The Computation of the Velocity Field

Abstract

The organization of movement in the changing retinal image provides a valuable source of information for analyzing the environment in terms of objects, their motion in space and their three-dimensional structure. A description of this movement is not provided to our visual system directly, however; it must be inferred from the pattern of changing intensity that reaches the eye. This paper examines the problem of motion measurement, which we formulate as the computation of an instantaneous two-dimensional velocity field from the changing image. Initial measurements of motion take place at the location of significant intensity changes, as suggested by Marr and Ullman (1981). These measurements provide only one component of local velocity, and must be integrated to compute the two-dimensional velocity field. A fundamental problem for this integration stage is that the velocity field is not determined uniquely from information available in the changing image. We formulate an additional constraint of smoothness of the velocity field, based on the physical assumption that surfaces are generally smooth, which allows the computation of a unique velocity field. A theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible. Empirical studies show the predictions of this computation to be consistent with human motion perception.