Bilateral Filtering and Anisotropic Difusion: Towards a Unified Viewpoint

Abstract

Bilateral filtering has recently been proposed as a noniterative alternative to anisotropic diffusion. In both these approaches, images are smoothed while edges are preserved. Unlike anisotropic difusion, bilateral filtering does not involve the solution of partial differential equations and can be implemented in a single iteration. Despite the difference in implementation, both methods are designed to prevent averaging across edges while smoothing an image. Their similarity suggests they can somehow be linked. Using a generalized representation for the intensity, we show that both can be related to adaptive smoothing. As a consequence, bilateral filtering can be applied to denoise and coherence-enhance degraded images with approaches similar to anisotropic difusion.