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Erschienen in:
2015 | OriginalPaper | Buchkapitel
How to Make nD Functions Digitally Well-Composed in a Self-dual Way
verfasst von : Nicolas Boutry, Thierry Géraud, Laurent Najman
Erschienen in: Mathematical Morphology and Its Applications to Signal and Image Processing
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Latecki
et al
. introduced the notion of 2D and 3D wellcomposed 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
n
D sets, integer-valued functions (graylevel images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in
n
D. Contrasting with a previous result stating that it is not possible to obtain a discrete
n
D self-dual digitally well-composed function with a local interpolation, we then propose and prove a selfdual 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.