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.