Equivalence between regular n-G-maps and n-surfaces

Authors:
Sylvie Alayrangues;Xavier Daragon;Jacques-Olivier Lachaud;Pascal Lienhardt
Affiliations:
LaBRI, Talence Cedex;ESIEE – Laboratoire A2SI, Noisy le Grand Cedex;LaBRI, Talence Cedex;SIC – bât SP2MI, Futuroscope Chasseneuil Cedex
Venue:
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Year:
2004

Citing 7
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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. We exhibit a local property characterising this subclass, which is easy to check algorithmatically. Finally, the proofs being constructive, we show how to switch from one representation to another effectively.