Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Handbook of combinatorics (vol. 2)
Dimensional properties of graphs and digital spaces
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
Split-and-merge algorithms defined on topological maps for 3D image segmentation
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Discrete Surfaces and Frontier Orders
Journal of Mathematical Imaging and Vision
Update operations on 3D simplicial decompositions of non-manifold objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
nD generalized map pyramids: Definition, representations and basic operations
Pattern Recognition
Equivalence between regular n-G-maps and n-surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Border operator for generalized maps
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
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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.