Kannan, Balakrishnan; Bino, Sebastian V; Unnikrishnan, A; Ram Kumar, P B(February 18, 2014)
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Abstract:
The focus of this article is to develop computationally efficient mathematical morphology
operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which
we build morphological operators. We develop a pair of dual adjunctions between the vertex set
and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This
allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend
it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries
and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H
and (ii) on the subhypergraphs of a hypergraph