Formulas for the number of (n-2)-gaps of binary objects in arbitrary dimension
Discrete Applied Mathematics
Linear Time Constant-Working Space Algorithm for Computing the Genus of a Digital Object
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
Digital stars and visibility of digital objects
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
A plate-based definition of discrete surfaces
Pattern Recognition Letters
Graphs with a path partition for structuring digital spaces
Information Sciences: an International Journal
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In this paper we define and study digital manifolds of arbitrary dimension, and provide (in particular)a general theoretical basis for curve or surface tracing in picture analysis. The studies involve properties such as one-dimensionality of digital curves and (n-1)-dimensionality of digital hypersurfaces that makes them discrete analogs of corresponding notions in continuous topology. The presented approach is fully based on the concept of adjacency relation and complements the concept of dimension as common in combinatorial topology. This work appears to be the first one on digital manifolds based on a graph-theoretical definition of dimension. In particular, in the n-dimensional digital space, a digital curve is a one-dimensional object and a digital hypersurface is an (n-1)-dimensional object, as it is in the case of curves and hypersurfaces in the Euclidean space. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. We also discuss possible applications of the presented definitions and results.