A note on a method for generating points uniformly on n-dimensional spheres
Communications of the ACM
Optimum linear approximation of the Euclidean norm to speed up vector median filtering
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 1)-Volume 1 - Volume 1
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
A Low Complexity Euclidean Norm Approximation
IEEE Transactions on Signal Processing
A quasi-Euclidean norm to speed up vector median filtering
IEEE Transactions on Image Processing
Comments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"
Pattern Recognition Letters
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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Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches [1-3] were based on minimizing the maximum error. Recently, Seol and Cheun [4] proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.