Abstract
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.
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Sochen, N., Kimmel, R. & Bruckstein, A. Diffusions and Confusions in Signal and Image Processing. Journal of Mathematical Imaging and Vision 14, 195–209 (2001). https://doi.org/10.1023/A:1011277827470
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DOI: https://doi.org/10.1023/A:1011277827470