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
Computing distance transformations in convex and non-convex domains
Pattern Recognition
Finding local maxima in a pseudo-Euclidean distance transform
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)
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
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
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Weighted distances based on neighborhood sequences for point-lattices
Discrete Applied Mathematics
Medial axis lookup table and test neighborhood computation for 3D chamfer norms
Pattern Recognition
Discrete Applied Mathematics
Neighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Medial axis LUT computation for chamfer norms using H-polytopes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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
Weighted neighborhood sequences in non-standard three-dimensional grids: parameter optimization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Fast distance transformation on irregular two-dimensional grids
Pattern Recognition
Anti-aliased Euclidean distance transform
Pattern Recognition Letters
Approximating Euclidean circles by neighbourhood sequences in a hexagonal grid
Theoretical Computer Science
On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension
Pattern Recognition Letters
Integer approximation of 3D chamfer mask coefficients using a scaling factor in anisotropic grids
Pattern Recognition Letters
Path-based distance with varying weights and neighborhood sequences
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Sparse object representations by digital distance functions
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Distance transform computation for digital distance functions
Theoretical Computer Science
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
Minimal-delay distance transform for neighborhood-sequence distances in 2D and 3D
Computer Vision and Image Understanding
Digital distances and integer sequences
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Linear combination of norms in improving approximation of Euclidean norm
Pattern Recognition Letters
Linear combination of weighted t-cost and chamfering weighted distances
Pattern Recognition Letters
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By combining weighted distances and distances based on neighbourhood sequences, a new family of distance functions with potentially low rotational dependency is obtained. The basic theory for these distance functions, including functional form of the distance between two points, is presented. By minimizing an error function, the weights and neighbourhood sequence that give the distance function with the lowest rotational dependency are derived. To verify that the low rotational dependency of the proposed distance function is valid also in applications, the constrained distance transform on a binary image is computed and compared with some traditionally used distance functions.