Distances defined by neighborhood sequences
Pattern Recognition
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Generalized distances in digital geometry
Information Sciences: an International Journal
Distance functions in digital geometry
Information Sciences: an International Journal
Lattice of octagonal distances in digital geometry
Pattern Recognition Letters
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On approximating Euclidean metrics by digital distances in 2D and 3D
Pattern Recognition Letters
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Characterization of digital circles in triangular grid
Pattern Recognition Letters
Algorithm for Generating a Digital Straight Line on a Triangular Grid
IEEE Transactions on Computers
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Approximating non-metrical Minkowski distances in 2D
Pattern Recognition Letters
Distance with generalized neighbourhood sequences in nD and ∞D
Discrete Applied Mathematics
Weighted distances based on neighborhood sequences for point-lattices
Discrete Applied Mathematics
Neighborhood Sequences in the Diamond Grid --- Algorithms with Four Neighbors
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Digital distance functions on three-dimensional grids
Theoretical Computer Science
Distance transform computation for digital distance functions
Theoretical Computer Science
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In this paper we compute distances with neighbourhood sequences in the cubic and in the triangular grids. First we give a formula which computes the distance with arbitrary neighbourhood sequence in the three-dimensional digital space. After this, using the injection of the triangular grid to the cubic grid, we modify the formula for Z^3 to the triangular plane. The distances in the triangular grid have some properties which are not present on the square and cubic grids. It may be non-symmetric, and it is possible that the distance depends on the ordering of elements of the initial part of the neighbourhood sequence. The distance depends on the ordering of the initial part (up to the kth element) of the neighbourhood sequence if and only if there is a permutation of these elements such that the distance (up to value k) is non-symmetric using the elements in this new order. This dependence means somehow more flexibility of the distances based on neighbourhood sequences on the triangular grid than in Z^n.