Ask, Erik; Kuang, Yubin; Åström, Karl **(2012)**. Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving* *, 3232 - 3235. 21st International Conference on Pattern Recognition (ICPR 2012). Tsukuba, Japan: IEEE--Institute of Electrical and Electronics Engineers Inc.

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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

Centre for Mathematical Sciences

Mathematical Imaging Group

Algebra

ELLIIT: the Linköping-Lund initiative on IT and mobile communication

Research Group:

Mathematical Imaging Group

Algebra

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.

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

ISBN:

978-4-9906441-1-6

LUP-ID:

45645dfb-c67c-4be9-8fb1-efafd9f2cfc1 | Link: https://lup.lub.lu.se/record/45645dfb-c67c-4be9-8fb1-efafd9f2cfc1
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