  Event cameras are bio-inspired sensors that perform well in challenging
illumination conditions and have high temporal resolution. However, their
concept is fundamentally different from traditional frame-based cameras. The
pixels of an event camera operate independently and asynchronously. They
measure changes of the logarithmic brightness and return them in the highly
discretised form of time-stamped events indicating a relative change of a
certain quantity since the last event. New models and algorithms are needed to
process this kind of measurements. The present work looks at several motion
estimation problems with event cameras. The flow of the events is modelled by a
general homographic warping in a space-time volume, and the objective is
formulated as a maximisation of contrast within the image of warped events. Our
core contribution consists of deriving globally optimal solutions to these
generally non-convex problems, which removes the dependency on a good initial
guess plaguing existing methods. Our methods rely on branch-and-bound
optimisation and employ novel and efficient, recursive upper and lower bounds
derived for six different contrast estimation functions. The practical validity
of our approach is demonstrated by a successful application to three different
event camera motion estimation problems.
