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

In this paper, firstly, we consider dilation and erosion operations of fuzzy morphology in a new point of view in order to clarify the similarity of relations between mathematical morphology and Dempster-Shafer theory (DST). Secondly, we propose a novel approach based on generalized Dempster-Shafer theory (GDST) for fuzzy morphology. This method, in contrast to previous methods, does not need any threshold to obtain final eroded⁄ dilated image, and also the dilation and erosion operations are carried out independently but complementary. The GDST based fuzzy morphology results various eroded⁄ dilated images in consecutive α-cuts that these images are convex. In other words, the eroded⁄ dilated image of α1-cut is a subset of an eroded⁄ dilated image of α2-cut where α1 ≤ α2 ⁄ α2 ≤ α1, respectively.