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Applying Soft Computing in Defining Spatial Relations pp 63–98Cite as

Mathematical Morphology and Spatial Relationships: Quantitative, Semi-Quantitative and Symbolic Settings

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 106))

Abstract

Basic mathematical morphology operations rely mainly on local information, based on the concept of structuring element. But mathematical morphology also deals with more global and structural information since several spatial relationships can be expressed in terms of morphological operations (mainly dilations). The aim of this paper is to show that this framework allows to represent in a unified way spatial relationships in various settings: a purely quantitative one if objects are precisely defined, a semi-quantitative one if objects are imprecise and represented as spatial fuzzy sets, and a qualitative one, for reasoning in a logical framework about space. This is made possible thanks to the strong algebraic structure of mathematical morphology, that finds equivalents in set theoretical terms, fuzzy operations and logical expressions.

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Authors and Affiliations

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

    Isabelle Bloch

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  1. Isabelle Bloch
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Editors and Affiliations

  1. CECS Department, EBW 201, University of Missouri, 65211-2060, Columbia, MO, USA

    Pascal Matsakis

  2. CIS Department, Philadelphia University, 19144, Philadelphia, PA, USA

    Les M. Sztandera

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© 2002 Physica-Verlag Heidelberg

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Bloch, I. (2002). Mathematical Morphology and Spatial Relationships: Quantitative, Semi-Quantitative and Symbolic Settings. In: Matsakis, P., Sztandera, L.M. (eds) Applying Soft Computing in Defining Spatial Relations. Studies in Fuzziness and Soft Computing, vol 106. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1752-2_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1752-2_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00294-0

  • Online ISBN: 978-3-7908-1752-2

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