  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-style framework. Minimal problems often
result in complex systems of polynomial equations. The existing
state-of-the-art methods for solving such systems are either based on Gr\"obner
bases and the action matrix method, which have been extensively studied and
optimized in the recent years or recently proposed approach based on a sparse
resultant computation using an extra variable.
  In this paper, we study an interesting alternative sparse resultant-based
method for solving sparse systems of polynomial equations by hiding one
variable. This approach results in a larger eigenvalue problem than the action
matrix and extra variable sparse resultant-based methods; however, it does not
need to compute an inverse or elimination of large matrices that may be
numerically unstable. The proposed approach includes several improvements to
the standard sparse resultant algorithms, which significantly improves the
efficiency and stability of the hidden variable resultant-based solvers as we
demonstrate on several interesting computer vision problems. We show that for
the studied problems, our sparse resultant based approach leads to more stable
solvers than the state-of-the-art Gr\"obner bases-based solvers as well as
existing sparse resultant-based solvers, especially in close to critical
configurations. Our new method can be fully automated and incorporated into
existing tools for the automatic generation of efficient minimal solvers.
