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

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.

Jacques-Olivier Lachaud

Professor of Computer Science

My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.