Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Discrete analytical hyperplanes
Graphical Models and Image Processing
On the Topological Properties of Quantized Spaces, I. The Notion of Dimension
Journal of the ACM (JACM)
Object discretizations in higher dimensions
Pattern Recognition Letters
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
On the definition and recognition of patterns in discrete spaces
On the definition and recognition of patterns in discrete spaces
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Graphs and Hypergraphs
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Curves, hypersurfaces, and good pairs of adjacency relations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
The number of gaps in binary pictures
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Counting gaps in binary pictures
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Dimension is a fundamental concept in topology. Mylopoulos and Pavlidis [17] provided a definition for discrete spaces. In the present paper we propose an alternative one for the case of planar digital objects. It makes up certain shortcomings of the definition from [17] and implies dimensionality properties analogous to those familiar from classical topology. We also establish relations between dimension of digital objects and their Euler characteristic.