  Visual repetition is ubiquitous in our world. It appears in human activity
(sports, cooking), animal behavior (a bee's waggle dance), natural phenomena
(leaves in the wind) and in urban environments (flashing lights). Estimating
visual repetition from realistic video is challenging as periodic motion is
rarely perfectly static and stationary. To better deal with realistic video, we
elevate the static and stationary assumptions often made by existing work. Our
spatiotemporal filtering approach, established on the theory of periodic
motion, effectively handles a wide variety of appearances and requires no
learning. Starting from motion in 3D we derive three periodic motion types by
decomposition of the motion field into its fundamental components. In addition,
three temporal motion continuities emerge from the field's temporal dynamics.
For the 2D perception of 3D motion we consider the viewpoint relative to the
motion; what follows are 18 cases of recurrent motion perception. To estimate
repetition under all circumstances, our theory implies constructing a mixture
of differential motion maps: gradient, divergence and curl. We temporally
convolve the motion maps with wavelet filters to estimate repetitive dynamics.
Our method is able to spatially segment repetitive motion directly from the
temporal filter responses densely computed over the motion maps. For
experimental verification of our claims, we use our novel dataset for
repetition estimation, better-reflecting reality with non-static and
non-stationary repetitive motion. On the task of repetition counting, we obtain
favorable results compared to a deep learning alternative.
