Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving
Ask, Erik; Kuang, Yubin; Åström, Karl (2012). Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of, 3232 - 3235. 21st International Conference on Pattern Recognition (ICPR 2012). Tsukuba, Japan: IEEE - Institute of Electrical and Electronics Engineers Inc.
Conference Proceeding/Paper
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Published
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English
Authors:
Ask, Erik
;
Kuang, Yubin
;
Åström, Karl
Department:
Mathematics (Faculty of Engineering)
Centre for Mathematical Sciences
Mathematical Imaging Group
Algebra
ELLIIT: the Linköping-Lund initiative on IT and mobile communication
Research Group:
Mathematical Imaging Group
Algebra
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 significant
speed increases are possible without loosing accuracy.
Keywords:
geometry ;
algebra ;
computer vision ;
Polynomial equation solving
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