Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Computer Vision and Image Understanding
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)
Arcs and Curves in Digital Pictures
Journal of the ACM (JACM)
Thin discrete triangular meshes
Theoretical Computer Science
Object discretizations in higher dimensions
Pattern Recognition Letters
Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
3D Line Voxelization and Connectivity Control
IEEE Computer Graphics and Applications
Computer
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
The number of gaps in binary pictures
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
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
Combinatorial relations for digital pictures
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
On the notion of dimension in digital spaces
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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An important concept in combinatorial image analysis is that of gap. In this paper we derive a simple formula for the number of gaps in a 2D binary picture. Our approach is based on introducing the notions of free vertex and free edge and studying their properties from point of view of combinatorial topology. The number of gaps characterizes the topological structure of a binary picture and is of potential interest in property-based image analysis.