Connective segmentation generalized to arbitrary complete lattices

Authors:
Seidon Alsaody;Jean Serra
Affiliations:
Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, Noisy le Grand Cedex, France and Uppsala University, Department of Mathematics, Uppsala, Sweden;Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, Noisy le Grand Cedex, France
Venue:
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Year:
2011

Citing 5
Cited 0

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Abstract

We begin by defining the setup and the framework of connective segmentation. Then we start from a theorem based on connective criteria, established for the power set of an arbitrary set. As the power set is an example of a complete lattice, we formulate and prove an analogue of the theorem for general complete lattices. Secondly, we consider partial partitions and partial connections. We recall the definitions, and quote a result that gives a characterization of (partial) connections. As a continuation of the work in the first part, we generalize this characterization to complete lattices as well. Finally we link these two approaches by means of a commutative diagram, in two manners.