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A New Fuzzy Connectivity Measure for Fuzzy Sets and Associated Fuzzy Attribute Openings

Nempont Olivier 1 Jamal Atif 2, 3 Elsa D. Angelini 1 Isabelle Bloch 1
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
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 draw- backs, 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 de- fine 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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https://hal.archives-ouvertes.fr/hal-00862582
Contributor : Jamal Atif <>
Submitted on : Tuesday, September 17, 2013 - 10:00:58 AM
Last modification on : Wednesday, October 14, 2020 - 4:06:16 AM

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Nempont Olivier, Jamal Atif, Elsa D. Angelini, Isabelle Bloch. A New Fuzzy Connectivity Measure for Fuzzy Sets and Associated Fuzzy Attribute Openings. Journal of Mathematical Imaging and Vision, Springer Verlag, 2009, 34, pp.107-136. ⟨10.1007/s10851-009-0136-3⟩. ⟨hal-00862582⟩

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