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Regular Metric: Definition and Characterization in the Discrete Plane

  • Conference paper
Mathematical Morphology: 40 Years On

Part of the book series: Computational Imaging and Vision ((CIVI,volume 30))

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Abstract

We say that a metric space is regular if a straight-line (in the metric space sense) passing through the center of a sphere has at least two diametrically opposite points. The normed vector spaces have this property. Nevertheless, this property might not be satisfied in some metric spaces. In this work, we give a characterization of an integer-valued translation-invariant regular metric defined on the discrete plane, in terms of a symmetric subset B that induces through a recursive Minkowski sum, a chain of subsets that are morphologically closed with respect to B.

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References

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Author information

Authors and Affiliations

  1. National Institute for Space Research, INPE, São José dos Campos, Brazil

    Gerald Jean Francis Banon

Authors
  1. Gerald Jean Francis Banon
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Editor information

Editors and Affiliations

  1. LSIIT, UMR 7005 CNRS-ULP, Illkirch, France

    Christian Ronse

  2. A2SI-ESIEE/IGM, UMR 8049 CNRS-UMLV, Noisy-le-Grand, France

    Laurent Najman

  3. CMM, École des Mines de Paris, Fontainebleau, France

    Etienne Decencière

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© 2005 Springer

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Banon, G.J.F. (2005). Regular Metric: Definition and Characterization in the Discrete Plane. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_22

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  • DOI: https://doi.org/10.1007/1-4020-3443-1_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-3442-8

  • Online ISBN: 978-1-4020-3443-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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