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
Another comment on “a note on distance transformation in digital images”
CVGIP: Image Understanding
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
On approximating Euclidean metrics by digital distances in 2D and 3D
Pattern Recognition Letters
Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5
Computer Vision and Image Understanding
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
Distance transforms for three-dimensional grids with non-cubic voxels
Computer Vision and Image Understanding
Weighted neighborhood sequences in non-standard three-dimensional grids: parameter optimization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension
Pattern Recognition Letters
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
A quasi-Euclidean norm to speed up vector median filtering
IEEE Transactions on Image Processing
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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In a previously reported work, a distance function was proposed which defines the distance between any pair of points as the weighted sum of their ordered coordinate differences. We call this distance function in this work as linear combination form of weighted distance (LWD), and observe that if an LWD is a norm, it can be expressed in an equivalent form, which is associated with a chamfering mask. We refer to this class of distance functions as chamfering weighted distances (CWD). In this work, properties of hyperspheres of CWDs in arbitrary dimension are discussed. We have derived expressions for the vertices, surface areas and volumes of n-D hyperspheres. These are used in defining geometric error measures to study the proximity of these distance functions to Euclidean metrics. We have also used other analytical error measures to consider their suitability in approximating Euclidean distances.