  We present a global optimization approach to optical flow estimation. The
approach optimizes a classical optical flow objective over the full space of
mappings between discrete grids. No descriptor matching is used. The highly
regular structure of the space of mappings enables optimizations that reduce
the computational complexity of the algorithm's inner loop from quadratic to
linear and support efficient matching of tens of thousands of nodes to tens of
thousands of displacements. We show that one-shot global optimization of a
classical Horn-Schunck-type objective over regular grids at a single resolution
is sufficient to initialize continuous interpolation and achieve
state-of-the-art performance on challenging modern benchmarks.
