  Analog computation with passive optical components can enhance processing
speeds and reduce power consumption, recently attracting renewed interest
thanks to the opportunities enabled by metasurfaces. Basic image processing
tasks, such as spatial differentiation, have been recently demonstrated based
on engineered nonlocalities in metasurfaces, but next-generation computational
schemes require more advanced capabilities. Here, we tailor nonlocalities in
space and time to design a metasurface that can perform mixed spatio-temporal
differentiation of an input image, realizing event-based edge detection with a
passive ultrathin silicon-based structured film compatible with standard
fabrication techniques. The metasurface detects the object edges only when the
object moves, and its design can be tailored to selectively enhance objects
moving at desired speeds. Our results point towards fully-passive processing of
spatio-temporal signals, for highly compact neuromorphic cameras.
