Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Relations in mathematical morphology with applications to graphs and rough sets
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
Relational granularity for hypergraphs
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Relational Mathematics
Mathematical morphology on hypergraphs: preliminary definitions and results
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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A relation on a hypergraph is a binary relation on the set consisting of the nodes and hyperedges together, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join-preserving mappings on the lattice of sub-hypergraphs. This paper studies the algebra of these relations, in particular the analogues of the familiar operations of complement and converse of relations. When generalizing from relations on a set to relations on a hypergraph we find that the Boolean algebra of relations is replaced by a weaker structure: a pair of isomorphic bi-Heyting algebras, one of which arises from the relations on the dual hypergraph. The paper also considers the representation of sub-hypergraphs as relations and applies the results obtained to mathematical morphology for hypergraphs.