Authors: Daqi Liu, Álvaro Parra, Tat-Jun Chin Description: 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 approx 300 seconds (a locally optimal solver takes approx 30 seconds on the same input), and has the potential to be further speeded-up using GPUs.