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Fuzzy Mathematical Morphology and Derived Spatial Relationships

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Fuzzy Techniques in Image Processing

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 52))

Summary

The joint importance of mathematical morphology in image processing and of fuzzy sets for representing imprecisely defined image objects has led to an increased interest in fuzzy mathematical morphology. In this chapter, we first review the main definitions of fuzzy mathematical morphology operators and show that the most important properties of classical mathematical morphology are kept. Then we use these operators, mainly fuzzy dilation, for defining some spatial relationships between fuzzy objects: distances, adjacency and boundary, directional relative position. Such spatial fuzzy relationships are important in pattern recognition (for instance model-based structural pattern recognition). Indeed, objects can be recognized in a scene using their own characteristics, but also using their relationships to other objects of the scene. Therefore the proposed operations and relationships between fuzzy objects lead to applications in structural pattern recognition under imprecision.

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Author information

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. Department of Applied Mathematics and Computer Science Fuzziness and Uncertainty Modelling Research Unit, Ghent University, Krijgslaan 281 (S9), 9000, Gent, Belgium

    Etienne E. Kerre  & Mike Nachtegael  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Bloch, I. (2000). Fuzzy Mathematical Morphology and Derived Spatial Relationships. In: Kerre, E.E., Nachtegael, M. (eds) Fuzzy Techniques in Image Processing. Studies in Fuzziness and Soft Computing, vol 52. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1847-5_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1847-5_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2475-9

  • Online ISBN: 978-3-7908-1847-5

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