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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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