Statistics of ambiguous rotations
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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.
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
Journal of Multivariate Analysis
© 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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