Affinity Functions in Fuzzy Connectedness Based Image Segmentation

Fuzzy connectedness (FC) constitutes an important class of image segmentation schemas. Although affinity functions represent the fundamental aspect (main variability parameter) of FC algorithms, they have not been studied systematically in the literature. In this paper, we present a through study to fill this gap. Our analysis is based on the notion of equivalent affinities: if any two equivalent affinities are used in the same FC schema to produce two versions of the algorithm, then these algorithms are strongly equivalent in the sense that they lead to identical segmentations. We give a complete characterization of the affinity equivalence and show that many natural parameters used in the definitions of affinity functions are redundant in the sense that different values of such parameters lead to equivalent affinities. We also show that two main affinity types, homogeneity based and object feature based, are equivalent, respectively, to the difference quotient of the intensity function and Rosenfeld’s degree of connectivity. In addition, we note that any segmentation obtained via relative fuzzy connectedness (RFC) algorithm can be viewed as segmentation obtained via absolute fuzzy connectedness (AFC) algorithm with an automatic threshold detection. We finish with theoretical and experimental analysis of possible ways of combining different affinities.