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International Workshop on Fuzzy Logic in Artificial Intelligence

FLAI 1997: Fuzzy Logic in Artificial Intelligence pp 149–165Cite as

Fuzzy morphology and fuzzy distances: New definitions and links in both euclidean and geodesic cases

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1566))

Abstract

The aim of this paper is to establish links between fuzzy morphology and fuzzy distances. We show how distances can be derived from fuzzy mathematical morphology, in particular fuzzy dilation, leading to interesting definitions involving membership information and spatial information. Conversely, we propose a way to define fuzzy morphological operations from fuzzy distances. We deal with both the Euclidean and the geodesic cases. In particular in the geodesic case, we propose a definition of fuzzy balls, from which fuzzy geodesic dilation and erosion are derived, based on fuzzy geodesic distances. These new operations enhance the set of fuzzy morphological operators, leading to transformations of a fuzzy set conditionally to another fuzzy set. The proposed definitions are valid in any dimension, in both Euclidean and geodesic cases.

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Authors and Affiliations

  1. École Nationale Supérieure des Télécommunications, département Images, CNRS URA820, 46 rue Barrault, 75013, Paris, France

    Isabelle Bloch

Authors
  1. Isabelle Bloch
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Editor information

Anca L. Ralescu James G. Shanahan

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© 1999 Springer-Verlag Berlin Heidelberg

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Bloch, I. (1999). Fuzzy morphology and fuzzy distances: New definitions and links in both euclidean and geodesic cases. In: Ralescu, A.L., Shanahan, J.G. (eds) Fuzzy Logic in Artificial Intelligence. FLAI 1997. Lecture Notes in Computer Science, vol 1566. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095076

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  • DOI: https://doi.org/10.1007/BFb0095076

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66374-4

  • Online ISBN: 978-3-540-48358-8

  • eBook Packages: Springer Book Archive

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