Complex diffusion processes for image filtering

Guy Gilboa, Yehoshua Y. Zeevi, Nir A. Sochen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

46 Scopus citations


A framework that naturally unifies smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the diffusion equation with the simplified Schrödinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex diffusion shows that the generalized diffusion has properties of both forward and inverse diffusion. An important observation, supported theoretically and numerically, is that the imaginary part can be regarded as an edge detector (smoothed second derivative), after rescaling by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, a nonlinear complex process for ramp preserving denoising is developed.

Original languageEnglish
Title of host publicationScale-Space and Morphology in Computer Vision - 3rd International Conference, Scale-Space 2001, Proceedings
EditorsMichael Kerckhove
PublisherSpringer Verlag
Number of pages9
ISBN (Electronic)9783540423171
StatePublished - 2001
Event3rd International Conference on Scale-Space and Morphology in Computer Vision, Scale-Space 2001 - Vancouver, Canada
Duration: 7 Jul 20018 Jul 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Conference on Scale-Space and Morphology in Computer Vision, Scale-Space 2001


  • Complex diffusion
  • Image denoising
  • Image enhancement
  • Image filtering
  • Nonlinear diffusion
  • Scale-space


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