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Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods

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Abstract

Let I :Ω→ℜ be a given bounded image function, where Ω is an open and bounded domain which belongs to ℜn. Let us consider n=2 for the purpose of illustration. Also, let S={xi}i∈Ω be a finite set of given points. We would like to find a contour Γ⊂Ω, such that Γ is an object boundary interpolating the points from S. We combine the ideas of the geodesic active contour (cf. Caselles et al. [7,8]) and of interpolation of points (cf. Zhao et al. [40]) in a level set approach developed by Osher and Sethian [33]. We present modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de l’INSA, INSA de Rouen, Place Emile Blondel, BP 08, 76 131, Mont-Saint-Aignan Cedex, France

    Christian Gout & Carole Le Guyader

  2. Department of Mathematics, University of California, Los Angeles, 405, Hilgard Avenue, Los Angeles, CA, 90095-1555, USA

    Luminita Vese

Authors
  1. Christian Gout
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  2. Carole Le Guyader
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  3. Luminita Vese
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Correspondence to Christian Gout.

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49L25, 74G65, 68U10

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Gout, C., Le Guyader, C. & Vese, L. Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods. Numer Algor 39, 155–173 (2005). https://doi.org/10.1007/s11075-004-3627-8

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  • DOI: https://doi.org/10.1007/s11075-004-3627-8

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