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Metrics for 3D Rotations: Comparison and Analysis

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Abstract

3D rotations arise in many computer vision, computer graphics, and robotics problems and evaluation of the distance between two 3D rotations is often an essential task. This paper presents a detailed analysis of six functions for measuring distance between 3D rotations that have been proposed in the literature. Based on the well-developed theory behind 3D rotations, we demonstrate that five of them are bi-invariant metrics on SO(3) but that only four of them are boundedly equivalent to each other. We conclude that it is both spatially and computationally more efficient to use quaternions for 3D rotations. Lastly, by treating the two rotations as a true and an estimated rotation matrix, we illustrate the geometry associated with iso-error measures.

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Authors and Affiliations

  1. School of Computer Science and Software Engineering, The University of Western Australia, Nedlands, WA, 6009, Australia

    Du Q. Huynh

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  1. Du Q. Huynh
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Correspondence to Du Q. Huynh.

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This research was in part supported by a UWA study leave grant.

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Huynh, D.Q. Metrics for 3D Rotations: Comparison and Analysis. J Math Imaging Vis 35, 155–164 (2009). https://doi.org/10.1007/s10851-009-0161-2

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  • DOI: https://doi.org/10.1007/s10851-009-0161-2

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