  It is well-known that natural images possess statistical regularities that
can be captured by bandpass decomposition and divisive normalization processes
that approximate early neural processing in the human visual system. We expand
on these studies and present new findings on the properties of space-time
natural statistics that are inherent in motion pictures. Our model relies on
the concept of temporal bandpass (e.g. lag) filtering in LGN and area V1, which
is similar to smoothed frame differencing of video frames. Specifically, we
model the statistics of the differences between adjacent or neighboring video
frames that have been slightly spatially displaced relative to one another. We
find that when these space-time differences are further subjected to locally
pooled divisive normalization, statistical regularities (or lack thereof) arise
that depend on the local motion trajectory. We find that bandpass and
divisively normalized frame-differences that are displaced along the motion
direction exhibit stronger statistical regularities than for other
displacements. Conversely, the direction-dependent regularities of displaced
frame differences can be used to estimate the image motion (optical flow) by
finding the space-time displacement paths that best preserve statistical
regularity.
