*2.1. Backlight Extraction*

As an early and fundamental approach, the max method [4] employs the maximum luminance of an image block to determine the luminance level of the corresponding BLU. It also explores replacing the maximum luminance with the average luminance. However, the former is sensitive to noise and suffers from light leakage [1] problem. The latter reduces image luminance and suffers from losing details in bright areas. To achieve a trade-off between the above two methods, the methods proposed in [1,5,6] consider both the maximum luminance and the average luminance to improve display quality. In [1], a decision rule is proposed to determine optimal backlight by comparing the light leakage and the clipping of image blocks. This method is effective for images with bright objects in a dark area. In [5,6], the difference between the maximum and the average luminance value of a block is used to adjust backlight based on the average value. In [7], the global information of the image is used to extract backlight. It proposes a threshold method using a Cumulative Distribution Function (CDF) to ensure the distortion of the compensated image within a certain range. Besides, the methods proposed in [8,9] are effective to reduce power consumption. Based on Otsu [18], Zhang, T.; Wang, Y.F. [10] introduced a local dimming algorithm to separate foreground and background pixels for backlight extraction. In [11], the Peak Signal to Noise Ratio (PSNR) = 30 is considered as the lowest standard to guarantee the image quality. In [12], a Gaussian distribution model is proposed to reduce power consumption and improve image quality. In Swarm Intelligence (SI), the authors of [13,14] transformed the local backlight dimming to an optimization problem to preserve the image quality with low power consumption. A guided firework algorithm proposed in [14] achieves higher performance than the one in [13]. Although there are other local dimming algorithms [15,16], most of them favor only specific characteristic of an image. Therefore, we propose a backlight extraction method to adapt to images with diverse characteristics, acquiring preferable display quality.

#### *2.2. Pixel Compensation*

A backlight extraction method is commonly followed with a corresponding pixel compensation method to offset the luminance reduction. In this section, we document the representative method [5] and the closest related method [10] to ours for readability. In [5], the compensated luminance is obtained using the nonlinear relationship between the maximum backlight and the extracted backlight. However, image distortion caused by overcompensation in this method decreases the image quality. In [10], the logarithm function is used to compensate for luminance based on the input image and the smoothed backlight image. It is effective to prevent overcompensation but less effective for bright images.

Our pixel compensation method aims to alleviate the overcompensation problem by adjusting the luminance of the pixel in the input image according to the backlight value. Besides, by the proposed IBHE, this method is effective for improving the quality of display images.
