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Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation

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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

In this paper, we investigate a new Gradient-Vector-Flow (GVF)([38])-inspired static external force field for active contour models, deriving from the edge map of a given image and allowing to increase the capture range. Contrary to prior related works, we reduce the number of unknowns to a single one v by assuming that the expected vector field is the gradient field of a scalar function. The model is phrased in terms of a functional minimization problem comprising a data fidelity term and a regularizer based on the super norm of Dv. The minimization is achieved by solving a second order singular degenerate parabolic equation. A comparison principle as well as the existence/uniqueness of a viscosity solution together with regularity results are established. Experimental results for image segmentation with details of the algorithm are also presented.

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Author information

Authors and Affiliations

  1. Laboratoire Jean-Alexandre Dieudonné, UMR 6621, Université de Nice Sophia Antipolis – CNRS, Faculté des Sciences Parc Valrose, 06108, Nice Cedex 02, France

    Laurence Guillot

  2. Institut des Sciences Appliquées de Rennes, IRMAR, UMR CNRS 6625, 20, Avenue des Buttes de Coësmes, CS 14315, 35043, Rennes Cedex, France

    Carole Le Guyader

Authors
  1. Laurence Guillot
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  2. Carole Le Guyader
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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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Guillot, L., Le Guyader, C. (2009). Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation. 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_8

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

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