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 GeneralizedDempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity ofdefinitions 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. Thedilation and erosion operations are carried out independently but complementarily. The GDSTbased FM results in various eroded and dilated images in consecutive α-cuts, making a nestedset of convex images, where each dilated image at a larger α-cut is a subset of the dilatedimage at a smaller α-cut. Dual statement applies to eroded images.