Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving

Erik Ask, Yubin Kuang, Karl Åström

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review


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.
Original languageEnglish
Title of host publication21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Print)978-4-9906441-1-6
Publication statusPublished - 2012
Event21st International Conference on Pattern Recognition (ICPR 2012) - Tsukuba, Japan
Duration: 2012 Nov 112012 Nov 15


Conference21st International Conference on Pattern Recognition (ICPR 2012)

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


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