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Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving

Ask, Erik LU ; Kuang, Yubin LU and Åström, Karl LU (2012) 21st International Conference on Pattern Recognition (ICPR 2012) In 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of p.3232-3235
Abstract
Numerous geometric problems in computer vision in-

volve the solution of systems of polynomial equations.

This is true for problems with minimal information, but

also for finding stationary points for overdetermined

problems. The state-of-the-art is based on the use of

numerical linear algebra on the large but sparse co-

efficient matrix that represents the expanded original

equation set. In this paper we present two simplifica-

tions that can be used (i) if the zero vector is one of

the solutions or (ii) if the equations display certain p-

fold symmetries. We evaluate the simplifications on a

few example problems and demonstrate that... (More)
Numerous geometric problems in computer vision in-

volve the solution of systems of polynomial equations.

This is true for problems with minimal information, but

also for finding stationary points for overdetermined

problems. The state-of-the-art is based on the use of

numerical linear algebra on the large but sparse co-

efficient matrix that represents the expanded original

equation set. In this paper we present two simplifica-

tions that can be used (i) if the zero vector is one of

the solutions or (ii) if the equations display certain p-

fold symmetries. We evaluate the simplifications on a

few example problems and demonstrate that significant

speed increases are possible without loosing accuracy. (Less)
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
keywords
geometry, algebra, computer vision, Polynomial equation solving
in
21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of
pages
4 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
21st International Conference on Pattern Recognition (ICPR 2012)
external identifiers
  • Scopus:84874559594
ISBN
978-4-9906441-1-6
language
English
LU publication?
yes
id
45645dfb-c67c-4be9-8fb1-efafd9f2cfc1 (old id 2971266)
date added to LUP
2013-02-05 11:15:01
date last changed
2017-01-01 08:00:44
@inproceedings{45645dfb-c67c-4be9-8fb1-efafd9f2cfc1,
  abstract     = {Numerous geometric problems in computer vision in-<br/><br>
volve the solution of systems of polynomial equations.<br/><br>
This is true for problems with minimal information, but<br/><br>
also for finding stationary points for overdetermined<br/><br>
problems. The state-of-the-art is based on the use of<br/><br>
numerical linear algebra on the large but sparse co-<br/><br>
efficient matrix that represents the expanded original<br/><br>
equation set. In this paper we present two simplifica-<br/><br>
tions that can be used (i) if the zero vector is one of<br/><br>
the solutions or (ii) if the equations display certain p-<br/><br>
fold symmetries. We evaluate the simplifications on a<br/><br>
few example problems and demonstrate that significant<br/><br>
speed increases are possible without loosing accuracy.},
  author       = {Ask, Erik and Kuang, Yubin and Åström, Karl},
  booktitle    = {21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of},
  isbn         = {978-4-9906441-1-6},
  keyword      = {geometry,algebra,computer vision,Polynomial equation solving},
  language     = {eng},
  pages        = {3232--3235},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving},
  year         = {2012},
}