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J Math Imaging Vis (2009) 34: 107136 DOI 10.1007/s10851-009-0136-3

Summary: J Math Imaging Vis (2009) 34: 107­136
DOI 10.1007/s10851-009-0136-3
A New Fuzzy Connectivity Measure for Fuzzy Sets
And Associated Fuzzy Attribute Openings
Olivier Nempont · Jamal Atif · Elsa Angelini ·
Isabelle Bloch
Published online: 14 February 2009
© Springer Science+Business Media, LLC 2009
Abstract Fuzzy set theory constitutes a powerful represen-
tation framework that can lead to more robustness in prob-
lems such as image segmentation and recognition. This ro-
bustness 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 defin-
ition leads to a nested family of hyperconnections associ-
ated with a tolerance parameter. We show that correspond-
ing connected components can be efficiently extracted using


Source: Angelini, Elsa -Département Traitement du Signal et des Images, Telecom ParisTech


Collections: Engineering; Biology and Medicine