Connectivity in Digital Pictures
Journal of the ACM (JACM)
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
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
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
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In this paper we investigate an approach of constructing a 3D digital line by taking the integer points within an offset of a certain radius of the line. Alternatively, we also investigate digital lines obtained through a "pseudo-offset" defined by a parallelepiped enclosing the integer points around the line. We show that if the offset radius (resp. side of the parallelepiped section) is greater than $\sqrt{3}$ (resp. 2$\sqrt{3}$), then the digital line is at least 1-connected. Extensive experiments show that the lines obtained feature satisfactory appearance.