Edge-preserving smoothing

Edge-preserving smoothing or edge-preserving filtering is an technique that smooths away noise or textures while retaining sharp edges. Examples are the median, bilateral, guided, anisotropic diffusion, and Kuwahara filters. In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g., by high gradient magnitudes. For example, the motivation for anisotropic diffusion (also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is a single time slice of the solution to the heat equation, that has the original image as its initial conditions. Anisotropic diffusion includes a variable conductance term that is determined using the differential structure of the image, such that the heat does not propagate over the edges of the image. The edge-preserving filters can conveniently be formulated in a general context of graph-based signal processing, where the graph adjacency matrix is first determined using the differential structure of the image, then the graph Laplacian is formulated (analogous to the anisotropic diffusion operator), and finally the approximate low-pass filter is constructed to amplify the eigenvectors of the graph Laplacian corresponding to its smallest eigenvalues. Since the edges only implicitly appear in constructing the edge-preserving filters, a typical filter uses some parameters, that can be tuned, to balance between aggressive averaging and edge preservation. A common default choice for the parameters of the filter is aimed for natural images and results in strong denoising at the cost of some smoothing of the edges. Requirements of the strict edge preservation commonly limit the smoothing power of the filter, such that a single application of the filter still results in unacceptably large noise away from the edges.