174
Views
3
CrossRef citations to date
0
Altmetric
Original Article

Image inpainting algorithm based on partial differential equation technique

&
Pages 292-300 | Accepted 17 Nov 2011, Published online: 12 Nov 2013

REFERENCES

  • Bertalmio M, Sapiro G, Ballester C, Caselles V. In Proceedings of SIGGRAPH 2000: Computer Graphics Annual Conference Series (Ed. K. Akeley), 2000, pp. 417–424 (ACM Press/ACM SIGGRAPH/Addison Wesley Longman, New York).
  • Ballester C, Bertalmio M, Caselles V, Sapiro G, Verdera J. Filling in by joint interpolation of vector fields and gray levels. IEEE Trans. Image Process., 2001, 10, 1200–1211.
  • Bertalmio M, Bertozzi AL, Sapiro G. Navier–Stokes, fluid dynamics and image and video inpainting. IEEE Comput. Vis. Patt. Recogn., 2001, 1, 355–362.
  • Tai XC, Osher S, Holm R. In Image Processing Based on Partial Differential Equations, 2006, pp. 3–33 (Springer, Heidelberg).
  • Chan TF, Shen J. Mathematical models for local non-texture inpaintings. SIAM J. Appl. Math., 2002, 62, 1019–1043.
  • Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D, 1992, 60, 259–268.
  • Chan TF, Kang SH, Shen J. Euler: elastica and curvature-based inpainting. SIAM J. Appl. Math., 2002, 63, 564–592.
  • Chan TF, Shen J, Vese L. Variational PDE models in image processing. Not. Am. Math. Soc., 2003, 50, 14–26.
  • Chan TF, Shen J. Non-texture inpainting by curvature-driven diffusions (CDD). J. Vis. Commun. Image Represent., 2001, 12, (4), 436–449.
  • Esedoglu S, Shen J. Digital inpainting based on the Mumford–Shah–Euler image model. Eur. J. Appl. Math., 2002, 13, 353–370,.
  • Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math., 1989, 42, 577–685.
  • Grossauer H, Scherzer O. Using the complex Ginzburg–Landau equation for digital inpainting in 2D and 3D. Lect. Notes Comput. Sci., 2003, 2695, 225–236.
  • Bornemann F, März T. Fast image inpainting based on coherence transport. J. Math. Imaging Vis., 2007, 28, 259–278.
  • Bertalmio M, Vese L, Sapiro G, Osher S. Simultaneous texture and structure image inpainting. IEEE Trans. Image Process., 2003, 12, 882–889.
  • Elad M, StarckQuerreDonoho JPD. Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA). Appl. Comput. Harmon. Anal., 2005, 19, 340–358.
  • Criminisi A, Perez P, Toyama K. Region filling and object removal by exemplar-based image inpainting. IEEE Trans. Image Process., 2004, 13, 1200–1212.
  • Wexler Y, Shechtman E, Irani M. Space–time video completion. IEEE Trans. Pattern Anal. Mach. Intell., 2007, 29, 1463–1476.
  • Fadili M, Starck J, Murtagh F. Inpainting and zooming using sparse representations. Comput. J., 2009, 52, 64–79.
  • Komodakis N, Tziritas G. Image completion using efficient belief propagation via priority scheduling and dynamic pruning. IEEE Trans. Image Process., 2007, 16, 2649–2661.
  • Aujol J, Ladjal S, Masnou S. Exemplar-based inpainting from a variational point of view. SIAM J. Math. Anal., 2010, 42, 1246–1285.
  • Costanzino N. Structure Inpainting via Variational Methods [online], 2002 (Providence, RI, LEMS). Available at: <http://www.lems.brown.edu/˜nc/> Accessed 6 October 2011.
  • Aubert G, Kornprobst P. Mathematical Problems in Image Processing, 2002 (Springer-Verlag, Berlin).
  • Wang LH, Zhou SL. Existence and uniqueness of weak solutions for a nonlinear parabolic equation related to image analysis. J. Part. Differ. Equ., 2006, 19, 97–112.
  • Huang H, Jia C, Huan Z. On weak solutions for an image denoising-deblurring model. Appl. Math. J. Chin. Univ., 2009, 24, 269–281.
  • Feng Z, Yin Z. On the weak solutions for a class of nonlinear parabolic equations related to image analysis. Nonlinear Anal.: Theory Methods Appl., 2009, 71, 2506–2517.
  • Feng Z, Yin Z. Weak solutions for a class of generalized nonlinear parabolic equations related to image analysis. J. Math. Anal. Appl., 2010, 368, 235–246.
  • Tai X. Global extrapolation with a parallel splitting method. Numer. Algorithm, 1991, 3, 527–440.
  • Weickert J, Romeny ter haarBM, Viergever MA. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans. Image Process., 1998, 7, 398–410.
  • Kuhne G, Weickert J, Viergever M, Effelsberg W. Fast implicit activ coutour models. Lect. Notes Comput. Sci., 2002, 2449, 133–140.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.