Image enhancement and denoising by complex diffusion processes

Guy Gilboa*, Nir Sochen, Yehoshua Y. Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.

Original languageEnglish
Pages (from-to)1020-1036
Number of pages17
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume26
Issue number8
DOIs
StatePublished - Aug 2004

Funding

FundersFunder number
BME Imaging Group of Columbia University
Fund for the Promotion of Research
Israel Academy of Science
Israeli Ministry of ScienceHPRN-CT-2002-00285
ONR-MURIN000M-01-1-0625
Ollendorf Minerva Center
Columbia University
European Commission
Tel Aviv University
Technion-Israel Institute of Technology

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