**d**) high contrast ratio image; and (**e**) CDF curves of the images.

Assuming that *h* denotes the histogram of the measured luminance using luminance meter, *h*(*x*) denotes the number of pixels whose luminance is *x*. Inspired by the method of calculating CR in [10], we calculated the average values of luminance that are greater than *P*<sup>90</sup> and lower than *P*10, respectively, to calculate CR to reduce the influence of the measurement error. *P*<sup>10</sup> and *P*<sup>90</sup> are the luminance of which the cumulative numbers account for 10% and 90% of the total pixels, respectively. *Mmax* and *Mmin* are the maximum and minimum of the measured luminance. CR and DR are calculated as follows.

$$\begin{cases} Avg\_{10} = \sum\_{\mathbf{x} < P\_{10}} (h\left(\mathbf{x}\right) \times \mathbf{x}) \stackrel{\star}{=} \sum\_{\mathbf{x} < P\_{10}} h\left(\mathbf{x}\right) \\ Avg\_{90} = \sum\_{\mathbf{x} > P\_{90}} (h\left(\mathbf{x}\right) \times \mathbf{x}) \stackrel{\star}{=} \sum\_{\mathbf{x} > P\_{90}} h\left(\mathbf{x}\right) \\ CR = Avg\_{90} \stackrel{\star}{\twoheadrightarrow} Avg\_{10} \\ DR = M\_{\max} \stackrel{\star}{\twoheadrightarrow} M\_{\min} \end{cases} \tag{18}$$

The objective evaluations are shown in Table 1. We can observe that all CR values of optimal backlights are better than that of the target backlights. DR values in Images (b) and (d) under optimal backlights are slightly lower than those under target backlights. The reason lies in that the luminance of the bright area is almost 255, which cannot be increased. In contrast, the luminance of the dark area is still decreased, resulting in a reduction in overall luminance. For most cases, the comparisons confirm the effectiveness of the proposed method.


