Distances defined by neighborhood sequences
Pattern Recognition
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
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
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Isosurfaces on optimal regular samples
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
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)
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
Topology Preserving Marching Cubes-like Algorithms on the Face-Centered Cubic Grid
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
Weighted distances based on neighbourhood sequences in non-standard three-dimensional grids
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Weighted neighbourhood sequences in non-standard three dimensional grids: metricity and algorithms
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Weighted distances based on neighborhood sequences for point-lattices
Discrete Applied Mathematics
Discrete Applied Mathematics
Weighted neighbourhood sequences in non-standard three dimensional grids: metricity and algorithms
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Digital distance functions on three-dimensional grids
Theoretical Computer Science
On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension
Pattern Recognition Letters
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
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Recently, a distance function was defined on the facecentered cubic and body-centered cubic grids by combining weights and neighborhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. We introduce four different error functions which are used to find the optimal weights and neighborhood sequences that can be used to define the distance functions with low rotational dependency.