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Journal of Mathematical Sciences

, Volume 207, Issue 2, pp 142–146 | Cite as

On Some Perturbations of the Total Variation Image Inpainting Method. Part III: Minimization Among Sets with Finite Perimeter

  • M. Bildhauer
  • M. Fuchs
Article

We propose a model for the restoration of images consisting only of completely black or completely white regions with the use of Caccioppoli sets.

Keywords

Radon Radon Measure Volume Constraint White Region Bound Lipschitz Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Arias, V. Casseles, and G. Sapiro, A Variational Framework for Non-Local Image Inpainting, IMA Preprint Series No. 2265 (2009).Google Scholar
  2. 2.
    M. Burger, L. He, and C.-B. Schönlieb, “Cahn-Hilliard inpainting and a generalization for grayvalue images,” SIAM J. Imaging Sci. 2, No. 4, 1129–1167 (2009).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    M. Bertalmio, V. Caselles, S. Masnou, and G. Sapiro, Inpainting. www.math.univlyon1.fr/masnou/fichiers/publications/survey.pdf
  4. 4.
    T. F. Chan, S. H. Kang, and J. Shen, “Euler’s elastica and curvature based inpaintings,” SIAM J. Appl. Math. 63, No. 2, 564–592 (2002).MATHMathSciNetGoogle Scholar
  5. 5.
    T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, No. 3, 1019–1043 (2001/02).Google Scholar
  6. 6.
    K. Papafitsoros, B. Sengul, and C.-B. Schönlieb, Combined First and Second Order Total Variation Impainting Using Split Bregman, IPOL Preprint (2012).Google Scholar
  7. 7.
    J. Shen, Inpainting and the fundamental problem of image processing, SIAM News 36, No. 5, 1–4 (2003).Google Scholar
  8. 8.
    M. Bildhauer and M. Fuchs, “On some perturbations of the total variation image inpainting method. Part I: Regularity theory,” J. Math. Sci., New York 202, No. 2, 154–169 (2014).CrossRefMATHGoogle Scholar
  9. 9.
    M. Bildhauer and M. Fuchs, “On some perturbations of the total variation image inpainting method. Part II: Relaxation and dual variational formulation,” J. Math. Sci., New York Google Scholar
  10. 10.
    L. Ambrosio, N. Fusco, and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford (2000).MATHGoogle Scholar
  11. 11.
    E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel (1984).CrossRefMATHGoogle Scholar
  12. 12.
    I. Tamanini, “Regularity results for almost minimal oriented hypersurfaces,” Quaderni del Departimento di Matematica del Univ. di Lecce. Q1. 1984.Google Scholar
  13. 13.
    M. Giaquinta, G. Modica, and J. Souček, “Functionals with linear growth in the calculus of variations. I,” Commentat. Math. Univ. Carol. 20, No. 1, 143–156 (1979).MATHGoogle Scholar
  14. 14.
    M. Giaquinta, G. Modica, and J. Souček, “Functionals with linear growth in the calculus of variations. II,” Commentat. Math. Univ. Carol. 20, No. 1, 157–172 (1979).MATHGoogle Scholar
  15. 15.
    Qinglan Xia, “Regularity of minimizers of quasi perimeters with a volume constraint,” Interfaces Free Bound. 7, No. 3, 339–352 (2005).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Universität des Saarlandes, Fachbereich 6.1 MathematikSaarbrückenGermany

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