A RETINEX based Haze Removal Method Sudharsan Parthasarathy Department of Electronics and Communication Engineering National Institute of Technology Calicut Kerala, India Email:sudharsan.vparthasarathy@gmail.com Praveen Sankaran Department of Electronics and Communication Engineering National Institute of Technology Calicut Kerala, India Email: psankaran@nitc.ac.in Abstract—One of the most interesting problems in recent times in image processing and computer vision is fog, haze and rain removal from images. In this paper we shall consider the problem of haze removal. One of the latest haze removal algorithms proposed by Kaiming et al. [1] uses a dark channel prior based approach for haze removal. Though this approach gives very good results, this method is computationally complex. In this paper we propose a RETINEX based approach that gives good results and is also computationally simpler. I. I NTRODUCTION Images photographed in hazy or foggy conditions capture the scene correctly as the observer sees it. But there are applications like the landing system of aeroplanes or automatic car driving systems where it is important to see the objects that are obscured in the haze or fog. Haze removal methods can be divided into three broad categories viz. algorithms that use i) multiple images, ii) apriori information and iii) single image. Polarising filter based algorithm uses two or more images for haze removal. The algorithm works on the principle that ‘airlight’ of the image is polarized [2]. We will see the term ‘airlight’ in Section II. Another algorithm by Narasimhan et al. [3] for haze removal uses multiple images taken under different weather conditions. Haze removal algorithms using apriori information needs either user supplied depth information [4] or a 3D model [5]. Recently single image based haze removal models have been proposed. These models use the haze formation physical model that has been developed by Koschmieder [6]. Narasimhan et al. [7] describe in detail the physics behind the atmosphere optics and the haze formation model. In 2008, Tarel proposed a single image based haze removal algorithm [8]. He observed that a haze free image has higher local contrast than a hazy image. So he was able to obtain haze free image by maximizing the local contrast in the hazy image. The drawback of this approach is that it is not based on haze formation physical model and hence the haze free images appear unnatural due to over saturation of colours. Recently in 2011 Kaiming et al. [1] proposed a dark channel prior based approach. This approach gives us good results but it is computationally complex. In this paper we propose a retinex based approach for haze removal. This method uses the Koschmieder haze formation method and also reduces the computational time when com- pared to the dark channel prior method. In Section II we will see the Koschmieder haze formation model. In Section III we shall see Kaiming et al.’s dark channel prior method. In Section IV we shall describe the retinex model. In Section V we shall discuss the proposed retinex based haze removal approach. In Section VI we shall discuss the results in detail. II. KOSCHMIEDER MODEL The optical model used to describe the formation of haze proposed by Koschmieder [6] is given as I c (x)= J c (x)t(x) + (1 − t(x))A c (1) where I c (x) represents a hazy image. c represents Red, Green and Blue colour bands. J c (x) represents a haze free im- age in the three colour bands. t(x) represents the transmission map. We assume the transmission remains constant across all three color bands. A c represents the global atmospheric light in three colour bands. A c is a constant that affects all pixels in the image in the same manner. The challenge has been to obtain t(x) and A c from the hazy image I c (x) and hence find the haze free image J c (x). The term J c (x)t(x) is called direct attenuation and it is a multiplicative distortion of the scene radiance J c (x). The term (1 − t(x))A c is called airlight and it is an additive distortion of the scene radiance. In a homogeneous atmosphere, trans- mission t(x) can be expressed as t(x) = exp (−βd(x)) (2) where d(x) represents the depth of the scene and β represents the scattering coefficient of the atmosphere. III. DARK CHANNEL PRIOR METHOD Dark channel prior method [1] is based on the principle that in a haze free image the intensity of at least one of the three channels is very low(dark) and close to zero. The dark channel can be described as J dark (x)= min yǫΩ(x) ( min cǫr,g,b J c (y)) (3) where J is any arbitrary image, x and y represents the pixels of the image. J c is a color band of J and Ω(x) is a local patch area centered at pixel x of the image. A filter of size Ω(x)=15 is typically used. 978-1-4673-2605-6/12/$31.00 c  2012 IEEE