# Saturation-Based Airlight Color Restoration of Hazy Images
## 1 Introduction  
Scene analysis, target tracking, remote detection systems, and other outdoor image-based systems are affected by adverse atmospheric conditions caused by floating particles such as haze, clouds, or smog. Outdoor images and videos captured under bad weather often suffer from reduced visibility, low contrast, distorted colors, and low illumination intensity, which can degrade their quality and impact the performance of these systems. Therefore, researchers have conducted extensive studies to restore hazy images captured in adverse weather conditions [1, 2, 3, 4, 5, 6, 7, 8]. Typically, atmospheric particles such as fog and smog manifest as white or grayish colors in scenes, and previous research assumed this coloration and performed dehazing accordingly. However, hazy images captured under real-world weather conditions often exhibit color variations due to various environmental factors such as sand, chemical substances, sea, noise, and lighting conditions [9, 10, 11, 12]. Color-shifted hazy images have hindered the accurate color perception of scenes, and the intense coloration of dense haze has often resulted in worse visibility compared with standard hazy images. Consequently, conventional dehazing methods [1, 2, 3, 4, 5, 6, 7, 8] failed to restore the color of color-cast real hazyimages, often producing distorted color. Therefore, unlike typical hazy images, real hazy images have presented greater challenges in dehazing due to color-cast issues. Color correction-based dehazing algorithms have been proposed to restore color-cast images such as sandstorm images and underwater scenes. To address the issue of blurred visibility, [PERSON]'s atmospheric scattering model (ASM) [13; 14] has been used as a popular single-image dehazing method [1; 2; 3; 4; 5; 6]. ASM effectively defined various hazy images that required color correction, not limited to typical hazy images, and was used for various dehazing tasks, including underwater images [15; 16; 17; 18], sandstorm images [19; 20; 21], and color-cast remote detection images [22]. As [PERSON] et al. proposed a dark channel prior (DCP) effective in removing haze, visibility restoration studies for various color-cast images have been conducted based on DCP [17; 18; 19; 20; 21]. [PERSON] et al. [17] effectively restored underwater images by calculating the difference between the dark channel priors of green and blue channels and the red channel prior. [PERSON] et al. proposed halo-reduced dark channel prior dehazing (HRDCP) in which DCP was applied to the CIELAB(LAB) color space [20] to minimize the color distortion issue of the dehazing algorithm. Furthermore, [PERSON] et al. proposed normalized gamma transformation-based contrast-limited adaptive histogram equalization (NGCCLAHE) [21] as a revised method for compensating the insufficient contrast improvement function of HRDCP by applying a gamma correction formulation to contrast limited adaptive histogram equalization (CLAHE) [23], a well-known contrast improvement method. Both HRDCP and NGCCLAHE efficiently restored color-cast hazy images using the gray world hypothesis for white balancing. In addition, various other dehazing methods apply color constancy to the images [15; 16; 17; 22; 24]. Among them, weighted scene depth adaptive color constancy (WSDACC) [22] effectively removed color cast in heavily affected images by correcting the loss of ambient light extinction in the medium as an image formation model. However, existing color restoration studies have failed to consider the characteristics of haze models affected by ambient light, resulting in unsatisfactory results in some images. For example, color cast due to weather, scenes, or ambient light may exhibit colors similar to haze veils; however, existing methods are unable to address this, leading to output images with excessive grayscale or distorted colors. Furthermore, in cases where colorful objects occupy a wide area, distinguishing between the color of the haze and the objects is challenging, thereby posing limitations to existing methods.