[Lrde Annonce] New publication: How to Make nD Functions Digitally Well-Composed in a Self-Dual Way (ISMM'15)

I am happy to announce that the following paper has been accepted at the 12th International Symposium on Mathematical Morphology (ISMM'15), to be held on May 27-29 2015 in Reykjavik, Iceland. How to Make nD Functions Digitally Well-Composed in a Self-Dual Way Nicolas Boutry¹², Thierry Géraud¹, Laurent Najman² ¹ EPITA Research and Development Laboratory (LRDE) ² Université Paris-Est, LIGM, Équipe A3SI, ESIEE Paris https://www.lrde.epita.fr/wiki/Publications/boutry.15.ismm Abstract: Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the ``connectivities pa- radox'' 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 equi- valence of connectivities of the level set components in nD. Con- trasting 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 morpholo- gical tree of shapes.