  We present an optical flow estimation approach that operates on the full
four-dimensional cost volume. This direct approach shares the structural
benefits of leading stereo matching pipelines, which are known to yield high
accuracy. To this day, such approaches have been considered impractical due to
the size of the cost volume. We show that the full four-dimensional cost volume
can be constructed in a fraction of a second due to its regularity. We then
exploit this regularity further by adapting semi-global matching to the
four-dimensional setting. This yields a pipeline that achieves significantly
higher accuracy than state-of-the-art optical flow methods while being faster
than most. Our approach outperforms all published general-purpose optical flow
methods on both Sintel and KITTI 2015 benchmarks.
