A hybrid algorithm for calculating the global solution of the fundamental matrix problem

Abstract It is well-known that the fundamental matrix estimation problem is a non-convex problem and to date only local solutions can be claimed. The hybrid method is mainly based on some recent progress in global polynomial optimization techniques. By solving a hierarchy of semi-definite programming problems, the global solutions can be achieved or approximated as closely as desired at some relaxation order. To reduce the computational complexity and avoid numerical difficulties of this convex relaxation method when the number of unknown variables is large, the singular value decomposition (SVD) method combined with the interleaving parameterization method are integrated. The experimental results show that the proposed algorithm can calculate the global solution after only a few iterations and can achieve almost the same accuracy as the original convex relaxation method with much less time.