A shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented. The method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve. Three different ways of computing the representation are described. They result in three different representations: the curvature scale space image, the renormalized curvature scale space image, and the resampled curvature scale space image. The process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve. Several evolution and arc length evolution properties of planar curves are discussed.
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