International Journal of Computer Vision

, Volume 103, Issue 3, pp 267–305 | Cite as

Rotation Averaging

  • Richard Hartley
  • Jochen Trumpf
  • Yuchao Dai
  • Hongdong Li
Article

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.

Keywords

Geodesic distance Angular distance  Chordal distance  Quaternion distance \(L_1\) mean \(L_2\) mean conjugate rotation 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Richard Hartley
    • 1
  • Jochen Trumpf
    • 1
  • Yuchao Dai
    • 1
  • Hongdong Li
    • 1
  1. 1.Australian National UniversityCanberraAustralia

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