Distances defined by neighborhood sequences
Pattern Recognition
Distance functions in digital geometry
Information Sciences: an International Journal
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Efficient Uniform Cost Algorithm Applied to Distance Transforms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Octagonal distances for digital pictures
Information Sciences: an International Journal
Local distances for distance transformations in two and three dimensions
Pattern Recognition Letters
Best simple octagonal distances in digital geometry
Journal of Approximation Theory
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
Medial axis for chamfer distances: computing look-up tables and neighbuorhoods in 2D or 3D
Pattern Recognition Letters
Geometry of Digital Spaces
Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5
Computer Vision and Image Understanding
Multiseeded Fuzzy Segmentation on the Face Centered Cubic Grid
ICAPR '01 Proceedings of the Second International Conference on Advances in Pattern Recognition
Determination of discrete sampling grids with optimal topological and spectral properties
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
2D and 3D visibility in discrete geometry: an application to discrete geodesic paths
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Discrete Topology of (An*) Optimal Sampling Grids. Interest in Image Processing and Visualization
Journal of Mathematical Imaging and Vision
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Analytical Honeycomb Geometry for Raster and Volume Graphics
The Computer Journal
Distances with neighbourhood sequences in cubic and triangular grids
Pattern Recognition Letters
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
IEEE Transactions on Pattern Analysis and Machine Intelligence
On visual quality of optimal 3D sampling and reconstruction
GI '07 Proceedings of Graphics Interface 2007
General neighborhood sequences in Zn
Discrete Applied Mathematics
Distance with generalized neighbourhood sequences in nD and ∞D
Discrete Applied Mathematics
Exploration of a cluttered environment using Voronoi Transform and Fast Marching
Robotics and Autonomous Systems
Optimal sampling lattices and trivariate box splines
Optimal sampling lattices and trivariate box splines
A Connection between Z n and Generalized Triangular Grids
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Weighted distances based on neighborhood sequences for point-lattices
Discrete Applied Mathematics
Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors
International Journal of Imaging Systems and Technology - Contemporary Challenges in Combinatorial Image Analysis
Region-Based vs. Edge-Based Registration for 3D Motion Capture by Real Time Monoscopic Vision
MIRAGE '09 Proceedings of the 4th International Conference on Computer Vision/Computer Graphics CollaborationTechniques
Visible Vectors and Discrete Euclidean Medial Axis
Discrete & Computational Geometry
Neighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Neighborhood Sequences in the Diamond Grid --- Algorithms with Four Neighbors
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Weighted distances based on neighbourhood sequences in non-standard three-dimensional grids
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Weighted neighborhood sequences in non-standard three-dimensional grids: parameter optimization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Interpolation and Sampling on a Honeycomb Lattice
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Resolution pyramids on the FCC and BCC grids
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Topology preserving digitization with FCC and BCC grids
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Distance transform computation for digital distance functions
Theoretical Computer Science
Computer Vision and Image Understanding
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In this paper, we examine five different three-dimensional grids suited for image processing. Digital distance functions are defined on the cubic, face-centered cubic, body-centered cubic, honeycomb, and diamond grids. We give the parameters that minimize an error function that favors distance functions with low rotational dependency. We also give an algorithm for computing the distance transform-the tool by which these distance functions can be applied in image processing applications.