Mathematical Morphology and Eikonal Equations on Graphs for Nonlocal Image and Data Processing

Abstract : Mathematical morphology (MM) offers a wide range of operators to address various image processing problems. These operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). In this paper, we introduce a novel formulation of MM formalized as a framework of partial difference equations (PdEs) over weighted graphs of arbitrary topology. Then, we present and analyze a new family of morphological operators defined on weighted graphs. The proposed framework recovers local algebraic and PDEs-based formulations of MM. It also introduces nonlocal configurations for morphological image processing and extends PDEs-based methods to process any discrete data that can be described by a graph such as high dimensional data defined on irregular domains. Moreover, based on same ideas, we propose an adaptation of the eikonal equation on weighted graphs. Our formulation of the eikonal leads to novel applications of this equation such as nonlocal image segmentation and weighted distances or data clustering.
Liste complète des métadonnées

Littérature citée [47 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00365431
Contributeur : Vinh-Thong Ta <>
Soumis le : mardi 3 mars 2009 - 14:35:02
Dernière modification le : jeudi 8 novembre 2018 - 15:26:02
Document(s) archivé(s) le : vendredi 12 octobre 2012 - 12:45:16

Fichier

VinhThongTA_MMEE.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00365431, version 1

Citation

Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lézoray. Mathematical Morphology and Eikonal Equations on Graphs for Nonlocal Image and Data Processing. 2009. 〈hal-00365431〉

Partager

Métriques

Consultations de la notice

403

Téléchargements de fichiers

172