Some morphological operators in graph spaces

Abstract : We study some basic morphological operators acting on the lattice of all subgraphs of a (non-weighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new erosions, dilations, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G.
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Jean Cousty, Laurent Najman, Jean Serra. Some morphological operators in graph spaces. 9th International Symposium on Mathematical Morphology (ISMM 2009), Aug 2009, Groningen, Netherlands. pp.149-160, ⟨10.1007/978-3-642-03613-2_14⟩. ⟨hal-00622403⟩



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