Image segmentation using A-IFSs

The problem of segmentation in spite of all the work over the last decades, is still an important research field and also a critical preprocessing step for image processing, mostly due to the fact that finding a global optimal threshold that works well for all kind of images is indeed a near impossible task that, probably, will never be accomplished. During the past years, fuzzy logic theory has been successfully applied to image thresholding. Moreover, considering that for segmentation purposes, in most cases, image pixels have an inherent ambiguity in the predicate that they must fulfill in order to belong to an object, which results in the experts uncertainty in assigning the pixel to that object. In the context of fuzzy sets theory, Atanassov’s Intuitionistic fuzzy sets are a relevant and interesting extension since, uncertainty is one of the underlying ideas behind this theory. In this paper we describe a thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs). This approach uses Atanassov’s intuitionistic index values for representing the uncertainty of the expert in determining that the pixel belongs to the background or that it belongs to the object. We first introduce the general framework of this approach and then its natural extension to multilevel thresholding. Segmentation experimental results and their performance evaluation for the calculation of one, two and three thresholds are presented.