Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations.

Perceptual studies suggest that the visual system may use a rigidity assumption in its recovery of three-dimensional structure from motion. Ullman [Perception 13, 255 (1984)] recently proposed a computational scheme that uses this assumption to recover the structure of rigid and nonrigid objects in motion. The scheme assumes the input to be discrete positions of elements in motion, under orthographic projection. We present formulations of Ullman's method that use velocity information and perspective projection in the recovery of structure. Theoretical and computer analyses show that the velocity-based formulations provide a rough estimate of structure quickly but are not robust over an extended time. The stable long-term recovery of structure requires disparate views of moving objects.