Visual Apparent Motion and Some Preferred Paths in the Rotation Group

The sequential presentation of two distinct stimulus objects to the visual system will, under certain conditions, induce an apparentmotion effect, called beta motion, in which the first object appears to smoothly transform into the second. This study is concerned with the kinds of paths selected by the visual system in effecting beta motion in which the metric structure of the object is preserved throughout. Two schemes are advanced according to which the visual system might operate. The first concentrates upon the manifold M in which the object appears to transform and the second upon the group G of transformations of M onto itself in which the particular transformation describing this motion lie. Under the identification of M with the 2-sphere S2, each scheme specifies the action-minimizing curves in the rotation group SO(3) for a particular "natural" Riemannian metric. An experiment is described in which a determination is made of the actual paths taken by an object under: going various rigid-motion beta motions. The results obtained indicate that the visual system behaves more in accordance with the second scheme than with the first. A generalization of this result is briefly discussed.