A new fuzzy morphology approach based on the fuzzy-valued generalized Dempster-Shafer theory

Abstract

In this paper, a new Fuzzy Morphology (FM) based on the Generalized Dempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity of definitions between Mathematical Morphology (MM) and Dempster-Shafer Theory (DST), dilation and erosion morphological operations are studied from a different viewpoint. Then, based on this similarity, a FM based on the GDST is proposed. Unlike previous FM's, proposed FM does not need any threshold to obtain final eroded or dilated set/image. The dilation and erosion operations are carried out independently but complementarily. The GDST based FM results in various eroded and dilated images in consecutive α-cuts, making a nested set of convex images, where each dilated image at a larger α-cut is a subset of the dilated image at a smaller α-cut. Dual statement applies to eroded images.