Fuzzy connectedness (FC) constitutes an important class of image segmentation schemas. Although affinity functions represent the core aspect (main variability parameter) of FC algorithms, they have not been studied systematically in the literature. In this paper, we present a thorough 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 equivalent in the sense that they lead to identical segmentations. We give a complete characterization of the affinity equivalence and show that many natural definitions of affinity functions and their parameters used in the literature are redundant in the sense that different definitions and 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 demonstrate 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 and adaptive threshold detection. We finish with an analysis of possible ways of combining different component affinities that result in non equivalent affinities.
Conference Proceeding reprint.
Full version of the paper: Part 1 and Part 2 .
Last modified September 10, 2009.