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Simultaneous Multiple Rotation Averaging using Lagrangian Duality

Fredriksson, Johan LU and Olsson, Carl LU (2013) 11th Asian Conference on Computer Vision (ACCV 2012), 2012 7726. p.245-258
Abstract
Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations. In this paper we propose a simple procedure based on Lagrangian duality that can be used to verify global optimality of a local solution, by solving a linear system of equations. We show experimentally on real and synthetic data that unless the noise levels are extremely high this procedure always generates the globally optimal solution.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
computer vision, rotation averaging, optimization, duality
host publication
Lecture Notes in Computer Science (Computer Vision - ECCV 2012, 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part III)
volume
7726
pages
14 pages
publisher
Springer
conference name
11th Asian Conference on Computer Vision (ACCV 2012), 2012
conference dates
2012-11-05 - 2012-11-09
external identifiers
  • scopus:84875894004
ISSN
0302-9743
1611-3349
ISBN
978-3-642-37430-2 (print)
978-3-642-37431-9 (online)
language
English
LU publication?
yes
id
3b6b3d06-54ca-4096-ad4b-bd864e1af762 (old id 3327279)
alternative location
http://link.springer.com/chapter/10.1007/978-3-642-37431-9_19
date added to LUP
2016-04-01 10:08:09
date last changed
2024-06-17 12:02:57
@inproceedings{3b6b3d06-54ca-4096-ad4b-bd864e1af762,
  abstract     = {{Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations. In this paper we propose a simple procedure based on Lagrangian duality that can be used to verify global optimality of a local solution, by solving a linear system of equations. We show experimentally on real and synthetic data that unless the noise levels are extremely high this procedure always generates the globally optimal solution.}},
  author       = {{Fredriksson, Johan and Olsson, Carl}},
  booktitle    = {{Lecture Notes in Computer Science (Computer Vision - ECCV 2012, 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part III)}},
  isbn         = {{978-3-642-37430-2 (print)}},
  issn         = {{0302-9743}},
  keywords     = {{computer vision; rotation averaging; optimization; duality}},
  language     = {{eng}},
  pages        = {{245--258}},
  publisher    = {{Springer}},
  title        = {{Simultaneous Multiple Rotation Averaging using Lagrangian Duality}},
  url          = {{http://link.springer.com/chapter/10.1007/978-3-642-37431-9_19}},
  volume       = {{7726}},
  year         = {{2013}},
}