  The optical flow of natural scenes is a combination of the motion of the
observer and the independent motion of objects. Existing algorithms typically
focus on either recovering motion and structure under the assumption of a
purely static world or optical flow for general unconstrained scenes. We
combine these approaches in an optical flow algorithm that estimates an
explicit segmentation of moving objects from appearance and physical
constraints. In static regions we take advantage of strong constraints to
jointly estimate the camera motion and the 3D structure of the scene over
multiple frames. This allows us to also regularize the structure instead of the
motion. Our formulation uses a Plane+Parallax framework, which works even under
small baselines, and reduces the motion estimation to a one-dimensional search
problem, resulting in more accurate estimation. In moving regions the flow is
treated as unconstrained, and computed with an existing optical flow method.
The resulting Mostly-Rigid Flow (MR-Flow) method achieves state-of-the-art
results on both the MPI-Sintel and KITTI-2015 benchmarks.
