3-D Motion Recovery From Time-Varying Optical Flows

Previous research on analyzing time-varying image sequences has concentrated on finding the necessary (and sufficient) conditions for a unique 3-D solution. While such an approach provides useful theoretical insight, the resulting algorithms turn out to be too sensitive to be of pratical use. We claim that any robust algorithm must improve the 3-D solution adaptively over time. As the first step toward such a paradigm, in this paper we present an algorithm for 3-D motion computation, given time-varying optical flow fields. The surface of the object in the scene is assumed to be locally planar. It is also assumed that 3-D velocity vectors are piecewise constant over three consecutive frames (or 2 snapshots of flow field). Our formulation relates 3-D motion and object geometry with the optical flow vector as well as its spatial and temporal derivatives. The deformation parameters of the first kind, or equivalently, the first-order flow approximation (in space and time) is sufficient to recover rigid body motion and local surface structure from the local instantaneous flow field. We also demonstrate, through a sensitivity analysis carried out for synthetic and natural motions in space, that 3-D inference can be made reliably.