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Soft Computing

, Volume 23, Issue 6, pp 1833–1841 | Cite as

Total variation with nonlocal FT-Laplacian for patch-based inpainting

  • Irina PerfilievaEmail author
  • Pavel Vlašánek
Focus

Abstract

We consider the problem of inpainting for relatively large damaged areas where the best-known results are achieved using patches. We stem from the ROF-type model. We propose a new ROF model with nonlocal operators and modify it with the F-transform-based operators. As a result, the minimization is considered over a searching space restricted to a finite set of possible reconstructions; each of them is a result of a patch-based inpainting. The fidelity term in the proposed ROF model is estimated by the norm in a Sobolev-like space, which increases the overall quality of reconstruction.

Keywords

Inpainting Patch Fuzzy F-transform Total variation ROF model 

Notes

Acknowledgements

This work was partially supported by the Project LQ1602 IT4 Innovations excellence in science. The implementation of the F-transform technique is available as a part of the OpenCV framework (Module fuzzy, which is included in opencv_contrib and available at https://github.com/itseez/opencv_contrib).

Compliance with ethical standards

Conflict of interest

Authors Irina Perfilieva and Pavel Vlašánek declare that they have no conflict of interest.

Human and animal rights statement

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Ashikhmin M (2001) Synthesizing natural textures. In: Proceedings of the 2001 symposium on interactive 3D graphics. ACM, pp 217–226Google Scholar
  2. Bertalmio M, Sapiro G, Caselles V, Ballester C (2000) Image inpainting. In: Proceedings of the 27th annual conference on computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., pp 417–424Google Scholar
  3. Bertozzi A, Esedoglu S, Gillette A (2007) Inpainting of binary images using the Cahn–Hilliard equation. IEEE Trans Image Process 16:285–291MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bogischef V, Merget D, Tiefenbacher P, Rigoll G (2015) Subjective and 453 objective evaluation of image inpainting quality. In: IEEE international conference on image processing (ICIP). IEEE, pp 447–451Google Scholar
  5. Chan TF, Shen J (2001) Mathematical models of local non-texture inpaintings. SIAM J Appl Math 62(3):1019–1043MathSciNetzbMATHGoogle Scholar
  6. Chan T, Shen J, Kang S (2002) Euler’s elastica and curvature-based image inpainting. SIAM J Appl Math 63(2):564–592MathSciNetzbMATHGoogle Scholar
  7. Criminisi A, Pérez P, Toyama K (2004) Region filling and object removal by exemplar-based image inpainting. IEEE Trans Image Process 13(9):1200–1212CrossRefGoogle Scholar
  8. Daňková M, Štěpnička M (2006) Fuzzy transform as an additive normal form. Fuzzy Sets Syst 157(8):1024–1035MathSciNetCrossRefzbMATHGoogle Scholar
  9. De Bonet JS (1997) Multiresolution sampling procedure for analysis and synthesis of texture images. In: Proceedings of the 24th annual conference on computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., pp 361–368Google Scholar
  10. Di Martino F, Loia V, Perfilieva I, Sessa S (2008) An image coding/decoding method based on direct and inverse fuzzy transforms. Int J Approx Reason 48(1):110–131CrossRefzbMATHGoogle Scholar
  11. Efros AA, Freeman WT (2001) Image quilting for texture synthesis and transfer. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques. ACM, pp 341–346Google Scholar
  12. Efros AA, Leung TK (1999) Texture synthesis by non-parametric sampling. In: The proceedings of the seventh IEEE international conference on computer vision, vol 2. IEEE, pp 1033–1038Google Scholar
  13. Esedoglu S, Shen J (2002) Digital inpainting based on the Mumford–Shah–Euler image model. Eur J Appl Math 13:353–370MathSciNetCrossRefzbMATHGoogle Scholar
  14. Gilboa G, Osher S (2008) Nonlocal operators with applications to image processing. Multisc Model Simul 7(3):1005–1028MathSciNetCrossRefzbMATHGoogle Scholar
  15. Heeger DJ, Bergen JR (1995) Pyramid-based texture analysis/synthesis. In: Proceedings of the 22nd annual conference on computer graphics and interactive techniques. ACM, pp 229–238Google Scholar
  16. Perfilieva I (2006) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157(8):993–1023MathSciNetCrossRefzbMATHGoogle Scholar
  17. Perfilieva I, Vlašánek P (2014) Image reconstruction by means of F-transform. Knowl Based Syst 70:55–63CrossRefGoogle Scholar
  18. Perfilieva I, Vlašánek P, Wrublová M (2012) Fuzzy transform for image reconstruction. In: Kahraman C, Kerre EE, Bozbura FT (eds) Uncertainty modeling in knowledge engineering and decision making. World Scientific, SingaporeGoogle Scholar
  19. Perfilieva I, Holčapek M, Kreinovich V (2016) A new reconstruction from the F-transform components. Fuzzy Sets Syst 288:3–25MathSciNetCrossRefzbMATHGoogle Scholar
  20. Perfilieva I, Danková M (2009) Towards F-transform of a higher degree. In: IFSA/EUSFLAT conference. Citeseer, pp 585–588Google Scholar
  21. Rudin L, Osher S, Fatemi E (1992) Non linear total variation based noise removal algorithms. Physica 60:259–268MathSciNetzbMATHGoogle Scholar
  22. Stefanini L (2011) F-transform with parametric generalized fuzzy partitions. Fuzzy Sets Syst 180(1):98–120MathSciNetCrossRefzbMATHGoogle Scholar
  23. Tiefenbacher P, Bogischef V, Merget D, Rigoll G (2015) Subjective and objective evaluation of image inpainting quality. In: IEEE international conference on image processing (ICIP). IEEE, pp 447–451Google Scholar
  24. Vajgl M, Perfilieva I, Hod’áková P (2012) Advanced F-transform-based image fusion. Adv Fuzzy Syst 2012:4MathSciNetGoogle Scholar
  25. Vlašánek P, Perfilieva I (2013) Image reconstruction with usage of the F-transform. In: International joint conference CISIS’12-ICEUTE’12-SOCO’12 special sessions. Springer, Berlin, pp 507–514Google Scholar
  26. Vlašánek P, Perfilieva I (2013) Influence of various types of basic functions on image reconstruction using F-transform. In: European society for fuzzy logic and technology. Atlantis Press, pp 497–502Google Scholar
  27. Vlasanek P, Perfilieva I (2014) Interpolation techniques versus F-transform in application to image reconstruction. In: Fuzzy systems (FUZZ-IEEE), 2014 IEEE international conference. IEEE, pp 533–539Google Scholar
  28. Vlašánek P, Perfilieva I (2015) F-transform and discrete convolution. In: European society for fuzzy logic and technology. Atlantis PressGoogle Scholar
  29. You Y-L, Kaveh M (2000) Fourth-order partial differential equations for noise removal. IEEE Trans Image Process 9:1723–1730MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Ostrava, Centre of Excellence IT4InnovationsInstitute for Research and Applications of Fuzzy ModelingOstravaCzech Republic

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