Signal Processing: Image Communication 19 (2004) 507–516 Determination of image bimodality thresholds for different intensity distributions Omer Demirkaya*, Musa H. Asyali Department of Biostatistics, Epidemiology, and Scientific Computing King Faisal Specialist Hospital and Research Center, P.O. Box 3354, Riyadh 11211, Saudi Arabia Received 8 October 2002 Abstract Between-class variance has been first proposed as a criterion function to determine an optimal threshold to segment images into nearly homogenous regions. This discriminant function is also widely used as a first step in iterative image segmentation methods such as Markov random field based methods to speed up the convergence. The between-class variance algorithm always computes an optimal threshold regardless of its validity. In this study, we established the threshold values (for bimodality) of the normalized (by total variance) between-class variance function for different distributions. The theoretical values of the bimodality thresholds for uniform and normal distributions are derived. The threshold values in the case of uniform, normal and poisson distributions were estimated through an image simulation approach. Experiments on simulated bimodal images showed that the threshold value for bimodality is dependent on the underlying noise distribution. The efficacy of the new threshold values was demonstrated on computer-simulated images as well as on actual images. r 2004 Elsevier B.V. All rights reserved. Keywords: Image bimodality; Between-class variance; Image segmentation 1. Theory and background 1.1. Between-class variance Between-class variance was introduced first by Otsu [5] as a discriminant function to determine an optimum threshold from an image histogram to segment images into nearly homogenous regions. It is optimal in the sense that it minimizes the mean square error between the original image and the segmented binary image in which pixels of each region are assigned the mean intensity of their respective class. This function has been frequently referred to in the literature and re- ported to perform best [6]. It is used as a segmentation method to segment the attenuation images in positron emission tomography (PET) [8]. It is also frequently used for the initial separation of intensity distributions prior to the application of an iterative segmentation method for the purpose of reducing the convergence time [9]. ARTICLE IN PRESS *Corresponding author. Tel.: 966-1-464-7272,x32504; fax: 966-1-442-7854. E-mail address: demirkaya@ieee.org (O. Demirkaya). 0923-5965/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.image.2004.04.002