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Uncovering symmetries in polynomial systems

Larsson, Viktor LU and Åström, Kalle LU (2016) In Computer Vision – ECCV 2016 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part III 9907. p.252-267
Abstract

In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we present a simple and automatic method for finding these symmetries for a given problem. Finally we show two examples where these symmetries occur in real applications.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Computer Vision – ECCV 2016 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part III
editor
Leibe, Bastian; Matas, Jiri; Sebe, Nicu; Welling, Max; ; ; and
volume
9907
pages
16 pages
publisher
Springer Verlag
external identifiers
  • scopus:84990041155
  • wos:000389384800016
ISSN
1611-3349
0302-9743
ISBN
978-3-319-46486-2
978-3-319-46487-9
DOI
10.1007/978-3-319-46487-9_16
language
English
LU publication?
yes
id
1506a56c-c165-4b88-89cd-9dbfc521c5d5
date added to LUP
2016-10-24 07:41:26
date last changed
2018-05-29 10:22:14
@inproceedings{1506a56c-c165-4b88-89cd-9dbfc521c5d5,
  abstract     = {<p>In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we present a simple and automatic method for finding these symmetries for a given problem. Finally we show two examples where these symmetries occur in real applications.</p>},
  author       = {Larsson, Viktor and Åström, Kalle},
  booktitle    = {Computer Vision – ECCV 2016 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part III},
  editor       = {Leibe, Bastian and Matas, Jiri and Sebe, Nicu and Welling, Max},
  isbn         = { 978-3-319-46486-2},
  issn         = {1611-3349},
  language     = {eng},
  pages        = {252--267},
  publisher    = {Springer Verlag},
  title        = {Uncovering symmetries in polynomial systems},
  url          = {http://dx.doi.org/10.1007/978-3-319-46487-9_16},
  volume       = {9907},
  year         = {2016},
}