Diffusions and confusions in signal and image processing

In this paper we link, through simple examples, between three basic approac hes for signal and image denoising and segmentation: (1) PDE axiomatics, (2 ) energy minimization and (3) adaptive filtering. We show the relation betw een PDE's that are derived from a master energy functional, i.e. the Polyak ov harmonic action, and non-linear filters of robust statistics. This relat ion gives a simple and intuitive way of understanding geometric differentia l filters like the Beltrami flow. The relation between PDE's and filters is mediated through the short time kernel.