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
Computing distance transformations in convex and non-convex domains
Pattern Recognition
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Characterization of digital circles in triangular grid
Pattern Recognition Letters
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
A Connection between Z n and Generalized Triangular Grids
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
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
Geometric transformations on the hexagonal grid
IEEE Transactions on Image Processing
Digital distance functions on three-dimensional grids
Theoretical Computer Science
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In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used. In this paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal. This grid can be described by four coordinate values using axes of the directions of atomic bonds. In this way the sum of the coordinate values can be either zero or one. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. The metric and non-metric properties of some distances based on neighborhood sequences are also discussed. The constrained distance transformation and digital balls obtained by some distance functions are presented.