Relative Depth and Local Surface Orientation from Image Motions

摘要

A simple mathematical formalism is presented suggesting a mechanism for computing relative depth of any two texture elements characterized by the same relative motion parameters. The method is based on a ratio of a function of the angular velocities of the projecting rays corresponding to the two texture elements. The angular velocity of a ray cannot, however, be computed directly from the instantaneous characterization of motion of a 'retinal' point. It is shown how it can be obtained from the (linear) velocity of the image element on the projection surface and the first time derivative of its direction vector. A similar analysis produces a set of equations which directly yield local surface orientation relative to a given visual direction. The variables involved are scalar quantities directly measurable on the projection surface but, unlike the case of relative depth, the direction of (instantaneous) motion has to be computed by different means before the method can be applied. The relative merits of the two formalisms are briefly discussed. (Author)