A THEORY OF MULTISCALE, CURVATURE-BASED SHAPE REPRESENTATION FOR PLANAR CURVES

This paper presents a multiscale, curvature-based shape representation technique for planar curves that satisfies several criteria that are considered necessary for general-purpose shape representation methods. As a result, the representation is suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation. The method rests on the concept of 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 in this paper. These three methods 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 described in this paper. Some of these results show that evolution and arc length evolution do not change the physical interpretation of planar curves as object boundaries, and some characterize possible behaviors of planar curves during evolution and arc length evolution. Others impose constraints on the location of a planar curve as it evolves. Together, these results provide a sound theoretical foundation for the representation methods introduced in this paper.