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
Octagonal distances for digital pictures
Information Sciences: an International Journal
The t-cost distance in digital geometry
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
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
A note on a method for generating points uniformly on n-dimensional spheres
Communications of the ACM
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
General neighborhood sequences in Zn
Discrete Applied Mathematics
Distance with generalized neighbourhood sequences in nD and ∞D
Discrete Applied Mathematics
On Euclidean norm approximations
Pattern Recognition
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
Path-based distance with varying weights and neighborhood sequences
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
A Low Complexity Euclidean Norm Approximation
IEEE Transactions on Signal Processing
Comments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"
Pattern Recognition Letters
A quasi-Euclidean norm to speed up vector median filtering
IEEE Transactions on Image Processing
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
Linear combination of norms in improving approximation of Euclidean norm
Pattern Recognition Letters
Approximation of the euclidean distance by Chamfer distances
Acta Cybernetica
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Previously, we have studied linear combinations of a few pairs of norms, and reported their effectiveness in providing better approximation of Euclidean norms. In particular, we showed good approximation property of a combination of a pair of norms, namely CWD"e"u and WtD"i"s"r by experimentally computing their approximate maximum relative errors (MRE) with respect to the Euclidean norm. In this work, we have considered a pairing of any two members from the families of chamfering weighted distances (CWD) and weighted t-cost distances (WtD), respectively, and derive theoretical values of MREs with respect to the Euclidean norm by exploiting geometry of its hypersphere. Towards this we have computed the vertices of the hypersphere. Subsequently, in addition to our previously reported combination of CWD"e"u and WtD"i"s"r, we have also considered a few other combinations and showed their good approximation properties by computing theoretical MREs, as well as by validating those values experimentally. Further, by minimizing the theoretical expressions of MRE locally in the coefficient space of a linear combination, we obtain good approximators of Euclidean norm in any arbitrary dimension.