A Tutorial on Well-Composedness

Abstract : Due to digitization, usual discrete signals generally present topological paradoxes, such as the connectivity paradoxes of Rosenfeld. To get rid of those paradoxes, and to restore some topological properties to the objects contained in the image, like manifoldness, Latecki proposed a new class of images, called well-composed images, with no topological issues. Furthermore , well-composed images have some other interesting properties: for example, the Euler number is locally computable, boundaries of objects separate background from foreground, the tree of shapes is well-defined, and so on. Last, but not the least, some recent works in mathematical morphology have shown that very nice practical results can be obtained thanks to well-composed images. Believing in its prime importance in digital topology, we then propose this state-of-the-art of well-composedness, summarizing its different flavours, the different methods existing to produce well-composed signals, and the various topics that are related to well-composedness.
Type de document :
Article dans une revue
Journal of Mathematical Imaging and Vision, Springer Verlag, A Paraître
Liste complète des métadonnées

Littérature citée [177 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01609892
Contributeur : Laurent Najman <>
Soumis le : jeudi 12 octobre 2017 - 16:08:14
Dernière modification le : mercredi 18 octobre 2017 - 01:06:02

Fichier

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

Identifiants

  • HAL Id : hal-01609892, version 2

Collections

Citation

Nicolas Boutry, Thierry Géraud, Laurent Najman. A Tutorial on Well-Composedness. Journal of Mathematical Imaging and Vision, Springer Verlag, A Paraître. 〈hal-01609892v2〉

Partager

Métriques

Consultations de la notice

27

Téléchargements de fichiers

26