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A New Fuzzy Connectivity Measure for Fuzzy Sets

And Associated Fuzzy Attribute Openings

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Abstract

Fuzzy set theory constitutes a powerful representation framework that can lead to more robustness in problems such as image segmentation and recognition. This robustness results to some extent from the partial recovery of the continuity that is lost during digitization. In this paper we deal with connectivity measures on fuzzy sets. We show that usual fuzzy connectivity definitions have some drawbacks, and we propose a new definition that exhibits better properties, in particular in terms of continuity. This definition leads to a nested family of hyperconnections associated with a tolerance parameter. We show that corresponding connected components can be efficiently extracted using simple operations on a max-tree representation. Then we define attribute openings based on crisp or fuzzy criteria. We illustrate a potential use of these filters in a brain segmentation and recognition process.

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Authors and Affiliations

  1. TELECOM ParisTech, CNRS LTCI, UMR 5141, 46 rue Barrault, 75013, Paris, France

    Olivier Nempont, Elsa Angelini & Isabelle Bloch

  2. US ESPACE, IRD-Cayenne, route de Montabo, BP 165, 97323, Cayenne, French Guiana

    Jamal Atif

Authors
  1. Olivier Nempont
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  2. Jamal Atif
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  3. Elsa Angelini
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  4. Isabelle Bloch
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Correspondence to Olivier Nempont.

Additional information

This work has been partly supported by a grant from the National Cancer Institute (INCA).

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Nempont, O., Atif, J., Angelini, E. et al. A New Fuzzy Connectivity Measure for Fuzzy Sets. J Math Imaging Vis 34, 107–136 (2009). https://doi.org/10.1007/s10851-009-0136-3

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  • DOI: https://doi.org/10.1007/s10851-009-0136-3

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