Convergence Properties of Curvature Scale Space Representations

Curvature Scale Space (CSS) representations have been shown to be very useful for recognition of noisy curves of arbitrary shapes at unknown orientations and scales [10,14]. This paper contains a number of important results on the convergence properties of CSS representations and on the evolution and arc length evolution of planar curves [6,12]. The processes which convolve arc length parametric representations of planar curves with Gaussian functions are referred to as the evolution or arc length evolution of those curves. It has been shown that every closed planar curve will eventually become simple and convex during evolution and arc length evolution and will remain in that state. This result is important since it demonstrates that the computation of a CSS image always has a clearly defined termination point.