A New Fuzzy Connectivity Measure for Fuzzy Sets

  • Authors:

  • Olivier Nempont;Jamal Atif;Elsa Angelini;Isabelle Bloch

  • Affiliations:

  • TELECOM ParisTech, CNRS LTCI, UMR 5141, Paris, France 75013;US ESPACE, IRD-Cayenne, Cayenne, French Guiana 97323;TELECOM ParisTech, CNRS LTCI, UMR 5141, Paris, France 75013;TELECOM ParisTech, CNRS LTCI, UMR 5141, Paris, France 75013

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.