Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Fundamentals of surface voxelization
Graphical Models and Image Processing
Dimensional properties of graphs and digital spaces
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
Digital Picture Processing
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Discretization in 2D and 3D Orders
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Cell complexes and digital convexity
Digital and image geometry
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Discrete Surfaces and Frontier Orders
Journal of Mathematical Imaging and Vision
Continuous digitization in Khalimsky spaces
Journal of Approximation Theory
How to find a khalimsky-continuous approximation of a real-valued function
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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Among the different discretization schemes that have been proposed and studied in the literature, the supercover is a very natural one, and furthermore presents some interesting properties. On the other hand, an important structural property does not hold for the supercover in the classical framework: the supercover of a straight line (resp. a plane) is not a discrete curve (resp. surface) in general. We follow another approach based on a different, heterogenous discrete space which is an order, or a discrete topological space in the sense of Paul S. Alexandroff. Generalizing the supercover discretization scheme to such a space, we prove that the discretization of a plane in R3 is a discrete surface, and we prove that the discretization of the boundary of any closed convex set X is equal to the boundary of the discretization of X.