Diffusions and confusions in signal and image processing
In this paper we link, through simple examples, between three basic approaches for signal and image denoising and segmentation: (1) PDE axiomatics, (2) energy minimization and (3) adaptive filtering. We show the relation between PDE's that are derived from a master energy functional, i.e. the Polyakov harmonic action, and non-linear filters of robust statistics. This relation gives a simple and intuitive way of understanding geometric differential filters like the Beltrami flow. The relation between PDE's and filters is mediated through the short time kernel.
anisotropic diffusion selective smoothing geometric filtering