article

Hyperspheres of weighted distances in arbitrary dimension

Author:

Jayanta MukherjeeAuthors Info & Claims

Pattern Recognition Letters, Volume 34, Issue 2

Pages 117 - 123

https://doi.org/10.1016/j.patrec.2012.09.011

Published: 01 January 2013 Publication History

Abstract

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.

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Cited By

Mukherjee J(2016)Error analysis of octagonal distances defined by periodic neighborhood sequences for approximating Euclidean metrics in arbitrary dimensionPattern Recognition Letters10.1016/j.patrec.2016.02.01275:C(16-23)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1016/j.patrec.2016.02.012
Nagy BMir-Mohammad-Sadeghi H(2016)Digital Disks by Weighted Distances in the Triangular GridProceedings of the 19th IAPR International Conference on Discrete Geometry for Computer Imagery - Volume 964710.1007/978-3-319-32360-2_30(385-397)Online publication date: 18-Apr-2016
https://dl.acm.org/doi/10.1007/978-3-319-32360-2_30

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Comments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"

Mukherjee [Mukherjee, J., 2011. On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension. Pattern Recognition Lett. 32, 824-831] recently introduced a class of distance functions called weighted t-cost distances that ...

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Published In

cover image Pattern Recognition Letters

Pattern Recognition Letters Volume 34, Issue 2

January, 2013

132 pages

ISSN:0167-8655

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Copyright © Elsevier B.V. © 2012.

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Elsevier Science Inc.

United States

Publication History

Published: 01 January 2013

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Cited By

Mukherjee J(2016)Error analysis of octagonal distances defined by periodic neighborhood sequences for approximating Euclidean metrics in arbitrary dimensionPattern Recognition Letters10.1016/j.patrec.2016.02.01275:C(16-23)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1016/j.patrec.2016.02.012
Nagy BMir-Mohammad-Sadeghi H(2016)Digital Disks by Weighted Distances in the Triangular GridProceedings of the 19th IAPR International Conference on Discrete Geometry for Computer Imagery - Volume 964710.1007/978-3-319-32360-2_30(385-397)Online publication date: 18-Apr-2016
https://dl.acm.org/doi/10.1007/978-3-319-32360-2_30

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