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), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout (BEZOUT), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), 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.science/hal-01168723; https://hal.science/hal-01168723/document; https://hal.science/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.