  This paper presents novel techniques for recovering 3D dense scene flow,
based on differential analysis of 4D light fields. The key enabling result is a
per-ray linear equation, called the ray flow equation, that relates 3D scene
flow to 4D light field gradients. The ray flow equation is invariant to 3D
scene structure and applicable to a general class of scenes, but is
under-constrained (3 unknowns per equation). Thus, additional constraints must
be imposed to recover motion. We develop two families of scene flow algorithms
by leveraging the structural similarity between ray flow and optical flow
equations: local 'Lucas-Kanade' ray flow and global 'Horn-Schunck' ray flow,
inspired by corresponding optical flow methods. We also develop a combined
local-global method by utilizing the correspondence structure in the light
fields. We demonstrate high precision 3D scene flow recovery for a wide range
of scenarios, including rotation and non-rigid motion. We analyze the
theoretical and practical performance limits of the proposed techniques via the
light field structure tensor, a 3x3 matrix that encodes the local structure of
light fields. We envision that the proposed analysis and algorithms will lead
to design of future light-field cameras that are optimized for motion sensing,
in addition to depth sensing.
