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Mathematical Morphology and Its Applications to Image Processing pp 61–68Cite as

Minimal Generator Basis of a Finite Structural Opening

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Part of the Computational Imaging and Vision book series (CIVI,volume 2)

Abstract

In a pseudo-ring structure of the power space where the “max” plays the role of the addition and the Minkowski sum the role of the multiplication, all idealoids are invariance domain of an algebraic opening which is translation invariant. Since a finite structural opening is completely characterized by its invariance domain, the purpose of this paper is to find a “minimal generator basis” of a subset which is closed under union and translation, and which is the invariance domain of a finite structural opening, i.e. a minimal generator basis of the associated idealoid.

Key words

  • Dioid
  • idealoid
  • algebraic opening
  • structural opening
  • invariance domain
  • generator basis
  • prime set

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Author information

Authors and Affiliations

  1. Domaine de Corbeville, L.C.R., Thomson-CSF, 91401, Orsay, France

    Juliette Mattioli

Authors
  1. Juliette Mattioli
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Editor information

Editors and Affiliations

  1. Centre de Morphologie Mathématique, Ecole des Mines de Paris, Fontainebleau, France

    Jean Serra & Pierre Soille & 

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© 1994 Springer Science+Business Media Dordrecht

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Mattioli, J. (1994). Minimal Generator Basis of a Finite Structural Opening. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_9

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  • DOI: https://doi.org/10.1007/978-94-011-1040-2_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4453-0

  • Online ISBN: 978-94-011-1040-2

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