  Systems of polynomial equations arise frequently in computer vision,
especially in multiview geometry problems. Traditional methods for solving
these systems typically aim to eliminate variables to reach a univariate
polynomial, e.g., a tenth-order polynomial for 5-point pose estimation, using
clever manipulations, or more generally using Grobner basis, resultants, and
elimination templates, leading to successful algorithms for multiview geometry
and other problems. However, these methods do not work when the problem is
complex and when they do, they face efficiency and stability issues. Homotopy
Continuation (HC) can solve more complex problems without the stability issues,
and with guarantees of a global solution, but they are known to be slow. In
this paper we show that HC can be parallelized on a GPU, showing significant
speedups up to 26 times on polynomial benchmarks. We also show that GPU-HC can
be generically applied to a range of computer vision problems, including 4-view
triangulation and trifocal pose estimation with unknown focal length, which
cannot be solved with elimination template but they can be efficiently solved
with HC. GPU-HC opens the door to easy formulation and solution of a range of
computer vision problems.
