Mathematical morphology on hypergraphs, application to similarity and positive kernel
Identifieur interne : 000061 ( PascalFrancis/Checkpoint ); précédent : 000060; suivant : 000062Mathematical morphology on hypergraphs, application to similarity and positive kernel
Auteurs : Isabelle Bloch [France] ; Alain Bretto [France]Source :
- Computer vision and image understanding : (Print) [ 1077-3142 ] ; 2013.
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Abstract
The focus of this article is to develop mathematical morphology on hypergraphs. To this aim, we define lattice structures on hypergraphs on which we build mathematical morphology operators. We show some relations between these operators and the hypergraph structure, considering in particular transversals and duality notions. Then, as another contribution, we show how mathematical morphology can be used for classification or matching problems on data represented by hypergraphs: thanks to dilation operators, we define a similarity measure between hypergraphs, and we show that it is a kernel. A distance is finally introduced using this similarity notion.
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To this aim, we define lattice structures on hypergraphs on which we build mathematical morphology operators. We show some relations between these operators and the hypergraph structure, considering in particular transversals and duality notions. Then, as another contribution, we show how mathematical morphology can be used for classification or matching problems on data represented by hypergraphs: thanks to dilation operators, we define a similarity measure between hypergraphs, and we show that it is a kernel. 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