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International Journal of Computer Vision
Published in: International Journal of Computer Vision 3/2013

01-07-2013

Rotation Averaging

Authors: Richard Hartley, Jochen Trumpf, Yuchao Dai, Hongdong Li

Published in: International Journal of Computer Vision | Issue 3/2013

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Abstract

This paper is conceived as a tutorial on rotation averaging, summarizing the research that has been carried out in this area; it discusses methods for single-view and multiple-view rotation averaging, as well as providing proofs of convergence and convexity in many cases. However, at the same time it contains many new results, which were developed to fill gaps in knowledge, answering fundamental questions such as radius of convergence of the algorithms, and existence of local minima. These matters, or even proofs of correctness have in many cases not been considered in the Computer Vision literature. We consider three main problems: single rotation averaging, in which a single rotation is computed starting from several measurements; multiple-rotation averaging, in which absolute orientations are computed from several relative orientation measurements; and conjugate rotation averaging, which relates a pair of coordinate frames. This last is related to the hand-eye coordination problem and to multiple-camera calibration.
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Appendix
Available only for authorised users
Footnotes
1
La notion générale de variété est assez dificile à définir avec précision. [The general notion of a manifold is rather difficult to define with precision.] (Cartan 1951, p. 56.)
 
2
For convenience of notation, we consider the index \(n\) to mean \(0\), so that \(\mathtt{{R}}_{i+1}\) means \(\mathtt{{R}}_0\) and \(\mathtt{{R}}_{i,i+1}\) means \(\mathtt{{R}}_{n-1,0}\) when \(i = n-1\).
 
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Metadata
Title
Rotation Averaging
Authors
Richard Hartley
Jochen Trumpf
Yuchao Dai
Hongdong Li
Publication date
01-07-2013
Publisher
Springer US
Published in
International Journal of Computer Vision / Issue 3/2013
Print ISSN: 0920-5691
Electronic ISSN: 1573-1405
DOI
https://doi.org/10.1007/s11263-012-0601-0

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