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506 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 2, FEBRUARY 2011 A Novel 3-D Color Histogram Equalization Method With Uniform 1-D Gray Scale Histogram Ji-Hee Han, Sejung Yang, and Byung-Uk Lee, Member, IEEE Abstract—The majority of color histogram equalization methods do not yield uniform histogram in gray scale. After converting a color histogram equalized image into gray scale, the contrast of the converted image is worse than that of an 1-D gray scale histogram equalized image. We propose a novel 3-D color histogram equalization method that produces uniform distribution in gray scale histogram by defining a new cumulative probability density function in 3-D color space. Test results with natural and synthetic images are presented to compare and analyze various color histogram equalization algorithms based upon 3-D color histograms.We also present theoretical analysis for nonideal performance of existing methods. Index Terms—Color image enhancement, gray scale histogram equalization, 3-D color histogram equalization. I. INTRODUCTION THE USAGE of digital images has rapidly increased with growing public consumption of entertainment and communication appliances, such as digital TV’s, digital cameras, scanners, mobile phone cameras, and personal media players. The expectation of a higher image quality prompts researchers to develop cutting-edge techniques for image enhancement. Histogram equalization has been one of the most widely used techniques due to its effectiveness and simplicity in contrast enhancement. Therefore, histogram equalization has become embedded in most consumer digital cameras. Histogram equalization modifies the pixel values in such a way that the intensity histogram of the resulting image becomes uniform. The output image then makes use of all the possible brightness values, thus, resulting in enhanced contrast [1]. First, we will review previous studies on color histogram equalization methods based upon 3-D histograms. The histogram equalization of a color image is more complex than 1-D equalization due to multidimensional nature of color signal. A typical color image has three color components: red (R), green Manuscript received August 21, 2009; revised January 18, 2010 and June 02, 2010; accepted August 03, 2010. Date of publication August 26, 2010; date of current version January 14, 2011. This work was supported in part by the Ministry of Knowledge Economy (MKE), Korea Industrial Technology Foundation (KOTEF) through the Human Resource Training Project for Strategic Technology, the Acceleration Research Program of the Ministry of Education, Science and Technology of Korea and the Korea Science and Engineering Foundation, and Ewha W. University under Grant 2008-1806-1. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jesus Malo. The authors are with the Electronics Engineering Department, Ewha W. University, Seoul 120-750, Korea (e-mail: jiheehan87227@gmail.com; sejungyang@gmail.com; bulee@ewha.ac.kr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIP.2010.2068555 (G), and blue (B). Trahanias and Vanetsanopoulos [2] proposed to use a 3-D color histogram instead of independently applying 1-D histogram equalization to each R, G, and B channel. They defined ideal output probability density function (pdf) to be uniform in the color space, and the cumulative distribution function (cdf) to be accumulation of pdfs within a box of size in 3-D color space. Although uniform pdf in gray scale dramatically enhances contrast of the images, uniform pdf in 3-D color space does not result in uniform pdf in luminance domain with the box shape cdf. Most of the natural images that are equalized using this method show higher concentration of bright pixels. We analyze the theory behind this less-than-ideal performance of contrast enhancement in Section II. Menotti et al. [3] partially overcame this lack of contrast enhancement by defining a new cdf that is a multiplication of the marginal cdfs of each color channel. However, this heuristic method does not work properly when color correlation is low. Other approaches for multidimensional histogram equalization include weighted 1-D marginal histogram equalization [4], and iterative matching of 1-D marginal pdf [5]. This work elucidates the reason behind nonideal performance of 3-D color histogram equalization algorithms, and proposes a new definition of cdf in RGB color space that will result in uniform luminance distribution after equalization. Since gray scale histogram equalization is a powerful and effective tool for contrast enhancement, achieving uniform luminance pdf is an important feature for image enhancement. There are many other color histogram equalization methods that are not directly related to the 3-D histogram. Mlsna and Rodriguez [6] introduced a histogram explosion method in 3-D color space. This method expands the color space of an image by equalizing 1-D histogram along a line from a central point in color space to the R, G, and B boundary points. The same author also applied this method in CIELUV color space [7]. Pitas proposed a multichannel histogram equalization method [8] using conditional probability density functions in HSI color space, and Lucchese suggested an equalization in x-y color space [9]. Several new approaches are based upon optimization. Kim and Yang interpolated the discrete pdf with Gaussian functions and applied nonlinear optimization [10]. Morovic and Sun found 3-D color histogram transformation using linear programming [11]. Arici et al. defined a cost function composed of image change, histogram deviation from the target, and histogram smoothness [12]. Chen et al. proposed gray-level grouping (GLG) that groups adjacent low values of histogram bins and then redistributes these groups iteratively [13]. Most of the histogram equalization algorithms use a histogram of the whole image. However, the use of an adaptive or local histogram enhances each region with different mapping depending