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

Abstract : 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.
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Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Reykjavik, Iceland. 9082, pp.561-572, 2015, Lecture Note In Computer Sciences. 〈http://www.springer.com/fr/book/9783319187198〉. 〈10.1007/978-3-319-18720-4_47〉
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Nicolas Boutry, Thierry Géraud, Laurent Najman. How to Make nD Functions Digitally Well-Composed in a Self-dual Way. Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Reykjavik, Iceland. 9082, pp.561-572, 2015, Lecture Note In Computer Sciences. 〈http://www.springer.com/fr/book/9783319187198〉. 〈10.1007/978-3-319-18720-4_47〉. 〈hal-01168723〉

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