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Manish Singh, Jacqueline M. Fulvio; Testing the limits of good continuation: Does human vision extrapolate rate of change of curvature?. Journal of Vision 2005;5(8):470. doi: 10.1167/5.8.470.
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In recent work, we showed that (1) the visual system systematically takes into account the curvature of an inducing contour when extrapolating its shape behind an occluder, and (2) extrapolation shape is characterized by a systematic decay in curvature with increasing distance from the point of occlusion (Singh & Fulvio, PNAS 2005).
The current study investigated whether the visual system also extrapolates rate of change of curvature. We used arcs of Euler spirals as inducing contours — defined by a linear dependence of curvature on arc length: κ(s) = κ + γs. Five values of γ were used: 2 negative (decreasing curvature), zero (constant curvature), and 2 positive (increasing curvature). The inducing contour disappeared behind a half-disk occluder, at the center of its straight edge. Observers adjusted both the position and orientation of a short line probe around the curved portion of the half disk in order to extrapolate the inducing contour's shape. Measurements were taken at 6 distances from the point of occlusion.
For each inducer's extrapolation data, we computed the best-fitting parameters of an Euler-spiral model. The maximum-likelihood estimates for extrapolation γ exhibited no systematic dependence on inducer γ. Moreover, the γ estimates were consistently negative, i.e., extrapolated contours had decreasing curvature irrespective of whether the inducer curvature was increasing or decreasing. These results indicate that the visual system does not extrapolate rate of change of curvature. In addition, estimated extrapolation κ was inversely related to inducer γ: Extrapolation curvature was higher for inducing contours with negative γ (hence higher mean curvature). The results provide further support for a Bayesian model in which extrapolation shape derives from an interaction between (a) a likelihood tendency to continue estimated curvature, and (b) a prior tendency to minimize total curvature (Singh & Fulvio, 2005). Rate of change of curvature does not play a role.
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