Perception & Psychophysics 1989, 46(4), 333-337

Apparent Motion between shapes differing in location and orientation: A window technique for estimating path curvature

Michael K. McBeath, Roger Shepard

When a shape is alternately presented in two positions differing in both location and orientation, apparent motion tends to be experienced over a curved path. The curvature provides evidence about principles of object motion that may have been internalized in the perceptual system. This study introduces a technique for estimating deviation from a straight path. A shape was alternately presented on the two sides of a visual partition with a "window" just wide enough to accommodate the shape. Observers adjusted the location of the window to maximize the illusion of smooth passage of the shape through the window. In accordance with theoretical expectations, estimated deviations from rectilinear motion increased with the separation between the stimuli in spatial location, angular orientation, and time.

	Figure 1. Stimuli used in the present experiment. (a) The three shapes differing in width or elongation. (b) Layout of a visual display, showing two alternately presented positions of a shape to the left and right of a vertical partition. Observers adjusted the height of the window until the shape seemed to pass most smoothly through it. (c) Schematic portrayal of curved paths of differing height, h1 and h2.
Figure 2. Mean departures of the center of the adjusted window above a straight path between the centers of the two alternately presented stimuli. Each bar shows the obtained departure for one level of one of the four independent variables. The departure is averaged over all trials except those on which observers gave the lowest confidence rating (i.e.,"1"). The total height of each bar indicates the departure prescribed by kinematic geometry. The height of the hatched portion indicates the obtained departure estimated from the observers' adjustments of the window. The short vertical line at the top of the shaded portion indicates +/- 1 standard error of that obtained mean. In the upper left, the same data are replotted, for the tested separations and angular differences, as a percentage of the heights of the circular paths predicted by kinematic geometry.