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
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.