Partial Symmetry in Polynomial Systems and Its Application in Computer Vision

Abstract:
Algorithms for solving systems of polynomial equations

are key components for solving geometry problems in computer

vision. Fast and stable polynomial solvers are essential

for numerous applications e.g. minimal problems or

finding for all stationary points of certain algebraic errors.

Recently, full symmetry in the polynomial systems has been

utilized to simplify and speed up state-of-the-art polynomial

solvers based on Gr¨obner basis method. In this paper, we

further explore partial symmetry (i.e. where the symmetry

lies in a subset of the variables) in the polynomial systems.

We develop novel numerical schemes to utilize such partial

symmetry. We then demonstrate the advantage of our

schemes in several computer vision problems. In both synthetic

and real experiments, we show that utilizing partial

symmetry allow us to obtain faster and more accurate polynomial

solvers than the general solvers.