Fuzzy mathematical morphologies: A comparative study

-Fuzzy set theory has found a promising field of application in the domain of digital image processing, since fuzziness is an intrinsic property of images. For dealing with spatial information in this framework from the signal level to the highest decision level, several attempts have been made to define mathematical morphology on fuzzy sets. The purpose of this paper is to present and discuss the different ways to build a fuzzy mathematical morphology. We will compare their properties with respect to mathematical morphology and to fuzzy sets and interpret them in terms of logic and decision theory. Fuzzy s e t s Mathematical morphology Fuzzy mathematical morphology Dilation Erosion Opening Closing Fuzzification Triangular norms and conorms Stochastic geometry Approximate reasoning Decision making Uncertain and imprecise spatial information Data fusion