We study some basic morphological operators acting on the lattice of all subgraphs of a (non-weighted) graph \(\mathbb{G}\). To this end, we consider two dual adjunctions between the edge set and the vertex set of \(\mathbb{G}\). This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of \(\mathbb{G}\) and (ii) to extend it to subgraphs of \(\mathbb{G}\). Afterward, we propose several new erosions, dilations, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of \(\mathbb{G}\) and (ii) on the subgraphs of \(\mathbb{G}\).


Binary Image Machine Intelligence Impulse Noise Mathematical Morphology Morphological Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jean Cousty
    • 1
  • Laurent Najman
    • 1
  • Jean Serra
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge, Équipe A3SIUniversité Paris-EstESIEEFrance

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