International Journal of Computer Vision

, Volume 64, Issue 2–3, pp 203–219 | Cite as

Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

  • Alfio Borzi
  • Harald Grossauer
  • Otmar Scherzer
Article

Abstract

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed.

Keywords

Ginzburg-Landau equation inpainting diffusion filtering non-linear partial differential equations variational problems 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Alfio Borzi
    • 1
  • Harald Grossauer
    • 2
  • Otmar Scherzer
    • 2
  1. 1.Institute for MathematicsUniversity of GrazGrazAustria
  2. 2.Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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