Connectivity on Complete Lattices

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Connectivity on Complete Lattices
Classically, connectivity is a topological notion for sets, often introduced by means of arcs. A non topological axiomatics has been proposed by Matheron and Serra. The present paper extends it to complete sup-generated lattices. A connection turns out to be characterized by a family of openings labelled by the sup-generators, which partition each element of the lattice into maximal terms, of zero infima. When combined with partition closings, these openings generate strong sequential alternating filters. Starting from a first connection several others may be designed by acting on some dilations or symmetrical operators.When applying this theory to function lattices, one interprets the so-called connected operators in terms of actual connections, as well as the watershed mappings. But the theory encompasses the numerical functions and extends, among others, to multivariate lattices. Keywords : connectivity, complete lattices, mathematical morphology, connected operators, filters b...
Jean Serra
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where JMIV
Authors Jean Serra
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