Abstract
How abstract shape is perceived and represented poses crucial unsolved problems in human perception and cognition. Recent findings suggest that the visual system may encode contours as sets of connected constant curvature segments. Here we describe a model for how the visual system might recode a set of boundary points into a constant curvature representation. The model includes two free parameters that relate to the degree to which the visual system encodes shapes with high fidelity vs. the importance of simplicity in shape representations. We conducted two experiments to estimate these parameters empirically. Experiment 1 tested the limits of observers’ ability to discriminate a contour made up of two constant curvature segments from one made up of a single constant curvature segment. Experiment 2 tested observers’ ability to discriminate contours generated from cubic splines (which, mathematically, have no constant curvature segments) from constant curvature approximations of the contours, generated at various levels of precision. Results indicated a clear transition point at which discrimination becomes possible. The results were used to fix the two parameters in our model. In Experiment 3, we tested whether outputs from our parameterized model were predictive of perceptual performance in a shape recognition task. We generated shape pairs that had matched physical similarity but differed in representational similarity (i.e., the number of segments needed to describe the shapes) as assessed by our model. We found that pairs of shapes that were more representationally dissimilar were also easier to discriminate in a forced choice, same/different task. The results of these studies provide evidence for constant curvature shape representation in human visual perception and provide a testable model for how abstract shape descriptions might be encoded.
Highlights
Shape—of contours and objects, arrangements, and environments—is fundamental to human perception, cognition, and action
Performance improved rapidly with larger curvature ratios up to a ratio of 1.3:1, after which it flattened out and improved only marginally as the ratio got larger. This suggests that the critical point at which the visual system encodes two contours of similar curvature as different occurs somewhere between a ratio of 1.03:1 and 1.3:1
Our results showed a systematic relationship between limits in resolving differences in contour segments and curvature ratios
Summary
Shape—of contours and objects, arrangements, and environments—is fundamental to human perception, cognition, and action. An object’s shape determines its functions and often its name. A toy car or plastic horse lacks most of the crucial properties of real horses and cars, yet the categories of “car” or “horse” are evoked by these toys’ shapes. 1R01CA236791-01 from the NIH-NCI National Cancer Institute to PJK The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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