Abstract
Many combinatorial structures have been designed to represent the topology of space subdivisions and images. We focus here on two particular models, namely the n-G-maps used in geometric modeling and computational geometry and the n-surfaces used in discrete imagery. We show that a subclass of n-G-maps is equivalent to n-surfaces. To achieve this, we provide several characterizations of n-surfaces. Finally, the proofs being constructive, we show how to switch from one representation to another effectively.
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Alayrangues, S., Daragon, X., Lachaud, JO. et al. Equivalence between Closed Connected n-G-Maps without Multi-Incidence and n-Surfaces. J Math Imaging Vis 32, 1–22 (2008). https://doi.org/10.1007/s10851-008-0084-3
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DOI: https://doi.org/10.1007/s10851-008-0084-3