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A New Fuzzy Connectivity Measure for Fuzzy Sets -- And Associated Fuzzy Attribute Openings (2009)
| Venue: | J MATH IMAGING VIS (2009) 34: 107–136 |
BibTeX
@MISC{Nempont09anew,
author = {Olivier Nempont and Jamal Atif and Elsa Angelini and Isabelle Bloch},
title = { A New Fuzzy Connectivity Measure for Fuzzy Sets -- And Associated Fuzzy Attribute Openings},
year = {2009}
}
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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.
Keyphrases
fuzzy set new fuzzy connectivity measure math imaging vi associated fuzzy attribute opening simple operation image segmentation tolerance parameter powerful representation framework connected component robustness result max-tree representation new definition partial recovery recognition process usual fuzzy connectivity definition brain segmentation nested family attribute opening potential use fuzzy criterion connectivity measure abstract fuzzy
