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Metrics for 3D Rotations: Comparison and Analysis

Author:

Du Q. HuynhAuthors Info & Claims

Journal of Mathematical Imaging and Vision, Volume 35, Issue 2

Pages 155 - 164

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

Published: 01 October 2009 Publication History

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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cover image Journal of Mathematical Imaging and Vision

Journal of Mathematical Imaging and Vision Volume 35, Issue 2

October 2009

62 pages

ISSN:0924-9907

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Copyright © Copyright © 2009 Springer Science+Business Media, LLC.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 October 2009

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Wang RTan RYan ZLu C(2024)Orientation-Aware 3D SLAM in Alternating Magnetic Field from PowerlinesProceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies10.1145/36314467:4(1-25)Online publication date: 12-Jan-2024
https://dl.acm.org/doi/10.1145/3631446
von Arx DFischer CTorlakcik HPané SNelson BBoehler Q(2024)Simultaneous Localization and Actuation Using Electromagnetic Navigation SystemsIEEE Transactions on Robotics10.1109/TRO.2023.334032440(1292-1308)Online publication date: 1-Jan-2024
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