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Fuzzy Mathematical Morphology and Derived Spatial Relationships

  • Isabelle Bloch
Part of the Studies in Fuzziness and Soft Computing book series (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.

Keywords

Membership Function Fuzzy Number Hausdorff Distance Reference Object Mathematical Morphology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Isabelle Bloch
    • 1
  1. 1.Ecole Nationale Supérieure des Télécommunications, département TSICNRS URA 820ParisFrance

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