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Recovering 3-D Motion and Structure from 1st-Order Image Deformation

Recent research in motion analysis is concerned with finding a stable algorithm to recover 3-D motion and structure for practical use. We claim that any robust algorithm must improve the 3-D solution adaptively over time. As an initial step toward this goal, we investigate the behavior of the optical flow field over a short time period. This approach yields a new method for recovering 3-D motion and structure. The surface of the object is assumed to be locally planar. The 3-D velocity vectors are assumed to be constant or varying slowly. We prove the deformation parameter of the first kind, or equivalently the first order flow approximation (in space and time), is sufficient to recover 3-D rigid body motion and the surface normal. We also demonstrate, through sensitivity analysis and experiments, that 3-D inferences can be made reliably.