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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.