Motion Field and Optical Flow: Qualitative Properties

In this paper we show that the optical flow, a 2D field that can be associated with the variation of the image brightness pattern, and the 2D motion field, the projection on the image plane of the 3D velocity field of a moving scene, are in general different, unless very special conditions are satisfied. The optical flow, therefore, is ill-suited for computing structure from motion and for reconstructing the 3D velocity field, problems that require an accurate estimate of the 2D motion field. We then suggest a different use of the optical flow. We argue that stable qualitative properties of the 2D motion field give useful information about the 3D velocity field and the 3D structure of the scene, and that they can usually be obtained from the optical flow. To support this approach we show how the (smoothed) optical flow and 2D motion field, interpreted as vector fields tangent to flows of planar dynamical systems, may have the same qualitative properties from the point of view of the theory of structural stability of dynamical systems