Scene flow denotes the real 3-D motion of objects in the scene, as
opposed to optical flow, which only describes the projection of this motion
on the 2-D image plane. In contrast to structure from motion, where a single
camera moves through a static environment, scene flow does not relate to a rigid
world, but objects are allowed to move around freely and deform in a non-rigid
fashion. Since depth information is required to determine the 3-D motion of
objects, scene flow can not be computed without estimating the scene structure
as well. Unlike the stereo reconstruction problem, scene flow estimation has a
temporal component and stereo sequences are needed that provide at least
two views per time instance.
The figure shows an example of a model turning her head (click on the figures to enlarge). The left image shows the 3D reconstruction with the scene flow field superimposed as a vector plot. The flow vectors are colour coded depending on their magnitude: green indicates no or only small motion and red indicates large motion. The middle image only shows the scene flow vector field, while the right image depicts the magnitude of the scene flow in each point of the reconstructed surface.
In  we compute the scene flow by considering the
four-frame case depicted below. It consists of two consecutive image pairs of a
synchronised stereo sequence: the left and the right image at a time instance
t and the left and right image at time t+1. For our application we
assume a fixed stereo rig, i.e. there exists a single fundamental matrix that
describes the epipolar geometry of both stereo pairs. In the case of arbitrarily
moving cameras, however, our model can also be generalised to a temporally
varying fundamental matrix .
The above figure shows an example of a model closing his eyes and smiling (click on the figures to enlarge). The top row shows the left and right image at time t and the left and right image at time t + 1. The bottom row shows the 3D reconstruction with the scene flow field superimposed and the scene flow vector field.