Fast Optimal Multimodal Thresholding Based on Between-Class Variance Using a Mixture of Gamma Distributions Eidah Assidan and Ali El-Zaart Department of Computer Science College of Computer and Information Sciences King Saud University eidah7@hotmail.com , dr_elzaart@yahoo.com , and elzaart@ksu.edu.sa Abstract Images segmentation is an important issue for many applications as pattern recognition and computer vision. Thresholding is an important and fast technique used in most applications. Gaussian Otsu’s method is a thresholding technique based on between class variance. Gamma distribution models data more than Gaussian distribution. In this paper, we developed a new formula using Otsu’s method for estimating the optimal threshold values based on Gamma distribution. Our method applied on bimodal and multimodal images. Also It uses an iteratively rather than sequentially to decrease the number of operations. Further, using Gamma distribution give satisfying thresholding results in low-high contrast images where modes are symmetric or non-symmetric. For our results, we compared it with the original Gaussian Otsu’s method. Keywords: Gamma distribution, Thresholding, Between-Class Variance. 1. Introduction Image segmentation is an important issue in many image-processing applications for separating objects of interest and displaying them obviously. Many segmentation methods have been proposed and applied in many different applications [1, 2, 3, 4]. In thresholding techniques only, there are more than 40 thresholding methods [5]. However, many studies focus on thresholding techniques for segmentation. Thresholding based on between-class variance (BCV) separates the object from the background in most images. As well as many studies were invented to improve BCV methods [13, 8]. In [14] the obtaining threshold value is based in Genetic Algorithm (GA) by finding out the valley bottom between two peaks in the histogram of image. Also, paper [15] discusses the impact of class probability and class variance to find the threshold value. However, all these studies are based on Gaussian distribution to find the threshold value, which gives limited results restricted by symmetric modes. Our contribution in this paper is to improve the Otsu’s method [6, 7] in the case of non- symmetrical histogram by using Gamma distribution. We applied our method for estimating the optimal threshold values on bimodal and multimodal images. In addition, using iteratively algorithm rather than sequential. A similar study was an improvement in minimum cross entropy thresholding (MCET) method by using Gamma distribution [10, 12]. It is shows that used Gamma distribution to improve both bimodal and multimodal thresholding methods give good results which encourage us to use Gamma distribution to improve another method (Otsu’s method) and develop our method. Furthermore, Gamma distribution has the ability to deal with low-high contrast images where modes (intensity value distribution in the histogram) are symmetric or non-symmetric. While Gaussian distribution that has been used in old Otsu’s method is suitable more for symmetric mode, but it gives limited results in non-symmetric mode. This paper is organized as follows: Section 2 describes Gamma distribution concept. In section 3, we present our new formula to find the optimal threshold value on bimodal and multimodal images. Section 4 provides experimental results of the new formula on bimodal and multimodal images. Finally, conclusion and future work is presented in section 5. 2. Gamma Distribution Histogram represents statistical information of image pixels. It describes pixels intensity distribution in an image by graphing the number of pixels intensity Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009 978-1-4244-2794-9/09/$25.00 ©2009 IEEE 2673