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Image Denoising by Harmonic Mean Curvature Flow

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

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Abstract

We propose a noise-removal method for vector-valued images by considering the negative gradient flow (the biharmonic map heat flow) of the intrinsic Bi-energy on Riemannian manifold of non-positive curvature. This method represents a natural generalization of both harmonic maps and minimal immersions. It is derived by finding the critical point of the variational problem associated to the integral of the squared norm of the tension-field (Bi-harmonic map) or of the mean curvature vector field (Bi-minimal immersion). In local coordinates, this method yields a fourth order non-linear system of PDE’s that we, numerically, solve by an explicit finite difference method. Experiments on real color-image endowed with the Helmholtz and Stiles metrics show that the proposed method is effective, accurate and highly robust.

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Authors and Affiliations

  1. Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis ENIT-LAMSIN, B.P. 37, 1002, Tunis Belvédère, Tunisia

    Mourad Zéraï

Authors
  1. Mourad Zéraï
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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Zéraï, M. (2009). Image Denoising by Harmonic Mean Curvature Flow. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_47

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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