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Unifying Quantitative, Semi-quantitative and Qualitative Spatial Relation Knowledge Representations Using Mathematical Morphology

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Geometry, Morphology, and Computational Imaging

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2616))

Abstract

One of the powerful features of mathematical morphology lies in its strong algebraic structure, that finds equivalents in set theoretical terms, fuzzy sets theory and logics. Moreover this theory is able to deal with global and structural information since several spatial relationships can be expressed in terms of morphological operations. The aim of this paper is to show that the framework of mathematical morphology allows to represent in a unified way spatial relationships in various settings: a purely quantitative one if objects are precisely defined, a semiquantitative one if objects are imprecise and represented as spatial fuzzy sets, and a qualitative one, for reasoning in a logical framework about space.

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Author information

Authors and Affiliations

  1. Département TSI - CNRS URA 820, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75013, Paris, France

    Isabelle Bloch

Authors
  1. Isabelle Bloch
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Editor information

Editors and Affiliations

  1. JAIST, School of Information Science, 1-1 Asahidai, Tatsunokuchi, 923-1202, Ishikawa, Japan

    Tetsuo Asano

  2. Computer Science Dept. and CITR, University of Auckland, Tamaki Campus, Glen Innes, 1005, Auckland, New Zealand

    Reinhard Klette

  3. LSIIT UMR 7005 CNRS-ULP, Parc d’Innovation, Boulevard Sebastien Brant, BP 10413, 67412, Illkirch, France

    Chrisitan Ronse

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© 2003 Springer-Verlag Berlin Heidelberg

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Bloch, I. (2003). Unifying Quantitative, Semi-quantitative and Qualitative Spatial Relation Knowledge Representations Using Mathematical Morphology. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_10

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  • DOI: https://doi.org/10.1007/3-540-36586-9_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00916-0

  • Online ISBN: 978-3-540-36586-0

  • eBook Packages: Springer Book Archive

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