  Many computer vision applications require robust and efficient estimation of
camera geometry. The robust estimation is usually based on solving camera
geometry problems from a minimal number of input data measurements, i.e.
solving minimal problems in a RANSAC framework. Minimal problems often result
in complex systems of polynomial equations. Many state-of-the-art efficient
polynomial solvers to these problems are based on Gr\"obner bases and the
action-matrix method that has been automatized and highly optimized in recent
years. In this paper we study an alternative algebraic method for solving
systems of polynomial equations, i.e., the sparse resultant-based method and
propose a novel approach to convert the resultant constraint to an eigenvalue
problem. This technique can significantly improve the efficiency and stability
of existing resultant-based solvers. We applied our new resultant-based method
to a large variety of computer vision problems and show that for most of the
considered problems, the new method leads to solvers that are the same size as
the the best available Gr\"obner basis solvers and of similar accuracy. For
some problems the new sparse-resultant based method leads to even smaller and
more stable solvers than the state-of-the-art Gr\"obner basis solvers. Our new
method can be fully automatized and incorporated into existing tools for
automatic generation of efficient polynomial solvers and as such it represents
a competitive alternative to popular Gr\"obner basis methods for minimal
problems in computer vision.
