## 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.

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.

Original language | English |
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Title of host publication | 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of |

Publisher | IEEE - Institute of Electrical and Electronics Engineers Inc. |

Pages | 3232-3235 |

Number of pages | 4 |

ISBN (Print) | 978-4-9906441-1-6 |

Publication status | Published - 2012 |

Event | 21st International Conference on Pattern Recognition (ICPR 2012) - Tsukuba, Japan Duration: 2012 Nov 11 → 2012 Nov 15 |

### Conference

Conference | 21st International Conference on Pattern Recognition (ICPR 2012) |
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Country/Territory | Japan |

City | Tsukuba |

Period | 2012/11/11 → 2012/11/15 |

### Bibliographical note

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.## Subject classification (UKÄ)

- Mathematics

## Free keywords

- geometry
- algebra
- computer vision
- Polynomial equation solving