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)
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:
https://lup.lub.lu.se/record/2971266
- author
- Ask, Erik
LU
; Kuang, Yubin
LU
and Åström, Karl
LU
- organization
- publishing date
- 2012
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- geometry, algebra, computer vision, Polynomial equation solving
- host publication
- 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)
- conference location
- Tsukuba, Japan
- conference dates
- 2012-11-11 - 2012-11-15
- external identifiers
-
- scopus:84874559594
- ISBN
- 978-4-9906441-1-6
- language
- English
- LU publication?
- yes
- additional info
- The proceedings of ICPR 2012 will in the future be available at IEEE Xplore. The page reference given above refer to the proceedings published on USB by IEEE, and distributed to the participants during the conference.
- id
- 45645dfb-c67c-4be9-8fb1-efafd9f2cfc1 (old id 2971266)
- date added to LUP
- 2016-04-04 10:57:54
- date last changed
- 2022-02-13 20:33:34
@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}},
keywords = {{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}},
}