Representing Three Dimensional Curves with Critical Points.

This paper proposes a representation of a three dimensional curve by points of extremal curvature, or critical points, and describes a method of forming such a representation from discrete data. A continuous parametric curve is constructed by approximating each component with a cubic spline, and the critical points are identified by finding local maxima of curvature. The curve at each critical point is characterized by the curvature, torsion, position, tangent and normal, that are computed analytically from the parametric representation. The method is illustrated with an example of its application to discrete contours extracted from an image. The proposed representation will be used to extend existing two dimensional methods of shape recognition to three dimensions.