Generalized Rough Sets, Entropy, and Image Ambiguity Measures

Quantifying ambiguities in images using fuzzy set theory has been of utmost interest to researchers in the field of image processing. In this paper, we present the use of rough set theory and its certain generalizations for quantifying ambiguities in images and compare it to the use of fuzzy set theory. We propose classes of entropy measures based on rough set theory and its certain generalizations, and perform rigorous theoretical analysis to provide some properties which they satisfy. Grayness and spatial ambiguities in images are then quantified using the proposed entropy measures. We demonstrate the utility and effectiveness of the proposed entropy measures by considering some elementary image processing applications. We also propose a new measure called average image ambiguity in this context.