From Structuring Elements to Structuring Neighborhood Systems

International audienceIn the context of mathematical morphology based on structuring elements to define erosion and dilation, this paper generalizesthe notion of a structuring element to a new setting called structuringneighborhood systems. While a structuring element is often defined as asubset of the space, a structuring neighborhood is a subset of the subsetsof the space. This yields an extended definition of erosion; dilation canbe obtained as well by a duality principle. With respect to the classicalframework, this extension is sound in many ways. It is also strictly moreexpressive, for any structuring element can be represented as a structuring neighborhood but the converse is not true. A direct applicationof this framework is to generalize modal morpho-logic to a topologicalsetting