Interpretation of image flow: Rigid curved surfaces in motion

A new method is described for interpreting image flow (or optical flow) in a small field of view produced by a rigidly moving curved surface. The equations relating the shape and motion of the surface to the image flow are formulated. These equations are solved to obtain explicit analytic expressions for the motion, orientation, and curvatures of the surface in terms of the spatial derivatives (up to second order) of the image flow. We state and prove some new theoretical results concerning the existence of multiple interpretations. Numerical examples are given for some interesting cases where multiple solutions exist. The solution method described here is simpler and more direct than previous methods. The method and the representation described here are part of a unified approach for the interpretation of image motion in a variety of cases (e.g., planar/curved surfaces, constant/accelerated motion, etc.). Thus the representation and the method of analysis adopted here have some advantages in comparison with previous approaches.