How to Make nD Functions Digitally Well-Composed in a Self-dual Way

• Main Authors: Boutry, Nicolas, Géraud, Thierry, Najman, Laurent
• Other Authors: Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Laboratoire de Recherche et de Développement de l'EPITA (LRDE), Ecole Pour l'Informatique et les Techniques Avancées (EPITA), Benediktsson, J.A., Chanussot, J., Najman, L., Talbot, H.
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-01168723; https://hal.archives-ouvertes.fr/hal-01168723/document; https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf; https://doi.org/10.1007/978-3-319-18720-4_47

International audience Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the " connectivities paradox " of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of " digital well-composedness " to nD sets, integer-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in nD. Contrasting with a previous result stating that it is not possible to obtain a discrete nD self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.