Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving
Författare
Summary, in English
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.
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.
Avdelning/ar
- Matematik LTH
- Matematikcentrum
- Mathematical Imaging Group
- Algebra
- ELLIIT: the Linköping-Lund initiative on IT and mobile communication
Publiceringsår
2012
Språk
Engelska
Sidor
3232-3235
Publikation/Tidskrift/Serie
21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of
Dokumenttyp
Konferensbidrag
Förlag
IEEE - Institute of Electrical and Electronics Engineers Inc.
Ämne
- Mathematics
Nyckelord
- geometry
- algebra
- computer vision
- Polynomial equation solving
Conference name
21st International Conference on Pattern Recognition (ICPR 2012)
Conference date
2012-11-11 - 2012-11-15
Conference place
Tsukuba, Japan
Status
Published
Forskningsgrupp
- Mathematical Imaging Group
- Algebra
ISBN/ISSN/Övrigt
- ISBN: 978-4-9906441-1-6