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International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing

ISMM 2017: Mathematical Morphology and Its Applications to Signal and Image Processing pp 16–27Cite as

Morphological Links Between Formal Concepts and Hypergraphs

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10225))

Abstract

Hypergraphs can be built from a formal context, and conversely formal contexts can be derived from a hypergraph. Establishing such links allows exploiting morphological operators developed in one framework to derive new operators in the other one. As an example, the combination of derivation operators on formal concepts leads to closing operators on hypergraphs which are not the composition of dilations and erosions. Several other examples are investigated in this paper, with the aim of processing formal contexts and hypergraphs, and navigating in such structures.

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Notes

  1. 1.

    In this paper we consider only the four basic operators (dilation, erosion, opening, closing).

  2. 2.

    In the table we denote by \(Inv(\varphi )\) the set of fixed points of an operator \(\varphi \) (i.e. \(x \in Inv(\varphi )\) iff \(\varphi (x)=x\)).

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Acknowledgments

This work has been partly supported by the French ANR LOGIMA project.

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Authors and Affiliations

  1. LTCI, Télécom ParisTech, Université Paris-Saclay, Paris, France

    Isabelle Bloch

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  1. Isabelle Bloch
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Correspondence to Isabelle Bloch .

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Editors and Affiliations

  1. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Jesús Angulo

  2. MINES ParisTech, PSL-Research University , Fontainebleau, France

    Santiago Velasco-Forero

  3. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Fernand Meyer

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Bloch, I. (2017). Morphological Links Between Formal Concepts and Hypergraphs. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-57240-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57239-0

  • Online ISBN: 978-3-319-57240-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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