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InThe two experiments in this study suggest that fast internal tracing of curves is employed by the visual system in the perception of certain shape properties and spatial relations. The experimental task in the first experiment was to determine, as rapidly as possible, whether two Xs lay on the same curve or on different curves in a visual display. Mean response time for "same" responses increased monotonically with increasing distance along the curve between the Xs. The task in the second experiment was to decide either that a curve joining two Xs was unbroken or that the curve had a gap. Decision times again increased as the length of the curve joining the Xs was increased. The results of both experiments suggest that people can trace curves in a visual display internally at high speed (the average rate of tracing was about 40°of visual angle per second). Curve tracing may be an important visual process used to integrate information from different parts of a visual display.The perception of shape properties and of spatial relations plays an important role in the visual recognition of objects, in visually guided manipulation, and in navigation in the environment. It is not surprising, therefore, that humans can quickly and effortlessly perceive a large variety of spatial relations among items in a visual scene. Even a simple display such as Figure 1 contains a large number of spatial relations that can be perceived immediately when required. For example, (1) Is there a closed curve in the display? (2) How many dots are there? (3) Is there a dot inside the closed curve? (4) Is there an X lying on a curve? (5) Are there two Xs lying on a common curve? Human observers can answer such questions accurately and immediately by merely looking at the figure.For an observer to decide that a particular spatial relation exists between two elements in a display, he or she must somehow consider the elements in relation to each other and compute the relation between them. The human visual system can establish a variety of shape propertiesWe thank StephenKosslynfor extensiveand useful commentson an earlierdraftof the manuscript, and MerrillHiscockand Thomas Wishart for providing equipmentused in the experiments reportedin this paper. We also gratefully acknowledge the support of the Center for Cognitive Scienceat the Massachusetts Institute of Technology. The research was supportedby University of Saskatchewan internal research grants 3-773-936 and l-400-012-790-R, and NSERC Grant A2579 awarded to Pierre Jolicoeur. Requests for reprints shouldbe sent to P. Jolicoeur. Department of Psychology . University of Waterloo,Waterloo,Ontario. Canada N2L 3GI. and spatial relations with intriguing proficiency. The perception of spatial properties and relations that are complex from a computational standpoint nevertheless often appear to us as immediate and effortless. When we perceive such relations, we usually do not know how we arrive at our decision-we simply see the relation. Therefore, systematic empirical study is required to un...
Subjects decided whether 2 dots were on the same curve or 2 different curves, and the curvature of the curves or the proximity of other (distractor) curves to the target curve was varied. Response time increased as the arc length of the curve connecting the 2 dots increased, suggesting that the curve was traced to perform the task. Tracing rate was faster for low- than high-curvature contours and was increasingly slower as distractor contours were increasingly proximal to the traced curve. Proximity results were predicted by a model in which response time depends on the ratio of the distance between the dots and the distance between adjacent lines. Curve tracing operations used to integrate information along contours are sensitive to several properties of the contours. The implications of the sensitivity of tracing operations to these curve properties are discussed.
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