Psychophysical judgment of curvatures

In this study we explored psychophysical judgments (magnitude estimation) of the curvature of visual lines. Prior research has lacked a rigorous definition of curvature, but here it was defined as the reverse of the ray of the osculating circle tangent to the curve in the given point. Four different functions were evaluated: hyperbole, sinusoid, parabola, and a cubic function. Using the method of magnitude estimation to judge 20 exemplar curves from each of the families, three respondents made a total of 1440 estimations each. Responses to all four families of curves were fit well by Stevens' power function with an exponent less than 1. One application of this research is the use of such curves as variables in assessing illusions of curvature.