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Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

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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.

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Authors and Affiliations

  1. Institute for Mathematics, University of Graz, Heinrichstr. 36, A-8010, Graz, Austria

    Alfio Borzi

  2. Department of Computer Science, University of Innsbruck, Technikerstr. 21a/2, A-6020, Innsbruck, Austria

    Harald Grossauer & Otmar Scherzer

Authors
  1. Alfio Borzi
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  2. Harald Grossauer
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  3. Otmar Scherzer
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First online version published in June, 2005

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Borzi, A., Grossauer, H. & Scherzer, O. Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation. Int J Comput Vision 64, 203–219 (2005). https://doi.org/10.1007/s11263-005-1844-9

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  • DOI: https://doi.org/10.1007/s11263-005-1844-9

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