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Statistics of ambiguous rotations

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Arnold_2017_Statistics_ambiguous_JMA_AAM.pdf (221.6Kb)
Date
05/2018
Author
Arnold, R.
Jupp, P. E.
Schaeben, H.
Keywords
Frame
Orientation
Regression
Symmetric array
Symmetry
Test of location
Test of uniformity
QA Mathematics
T-NDAS
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Abstract
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.
Citation
Arnold , R , Jupp , P E & Schaeben , H 2018 , ' Statistics of ambiguous rotations ' , Journal of Multivariate Analysis , vol. 165 , pp. 73-85 . https://doi.org/10.1016/j.jmva.2017.10.007
Publication
Journal of Multivariate Analysis
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.jmva.2017.10.007
ISSN
0047-259X
Type
Journal article
Rights
© 2017 Elsevier Ltd. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jmva.2017.10.007
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/16511

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