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From Structuring Elements to Structuring Neighborhood Systems

Abstract : In the context of mathematical morphology based on structuring elements to define erosion and dilation, this paper generalizes the notion of a structuring element to a new setting called structuring neighborhood systems. While a structuring element is often defined as a subset of the space, a structuring neighborhood is a subset of the subsets of the space. This yields an extended definition of erosion; dilation can be obtained as well by a duality principle. With respect to the classical framework, this extension is sound in many ways. It is also strictly more expressive, for any structuring element can be represented as a structuring neighborhood but the converse is not true. A direct application of this framework is to generalize modal morpho-logic to a topological setting.
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Submitted on : Saturday, September 14, 2019 - 6:57:08 PM
Last modification on : Wednesday, September 22, 2021 - 3:02:02 AM



Alexandre Goy, Marc Aiguier, Isabelle Bloch. From Structuring Elements to Structuring Neighborhood Systems. 14th International Symposium on Mathematical Morphology (ISMM), 2019, Saarbr\"ucken, Germany. pp.16-28, ⟨10.1007/978-3-030-20867-7_2⟩. ⟨hal-02288568⟩



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