Rotation Averaging

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 i...

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Bibliographic Details
Published in:International journal of computer vision Vol. 103; no. 3; pp. 267 - 305
Main Authors: Hartley, Richard, Trumpf, Jochen, Dai, Yuchao, Li, Hongdong
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2013
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Applied sciences
Artificial Intelligence
Automation
Averaging
Calibration
Cameras
Computation
Computer Imaging
Computer Science
Computer science; control theory; systems
Computer systems performance. Reliability
Computer vision
Conjugates
Convergence
Coordinate transformations
Exact sciences and technology
Image Processing and Computer Vision
Machine vision
Motor ability
Orientation
Pattern Recognition
Pattern Recognition and Graphics
Pattern recognition. Digital image processing. Computational geometry
Proving
Robots
Software
Speech and sound recognition and synthesis. Linguistics
Studies
Vision
Vision systems
conjugate rotation
Geodesic distance
Chordal distance
mean
Quaternion distance
Angular distance
Averaging method
Computer vision
Coordination
Quaternion
Video cameras
Calibration
L
Program verification
Multiple view
Educational software program
Geodesic
Convexity
Proof theory
Responder
ISSN:0920-5691, 1573-1405
Online Access:Get full text
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Description
Summary: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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ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-012-0601-0