An invariant for wheel-generated motions and the logic of its determination

Observers appear to perceive the paths of abstract centers of point-light configurations in making judgments about movement. For configurations on rolling wheels a metric was derived that described the relative vertical motion of this point. It was hypothesized that the smaller the metric the more the stimulus should appear to move in a wheel-like manner with linear translation. In two experiments observers viewed pairs of stimuli and were asked to select either the event that appeared most wheel-like or the one that hopped the most. Viewers consistently selected the stimulus with the smaller metric as being more wheel-like, with a frequency that increased with the difference between metrics. The inverse of this pattern was found for those observers requested to select the stimulus that hopped most. In a second set of two experiments observers drew the translational paths of these stimuli. Their drawings corresponded to the motion paths of configural centroids. Together, these results strongly suggest that observers perceive the translational component of the motion of the configurations as the path described by their centroids, or geometric centers. We propose that this description of the stimulus event is determined by the logical ordering of information extraction provided by the perceptural system, and discuss this logic and cases where it seems evident.