Time, distance, and feature trade-offs in visual apparent motion.

A model of visual apparent motion is derived from four observations on path selection in ambiguous displays in which apparent motion of illuminated dots could, in principle, be perceived along many possible paths: (a) Whereas motion over each path is clearly visible when its stimulus is presented in isolation, motion is usually seen over only one path when two or more such stimuli are combined (competition), (b) Path selection is nearly independent of viewing distance (scale invariance). (c) At transition points between paths (' and j (where apparent motion is equally likely to be perceived along / and j), the time t and distance d between successive points along the paths are described by a log linear d/t relationship; that is, t = A B log (d/d,). (d) When successive elements along a path differ in orientation or size, the perceived motion along this path is not necessarily weaker than motion along a path composed entirely of identical elements. The model is a form of strength theory in which the path with greatest strength 5 becomes the dominant path. From scale invariance, we prove that the contributions of time and distance to stimulus strength are independent. From the log linear d/t relationship, we derive the precise trade-off function between d and / and show the existence of an optimal interstimulus interval to maximize the strength for any path. The model accounts well for the path-selection data and suggests a neural interpretation in which motion perception is based on the outputs of elementary detectors that are scaled replicas of each other, all having the same geometry and time delays, and differing only in size and orientation.