Abstract

The minimal mapping theory, a computational theory for apparent motion,¹ postulates that the motion correspondence process matches features in consecutive viewing frames so as to minimize their total distance traveled. We explored some computational properties of this theory. For rotating objects we found that the correct matching percentage of minimal mapping algorithms decreases with angular displacement. An alternative theory, the structural theory, postulates that the matching is such that it minimizes 2-D structural changes of the object. The performance of structural algorithms is independent of the angular displacement, being poorer than that of the minimal mapping theory for small angles, but better at high angles. The best of both worlds may be obtained by a hybrid theory of the above two. We also explored the inclusion of motion inertia² into the minimal mapping theory. This was done by an increase, through a simple cosinusoidal law, of the effective distance between features in consecutive frames whose putative motion is in a direction different from that of the past motion. This modification accounts for the extant psychophysical data on ambiguous motion.² Surprisingly, the predictions of this inertial minimal mapping theory include noncrossing in transversal collision experiments and better performances under rotation.

© 1986 Optical Society of America