Algebraic methods in computer vision

Many problems in computer vision, but also in other field such as robotics, control design or economics, can be formulated using systems of polynomial equations. Often, these systems are non-trivial and therefore special algorithms have to be designed to obtain numerically robust and computational efficient solvers. In this talk we will briefly discuss two methods for creating such efficient solvers of systems of polynomial equations. The first one is based on Groebner basis methods for solving systems of polynomial equations and the second one is based on methods for solving polynomial eigenvalue problems and resultants. We will also introduce an automatic generator of Groebner basis solvers which could be used even by non-experts to efficiently solve polynomial problems. Finally, we will demonstrate the usefulness of our approach by presenting new, efficient and numerically stable solutions to several important problems from computer vision and robotics.