Bilateral Filtering and Anisotropic Diffusion: Towards a Unified Viewpoint

bilateral filtering, anisotropic diffusion, adaptive smoothing, denoising 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, 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, we also show that bilateral filtering can be applied to denoise and coherence-enhance degraded images with approaches similar to anisotropic diffusion.