Scale-Based Descriptions of Planar Curves

The problem posed in this paper is the description of planar curves at varying levels of detail. Five necessary conditiong are imposed on any candidate solution method. Two candidate methods are rejected. A new method that uses well-known Gaussian smoothing techniques but applies them in a path-based coordinate system is described. By smoothing with respect to a path-length parameter the difficulties of other methods are overcome. An example shows how the method extracts the major features of a curve, at varying levels of detail, based on segmentation at zeroes of the curvature, $\kappa$. The method satisfies the five necessary criteria.