A Discrete Cross-Diffusion Model for Image Restoration

  • Adérito Araújo
  • Silvia Barbeiro
  • Eduardo Cuesta
  • Ángel Durán
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


In this paper a fully discrete cross-diffusion model for image restoration is introduced. The image is represented by a two-component vector field, and the restoration process is governed by a nonlinear cross-diffusion difference system. We explore numerically the potentialities of using the nonlinear cross-diffusion approach as an image filter, in particular as a preprocessing step for image segmentation.



This work was supported by Spanish Ministerio de Economía y Competitividad under the Research Grant MTM2014-54710-P. A. Araújo and S. Barbeiro were also supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Adérito Araújo
    • 1
  • Silvia Barbeiro
    • 1
  • Eduardo Cuesta
    • 2
  • Ángel Durán
    • 2
  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Applied MathematicsUniversity of ValladolidValladolidSpain

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