Similarity between Hypergraphs Based on Mathematical Morphology

Isabelle Bloch (1) , Alain Bretto (2) , Aurélie Leborgne (3)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Equipe CODAG - Laboratoire GREYC - UMR6072
3 imagine - Extraction de Caractéristiques et Identification

In the framework of structural representations for applications in image understanding, we establish links between similarities, hypergraph theory and mathematical morphology. We propose new similarity measures and pseudo-metrics on lattices of hypergraphs based on morphological operators. New forms of these operators on hypergraphs are introduced as well. Some examples based on various dilations and openings on hypergraphs illustrate the relevance of our approach.

Mots clés: Hypergraphs; similarity; pseudo-metric; valuation; mathematical morphology on hypergraphs

Domaines: Mathématique discrète [cs.DM]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]

Isabelle Bloch, Alain Bretto, Aurélie Leborgne. Similarity between Hypergraphs Based on Mathematical Morphology. 11th International Symposium, ISMM 2013, May 2013, Uppsala, Sweden. ⟨10.1007/978-3-642-38294-9_1⟩. ⟨hal-01283941⟩