Some remarks on topological structures in the context of fuzzy relational mathematical morphology

摘要

In this paper, we develop a topological viewpoint on the subject of mathematical morphology. We show that erosion can be interpreted as a certain "remote" interior operator; in its turn dilation can be interpreted as a "remote" closure operator. Two categories are constructed, whose objects are "topological-type" structures obtained by combining operations of erosion and dilation.