Bilateral filtering and anisotropic diffusion: Towards a unified viewpoint

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 diffusion, bi-lateral 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 diffusion.