Issue No. 07 - July (2012 vol. 34)
Zuzana Kukelova , Czech Technical University in Prague, Prague
Martin Bujnak , Czech Technical University in Prague, Prague
Tomas Pajdla , Czech Technical University in Prague, Prague
We present a method for solving systems of polynomial equations appearing in computer vision. This method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state-of-the-art Gröbner basis method since eigenvalue problems are well studied, easy to understand, and efficient and robust algorithms for solving these problems are available. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems (PEPs) and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem. We propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems. To show the applicability of the proposed polynomial eigenvalue method, we present the polynomial eigenvalue solutions to several important minimal relative pose problems.
Structure from motion, relative camera pose, minimal problems, polynomial eigenvalue problems.
Zuzana Kukelova, Martin Bujnak, Tomas Pajdla, "Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 34, no. , pp. 1381-1393, July 2012, doi:10.1109/TPAMI.2011.230