Curve encoding and the detection of discontinuities

Two important features of the perception of plane curves are discontinuities in the curve and regions of high curvature. A method is presented, suitable for an open or closed curve, that given an ordered sequence of points will detect discontinuities in the perceived curve. The method is based on a local iterative process that attempts to obtain a set of cubic splines. The attempt fails when a sharp change occurs and this signals a discontinuity. Further iterations produce a smooth representation between the discontinuities. The given points may be irregularly spaced and no regular grid is superimposed on the data. The results obtained are orientation dependent and this appears to mimic our perception of curves.