Connectivity in Digital Pictures
Journal of the ACM (JACM)
Arcs and Curves in Digital Pictures
Journal of the ACM (JACM)
Foundations of Image Understanding
Foundations of Image Understanding
The Discrete Analytical Hyperspheres
IEEE Transactions on Visualization and Computer Graphics
3D Line Voxelization and Connectivity Control
IEEE Computer Graphics and Applications
Segmentation and Length Estimation of 3D Discrete Curves
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Voronoi diagrams of semi-algebraic sets
Voronoi diagrams of semi-algebraic sets
Linear segmentation of discrete curves into blurred segments
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
The offset to an algebraic curve and an application to conics
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Characterization of the closest discrete approximation of a line in the 3-dimensional space
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
An arithmetic and combinatorial approach to three-dimensional discrete lines
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Connectedness of offset digitizations in higher dimensions
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Hi-index | 0.00 |
In this paper we investigate an approach of constructing a digital curve by taking the integer points within an offset of a certain radius of a continuous curve. Our considerations apply to digitizations of arbitrary curves in arbitrary dimension n. As main theoretical results, we first show that if the offset radius is greater than or equal to √n/2,then the obtained digital curve features maximal connectivity. We also demonstrate that the radius value √n/2 is the minimal possible that always guarantees such a connectivity. Moreover, we prove that a radius length greater than or equal to √n - 1/2 guarantees 0-connectivity, and that this is the minimal possible value with this property. Thus, we answer the question about the minimal offset size that guarantees maximal or minimal connectivity of an offset digital curve.