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

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.

Proc. Int. Work. Combinatorial Image Analysis (IWCIA'2004), Auckland, New Zealand, December 1-3, volume 3322 of Lecture Notes in Computer Science, pp 122–136, 2004. Springer