Diffusions and confusions in signal and image processing

N. Sochen*, R. Kimmel, A. M. Bruckstein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


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.

Original languageEnglish
Pages (from-to)195-209
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Issue number3
StatePublished - May 2001


  • Anisotropic diffusion
  • Geometric filtering
  • Selective smoothing


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