Contour Evolution,Neighborhood Deformation,and Global Image Flow: Planar Surfaces in Motion

In the kinematic analysis of time-varying imagery, where the goal is to recover object surface structure and space motion from image flow, an appropriate representation for the flow field consists of a set of deformation parameters that describe the rate of change of an image neighborhood. In this paper we develop methods for extracting these deformation param eters from evolving contours in an image sequence, the image contours being manifestations of surface texture seen in perspective projection. Our results follow directly from the analytic structure of the underlying image flow; no heuristics are imposed. The deformation parameters we seek are actu ally linear combinations of the Taylor series coefficients (through second derivatives) of the local image flow field. Thus, a by-product of our approach is a second-order polyno mial approximation to the image flow in the neighborhood of a contour. For curved surfaces this approximation is only locally valid, but for planar surfaces it is globally valid (i.e., it is exact). Our analysis reveals an "aperture problem in the large" in which insufficient contour structure leaves the set of 12 deformation parameters underdetermined. We also assess the sensitivity of our method to the simulated effects of noise in the "normal flow" around contours as well as the angular field of view subtended by contours. The sensitivity analysis is carried out in the context of planar surfaces executing general rigid-body motions in space. Future work will address the additional considerations relevant to curved surface patches.