Abstract

Perceptual studies suggest that the visual system uses the rigidity assumption to recover 3-D structure from motion. Computational studies show that the rigidity assumption allows a unique 3-D interpretation from motion information integrated over a small extent in space and time. Most algorithms for recovering structure, however, are sensitive to noise and only interpret rigid motions. Ullman¹ proposed the “incremental rigidity scheme” that interprets rigid and nonrigid motions and develops a 3-D model over an extended time. As new views of points appear, a new model is computed that represents the most rigid transformation from the current model. We present a formulation of Ullman’s method that uses velocity information for recovering structure. Theoretical and computer analyses show that this continuous formulation provides a quick estimate of structure but is not robust over an extended time period. The stable long-term recovery of structure requires disparate views of moving objects. For rotation about a fixed axis, the rate of convergence and quality of the 3-D solution decreases with smaller angular displacements between frames. In the limit of the continuous formulation, the solution is no longer stable. Our analysis raises important questions for the human recovery of structure from motion.

© 1985 Optical Society of America