ON INVARIANT CURVE EVOLUTION AND IMAGE-ANALYSIS

This paper deals with the mathematical theory of invariant curve evolu tion. We present a high-level procedure for the formulation of geometr ic heat flows which are invariant with respect to a given Lie group. T his approach is based on the classical theory of differential invarian ts. The affine group is then analyzed in detail. Indeed, we give a rat her complete description of the properties of the affine geometric hea t equation. We moreover extend the results of [38] from the convex to the nonconvex case. The paper concludes with a summary of recent appli cations of curve evolution theory to image analysis.