Partial Symmetry in Polynomial Systems and Its Applications 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 Gröbner 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.