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| Abstract: | The focus of this paper 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 hyperedge 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. This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs |
| Description: | ISRN Discrete Mathematics Volume 2014, Article ID 436419, 6 pages |
| URI: | http://dyuthi.cusat.ac.in/purl/4222 |
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| Mathematical Mo ... peredge Correspondence.pdf | (2.544Mb) |
| 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 |
| Description: | arXiv preprint arXiv:1402.4258 |
| URI: | http://dyuthi.cusat.ac.in/purl/4225 |
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| Morphological filtering on hypergraphs.pdf | (203.1Kb) |
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