CLOSED-FORM SOLUTIONS TO IMAGE FLOW EQUATIONS.

A major source of three-dimensional (3-D) information about objects in the world is available to the observer in the form of time-varying imagery. Relative motion between textured objects and observer generates a time-varying optic array at the image, from which image motion of contours, edge fragments and feature points can be extracted. These dynamic features serve to sample the underlying image-flow field. Closed-form solutions are given for the structure and motion of planar and curved surface patches from monocular image flow and its derivatives through second order. Both planar and curved surface solutions require, at most, the solution of a cubic equation. The analytic solution for curved surface patches combines the transformation of Longuet-Higgins and Prazdny with the planar surface solution of Subbarao and Waxman. Insights regarding uniqueness of solutions also emerge.