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MATLAB/Python Codes for the Image Inpainting Problem

This is a detailed MATLAB/Python implementation of classic inpainting methods.

All the scripts provided are used in the book "Partial Differential Equation Methods for Image Inpainting" by Carola-Bibiane Schönlieb, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2015:

Please use the following entry to cite this code:

 @software{ParSch2016,
  author       = {Simone Parisotto and
                  Carola-Bibiane Sch\"{o}nlieb},
  title        = {{MATLAB/Python Codes for the Image Inpainting 
                   Problem}},
  month        = dec,
  year         = 2020,
  publisher    = {Zenodo},
  version      = {3.0.0},
  doi          = {10.5281/zenodo.4315173},
  url          = {https://doi.org/10.5281/zenodo.4315173}
}

1) Absolute Minimizing Lipschitz Extension Inpainting (AMLE)

Used to reproduce Figure 4.10 in the book.

Bibliography:

• Caselles, V., Morel, J. M., & Sbert, C. (1998). An axiomatic approach to image interpolation. Image Processing, IEEE Transactions on, 7(3), 376-386.
• Almansa, A. (2002). Echantillonnage, interpolation et detection: applications en imagerie satellitaire (Doctoral dissertation, Cachan, Ecole normale superieure).

2) Harmonic Inpainting

Used to reproduce Figure 2.2 in the book. This program solves harmonic inpainting via a discrete heat flow.

Bibliography:

• Shen, J., & Chan, T. F. (2002). Mathematical models for local nontexture inpaintings. SIAM Journal on Applied Mathematics, 62(3), 1019-1043.

3) Mumford-Shah Inpainting with Ambrosio-Tortorelli approximation

Note: Used to reproduce Figure 7.3 in the book.

Bibliography:

• Esedoglu, S., & Shen, J. (2002). Digital inpainting based on the Mumford-Shah-Euler image model. European Journal of Applied Mathematics, 13(04), 353-370.

4) Cahn-Hilliard Inpainting

Used to reproduce Figure 5.9 in the book.

Bibliography:

• Bertozzi, A., Esedoglu, S. & Gillette, A. (2007). Inpainting of binary images using the Cahn-Hilliard equation, IEEE Transactions on image processing 16.1 pp. 285-291 (2007).
• Schoenlieb, C.-B. & Bertozzi, A. (2011). Unconditionally stable schemes for higher order inpainting, Communications in Mathematical Sciences, Volume 9, Issue 2, pp. 413-457 (2011).

5) Transport Inpainting

Refer to Section 6.1 in the book. (Both Grayscale / Color Images).

Bibliography:

• Bertalmio, M. (2001). Processing of flat and non-flat image information on arbitrary manifolds using partial differential equations.PhD Thesis, 2001.

License

BSD-3-Clause