Size invariance in curve tracing

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Abstract
Subjects decided whether two dots were on the same curve or on different curves in patterns consisting of two curves and two dots in displays that had an exposure duration of 200 msec or that remained in view until the subjects' response. The overall size of the patterns was varied by a factor of two. Furthermore, across experiments, we manipulated the predictability of the size of the pattern on a particular trial. On half of the trials, the two dots were on the same curve; across these trials, the distance between the dots, along the curve, was manipulated systematically while the Euclidean distance between the dots was held constant. On the other half of the trials, the two dots were on different curves. The time to respond same increased monotonically as curve distance between the dots increased, suggesting that subjects mentally traced the curve in order to perform the task. The absolute size of the pattern had little or no effect on the response times, indicating that it was curve distance relative to the overall pattern size, rather than absolute distance, that controlled response times. Furthermore, expectancies about pattern size had essentially no effect on performance. Taken together, the results suggest that the rate of tracing is determined by various stimulus properties that covary with the overall size of the pattern on which tracing takes place, such as the distance between the traced curve and nearby distractor curves, or the curvature of the traced curve.