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Conference Papers Year : 2019

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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Dates and versions

hal-02288568 , version 1 (14-09-2019)

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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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