Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images

Jesus Angulo 1 Santiago Velasco-Forero 1
1 CMM - Centre de Morphologie Mathématique
Abstract : Mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures. Let us consider an image model where at each pixel is given a univariate Gaussian distribution. This model is interesting to represent for each pixel the measured mean intensity as well as the variance (or uncertainty) for such measurement. The aim of this paper is to formulate morphological operators for these images by embedding Gaussian distribution pixel values on the Poincaré upper-half plane. More precisely, it is explored how to endow this classical hyperbolic space with partial orderings which lead to a complete lattice structure.
Type de document :
Communication dans un congrès
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger
https://hal-mines-paristech.archives-ouvertes.fr/hal-01536381
Contributeur : Jesus Angulo <>
Soumis le : dimanche 11 juin 2017 - 12:24:30
Dernière modification le : lundi 12 novembre 2018 - 10:56:29
Document(s) archivé(s) le : mercredi 13 décembre 2017 - 11:13:07

Fichier

HyperbolicMM_GSI13_final.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

ENSMP | INSTITUT-TELECOM | ENSMP_CMM | PARISTECH | PSL

Citation

Jesus Angulo, Santiago Velasco-Forero. Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images. First International Conference on Geometric Science of Information (GSI'2013), Aug 2013, Paris, France. pp.535 - 542, ⟨10.1007/978-3-642-40020-9_59⟩. ⟨hal-01536381⟩

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

141

Téléchargements de fichiers

85

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD