# Improved Color Attenuation Prior for Single-Image Haze Removal
## 1 Introduction  
The prevalence of consumer cameras and the urgent need for groundbreaking work in surveillance or autonomous driving systems have demanded the rapid development of image/video processing algorithms. Among them, the task of eliminating unwanted-but-inevitable weather phenomena from an image has drawn increasing attention in recent years. Generally, this image processing problem is known as visibility restoration. A myriad of algorithms have been proposed to recover the visual quality of weather-degraded images to be as similar as possible to the original ones taken under clear weather conditions. Low-light image enhancement [1; 2; 3; 4], rain removal [5; 6; 7; 8], and image dehazing [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27] are cases in point. Haze removal ones, of all the algorithms developed for visibility restoration, have positive impacts on both photography and computer vision applications. Not only does haze removal function properly in hazy, foggy, or misty weather, but it also is appropriate for removing the effect of yellow dust or dust storm on the captured image. Owing to rapid industrialization and urbanization yellow dust is a topical issue in Eastern Asian countries [28] and there is growing demand for a highly sophisticated visibility restoration algorithm. Generally, haze removal algorithms are categorized according to the number of input images they need. Due to sufficient input information, multi-image approaches [9; 10; 11; 12] are superior to single-image ones [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27] in terms of performance. Given the difficulty of collecting the external information, however, there is little interest from researchers. Accordingly, recent efforts largely have led to single-image dehazing using two-dimensional images without any external knowledge. Such an algorithm, nonetheless, needs to impose priors on the recovered image, for example, enhanced contrast or less attenuated color [23]. The most popular prior is the Dark Channel Prior (DCP), proposed by [PERSON] et al. [13], which assumes that there exists a dark pixel in every color channel of the local patch around all pixels. Shortly thereafter, the DCP has been improved in many directions [14; 15]. Otheralternative priors to DCP are the Color Attenuation Prior (CAP) [20], and a distribution of color pixels in the RGB space [18; 21]. [PERSON] et al. provided a comprehensive review of these methods [22]. A second approach to dehazing problems is to use machine learning techniques [20; 25; 27]. The mapping between a hazy image and its depth-correlated haze distribution is learned from data in this context. Nevertheless, the lack of real datasets of hazy images and their corresponding ground truth references imposes a limit on the performance of these methods. Yet a third way of approaching image dehazing problems is to consider dehazing as a traditional image enhancement task [23]. The goal is to produce a good quality dehazed image in lieu of estimating the haze distribution in this case. The means to accomplish this consist of contrast enhancement, Retinex-based and fusion-based techniques. The haze removal method presented in this paper is an improvement upon CAP in terms of both computational efficiency and the dehazed image's quality. This is achieved by examining the existing drawbacks of CAP, and then proposing effective solutions for individual ones. The first shortcoming of CAP lies in its data preparation stage when training the depth estimator. The synthetic ground truth depth maps are assumed to be uniformly distributed. Since existing pseudo random number generators cannot guarantee the uniform distribution, however, we propose the enhanced equidistribution that has been validated in our previous work [29; 30]. We also propose using a simple low-pass filter to remove the background noise and using a simple linear weight to get rid of the color distortion.