Estimating Curvature of Nondifferentiable Functions and Complex Shape Contours

Abstract

Salvadori and Luccio demonstrated that, for the purpose of psychophysical analysis, the curvature of a point on a continuous single-valued function can be quantified as the inverse ray of the circle osculating the function at the point of interest. While this method is mathematically sound, it does not allow for estimation of curvature in complex shapes containing discontinuities and irregularities such as sharp corners, closed contours, or line intersections—features that commonly occur in normal visual experience. In this paper, a simple modification of this algorithm is presented which overcomes these limitations by using discrete rather than continuous contour sampling, thereby allowing estimation of curvature for a wider variety of shape contours.