Exploiting p-fold symmetries for faster polynomial equation solving

Numerous geometric problems in computer vision involve 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 coefficient matrix that represents the expanded original equation set. In this paper we present two simplifications 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.