Anisotropic diffusion

Anisotropic diffusion, also called Perona-Malik diffusion, is a technique in image processing and computer vision that reduces image noise without removing significant parts of the image content, typically edges, lines or other details important for interpretation. It generalises the diffusion process that creates a scale space, in which an image is convolved with ever wider Gaussian filters. Ordinary Gaussian blurring is linear and space-invariant; anisotropic diffusion instead combines the original image with a filter that depends on the local content of the image, which makes it a non-linear and space-variant transformation. In the original formulation by Perona and Malik in 1987 the locally adapted filter is isotropic but approximates an impulse close to edges so that they are preserved. More general formulations let the filter be truly anisotropic along linear structures, giving shape-adapted smoothing or coherence enhancing diffusion. In practice it is implemented by approximating a generalised diffusion equation whose diffusion coefficient varies with image position.