Accéder directement au contenu Accéder directement à la navigation
Nouvelle interface
Pré-publication, Document de travail

Riemannian Mathematical Morphology

Abstract : This paper introduces mathematical morphology operators for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance used for the adjoint dilation/erosion. We then extend the canonic case to a most general framework of Riemannian operators based on the notion of admissible Riemannian structuring function. An alternative paradigm of morphological Riemannian operators involves an external structuring function which is parallel transported to each point on the manifold. Besides the definition of the various Riemannian dilation/erosion and Riemannian opening/closing, their main properties are studied. We generalize also some results on Lasry-Lions regularization for non-smooth images on Cartan-Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and manifold shape morphology are also considered. From a practical viewpoint, various useful image embedding into Riemannian manifolds are formalized, with some illustrative examples of morphological processing real-valued 3D surfaces.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

https://hal-mines-paristech.archives-ouvertes.fr/hal-00877144
Contributeur : Jesus Angulo Connectez-vous pour contacter le contributeur
Soumis le : lundi 28 octobre 2013 - 10:51:41
Dernière modification le : mardi 18 octobre 2022 - 11:02:08
Archivage à long terme le : : mercredi 29 janvier 2014 - 04:45:26

Fichier

RiemannianMorphology_Angulo_Ve...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00877144, version 1

Citation

Jesus Angulo, Santiago Velasco-Forero. Riemannian Mathematical Morphology. 2013. ⟨hal-00877144v1⟩

Partager

Métriques

Consultations de la notice

496

Téléchargements de fichiers

738