The evolution of mean curvature in image filtering

Abstract

A new formulation for inhomogeneous image diffusion is presented in which the image is regarded as a surface in 3-space. The evolution of this surface under diffusion is analyzed by classical methods of differential geometry. A nonlinear filtering theory is introduced in which only the divergence of the direction of the surface gradient is averaged. This averaging preserves edges and lines, as their direction is non-divergent, while noise is averaged since it does not have non-divergent consistency. Our approach achieves this objective by evolving the surface at a speed proportional to mean curvature leading to the minimization of the surface area and the imposition of regularity everywhere. Furthermore, we introduce a new filter that renders corners, as well as edges, invariant to the diffusion process. Experiments demonstrating the adequacy of this new theory are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>