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A Nonlocal Image Inpainting Problem Using the Linear Allen–Cahn Equation

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

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Abstract

Digital image inpainting problem deal with the interpolation of the damaged or missing regions of the image. In this paper we study the effect of the nonlocal image inpainting with respect to the local models and aim to demonstrate that linear fractional equations produce natural images, comparable to the ones obtained by the nonlinear equations. Simulations are obtained by the implementation of the finite difference method.

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Acknowledgments

The research is supported in part by the COST action 15225: Fractional-order systems-analysis, synthesis and their importance for future design. The research is also supported by the Croatian Science Foundation’s funding of the project “Microlocal defect tools in partial differential equations” (MiTPDE) with grant number 2449.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia

    Antun Lovro Brkić

  2. Department of Physics, Faculty of Science, University of Zagreb, Zagreb, Croatia

    Andrej Novak

Authors
  1. Antun Lovro Brkić
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  2. Andrej Novak
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Corresponding author

Correspondence to Andrej Novak .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Brkić, A.L., Novak, A. (2020). A Nonlocal Image Inpainting Problem Using the Linear Allen–Cahn Equation. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_17

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