Entropic and Relative Entropic Thresholding Techniques

Abstract

One of important features to be used for image thresholding is the gray-level co-occurrence matrix. A thereshold decomposes a co-occurrence matrix into four quadrants which correspond to background-to-background (BB), background-to-foreground (BF), foreground-to-background (FB), foreground-to-foreground (FF) respectively. In this paper, thresholding techniques based on maximization of Shannon’s entropy and minimization of relative entropy are studied and compared, particularly, those developed by N.R.P et al-S.K. Pal, Kittler-Illingworth and Change at al. The former (i.e., Pal-Pal’s technique) maximizes Shannon’s entropies of sum of BB and FF or sum of BF and FB, whereas, the latter (i.e., Kittler-Illingworth and Chang et al’s methods) minimizes the relative entropy between an original image and a thresholded image. Despite the difference in optimization, all the three approaches are indeed closely related. Conceptually, they are developed based on a general design rationale widely used in pattern classification, namely, while minimizing the differences of samples within class, the differences of samples between class are also maximized. As a result, their performances can be well explained in terms of the concepts of within class and between class.