  Contrast maximisation estimates the motion captured in an event stream by
maximising the sharpness of the motion compensated event image. To carry out
contrast maximisation, many previous works employ iterative optimisation
algorithms, such as conjugate gradient, which require good initialisation to
avoid converging to bad local minima. To alleviate this weakness, we propose a
new globally optimal event-based motion estimation algorithm. Based on
branch-and-bound (BnB), our method solves rotational (3DoF) motion estimation
on event streams, which supports practical applications such as video
stabilisation and attitude estimation. Underpinning our method are novel
bounding functions for contrast maximisation, whose theoretical validity is
rigorously established. We show concrete examples from public datasets where
globally optimal solutions are vital to the success of contrast maximisation.
Despite its exact nature, our algorithm is currently able to process a 50,000
event input in 300 seconds (a locally optimal solver takes 30 seconds on the
same input), and has the potential to be further speeded-up using GPUs.
