Similarity between Hypergraphs Based on Mathematical Morphology

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.