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Nicholas Baker, Philip J. Kellman; Constant Curvature Representations of Contour Shape. Journal of Vision 2019;19(10):94. https://doi.org/10.1167/19.10.94.
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© ARVO (1962-2015); The Authors (2016-present)
A fundamental problem in visual perception is explaining how an object’s bounding contour is recoded from subsymbolic inputs (e.g., activation of local contrast-sensitive units) into a symbolic representation of shape. Recoding should be informationally compact and support constancies such as invariance to planar transformations and scaling. One theory posits that this is accomplished in part by higher-order detectors of constant curvature (CC) segments (Garrigan & Kellman, 2011). We conducted psychophysical tests to specify a computational model of how shape might be built up from CC primitives. In Experiment 1, we tested subjects’ ability to detect differences in curvature between adjacent, smoothly connected CC segments. Subjects clicked on a point on an open contour to divide it into two segments and were tested with varied curvature differences to determine the minimum detectable curvature difference threshold. In Experiment 2, we measured the degree of fidelity of CC representations to the initial shape contour, where high fidelity representations include more segments. We briefly displayed a novel contour, then showed a second contour either identical to the first or an abstraction made up of a variable number of CC segments; subjects judged whether they were identical or not. The threshold at which the CC abstraction is indistinguishable from the original display represents the precision of an abstract representation. From these results, we formulated a fully specified computational model of shape representation from CC primitives. Experiment 3 tested the model by comparing subjects’ sensitivity to contour changes that do or do not result in a change in the CC representation based on whether the contour’s curvature changes systematically. Pilot data suggests that changes that result in a representational change are more detectable than changes that do not, even after equating the magnitude of change in each condition.
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