A New Fuzzy Morphology Approach Based on the Fuzzy - Valued Generalized Dempster - Shafer Theory

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 alpha-cuts, making a nested set of convex images, where each dilated image at a larger alpha-cut is a subset of the dilated image at a smaller alpha-cut. Dual statement applies to eroded images.