Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving

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.