  Estimating unknown rotations from noisy measurements is an important step in
SfM and other 3D vision tasks. Typically, local optimization methods
susceptible to returning suboptimal local minima are used to solve the rotation
averaging problem. A new wave of approaches that leverage convex relaxations
have provided the first formal guarantees of global optimality for state
estimation techniques involving SO(3). However, most of these guarantees are
only applicable when the measurement error introduced by noise is within a
certain bound that depends on the problem instance's structure. In this paper,
we cast rotation averaging as a polynomial optimization problem over unit
quaternions to produce the first rotation averaging method that is formally
guaranteed to provide a certifiably globally optimal solution for \textit{any}
problem instance. This is achieved by formulating and solving a sparse convex
sum of squares (SOS) relaxation of the problem. We provide an open source
implementation of our algorithm and experiments, demonstrating the benefits of
our globally optimal approach.
