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
Discrete representation of spatial objects in computer vision
Discrete representation of spatial objects in computer vision
Digital Picture Processing
Cell Complexes and Digital Convexity
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
New Notions for Discrete Topology
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Hausdorff Discretizations of Algebraic Sets and Diophantine Sets
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Object Discretization in Higher Dimensions
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Algorithm for computer control of a digital plotter
IBM Systems Journal
Discretization in 2D and 3D orders
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
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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 a "regular" set X (in a sense that will be precisely defined) is equal to the boundary of the discretization of X. This property has an immediate corollary for half-spaces and planes, and for convex sets.