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Computer Vision and Image Understanding 117, 4 (2013) 370-385

Versions disponibles :

v1 (24-05-2012)

v2 (12-07-2012)

Morphological filtering on graphs

Jean Cousty 1, Laurent Najman 1, Fabio Dias 1, Jean Serra 1

(01/04/2013)

We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) 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 openings, closings, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.

1 :	Laboratoire d'Informatique Gaspard-Monge (LIGM)
	Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049

Domaine

:

Informatique/Traitement des images

Mots Clés : Graphs – mathematical morphology – adjunctions – spatially variant morphology

hal-00700784, version 2

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Contributeur : Jean Cousty <>

Soumis le : Jeudi 12 Juillet 2012, 13:13:38

Dernière modification le : Mercredi 20 Mars 2013, 13:06:45