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Hao Wu, James Elder; What is Perceptual Curvature?. Journal of Vision 2016;16(12):812. doi: 10.1167/16.12.812.
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© 2017 Association for Research in Vision and Ophthalmology.
The curvature of a smooth curve in the plane is defined mathematically as the rotation of the tangent vector over an infinitesimal interval of the curve, but what is perceptual curvature? It must be something different, as the eye cannot resolve infinitesimals. Here we seek to understand how humans perceive the local curvature of natural shapes. Five observers viewed a sequence of white outline animal shapes at two viewing distances (75cm and 150cm). Each shape was scaled to have standard deviation of 1.56deg at 75cm. A random point on each shape was highlighted and the observer judged the curvature at this point. To avoid obscuring the contour, the judgement was made by placing a red dot at the perceived centre of curvature. We considered three models of perceptual curvature, each a function of an interval of the contour centred at the point of interest, based on the turning angle formed by the point of interest and the bounding points of the interval, and the sine and tangent of this angle. We first determined the subset of trials on which the signs of objective and perceptual curvature agreed, and then analyzed the correlation between the magnitudes of objective and perceptual curvature for this subset, as a function of the neighbourhood size. We found the turning angle model to be most predictive of perceptual curvature, with an optimal contour neighbourhood of 29arcmin at a viewing distance of 75cm. We expected the optimal neighbourhood at 150cm viewing distance to be either constant in a retinal frame (29arcmin) or in an object frame (14.5arcmin). What we found was intermediate (20arcmin), suggesting influence by both physiological and contextual factors.
Meeting abstract presented at VSS 2016
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