L. Alvarez, F. Guichard, P. Lions, and J. Morel, Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, vol.11, issue.3, pp.199-257, 1993.
DOI : 10.1007/BF00375127

A. K. and L. Grady, A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm, 2007.

F. Andreu, J. M. Mazon, J. D. Rossi, and J. Toledo, A nonlocal p-Laplacian evolution equation with Neumann boundary conditions, Journal de Math??matiques Pures et Appliqu??es, vol.90, issue.2, 2007.
DOI : 10.1016/j.matpur.2008.04.003

P. Bates and A. Chmaj, A Discrete Convolution Model??for Phase Transitions, Archive for Rational Mechanics and Analysis, vol.150, issue.4, pp.281-305, 1999.
DOI : 10.1007/s002050050189

M. Belkin, P. Niyogi, and V. Sindhwani, Manifold regularization: A geometric framework for learning from labeled and unlabeled examples, Journal of Machine Learning Research, vol.7, pp.2399-2434, 2006.

A. Bensoussan and J. Menaldi, Difference equations on weighted graphs, Journal of Convex Analysis, vol.12, issue.1, pp.13-44, 2004.

M. Bogoya, R. Ferreira, and J. D. Rossi, Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models, Proceedings of the American Mathematical Society, 2007.
DOI : 10.1090/S0002-9939-07-09205-2

S. Bougleux and A. Elmoataz, Image Smoothing and Segmentation by Graph Regularization, Advances in Visual Computing, 2005.
DOI : 10.1007/11595755_95

URL : https://hal.archives-ouvertes.fr/hal-00333551

S. Bougleux, A. Elmoataz, and M. Melkemi, Discrete Regularization on Weighted Graphs for Image and Mesh Filtering, Scale Space and Variational Methods in Computer Vision, 2007.
DOI : 10.1007/978-3-540-72823-8_12

URL : https://hal.archives-ouvertes.fr/hal-00333374

Y. Boykov, O. Veksler, and R. Zabih, Fast approximate energy minimization via graph cuts, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.11, pp.1222-1239, 2001.
DOI : 10.1109/34.969114

A. Buades, B. Coll, J. Morel, and C. Sbert, Non local demosaicing, 2007.

A. Buades, B. Coll, and J. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024

URL : https://hal.archives-ouvertes.fr/hal-00271141

T. Chan, S. Osher, and J. Shen, The digital TV filter and nonlinear denoising, IEEE Transactions on Image Processing, vol.10, issue.2, pp.231-241, 2001.
DOI : 10.1109/83.902288

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.3483

T. Chan and J. Shen, Image Processing and Analysis, 2005.
DOI : 10.1137/1.9780898717877

F. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 1997.
DOI : 10.1090/cbms/092

J. Darbon and M. Sigelle, Exact Optimization of Discrete Constrained Total Variation Minimization Problems, Proceedings of the 10th Int. Workshop on Combinatorial Image Analysis, 2004.
DOI : 10.1007/978-3-540-30503-3_40

A. Elmoataz, O. Lézoray, and S. Bougleux, Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing, IEEE Transactions on Image Processing, vol.17, issue.7, 2007.
DOI : 10.1109/TIP.2008.924284

URL : https://hal.archives-ouvertes.fr/hal-00163573

G. Gilboa and S. Osher, Nonlocal Linear Image Regularization and Supervised Segmentation, Multiscale Modeling & Simulation, vol.6, issue.2, pp.595-630, 2007.
DOI : 10.1137/060669358

G. Gilboa and S. Osher, Nonlocal Operators with Applications to Image Processing, Multiscale Modeling & Simulation, vol.7, issue.3, 2007.
DOI : 10.1137/070698592

C. Kervrann, J. Boulanger, and P. Coupé, Bayesian Non-local Means Filter, Image Redundancy and Adaptive Dictionaries for Noise Removal, Proc. of the 1st Int. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2007.
DOI : 10.1007/978-3-540-72823-8_45

URL : https://hal.archives-ouvertes.fr/hal-00645444

S. Kindermann, S. Osher, and P. W. Jones, Deblurring and Denoising of Images by Nonlocal Functionals, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1091-1115, 2005.
DOI : 10.1137/050622249

P. Mcdonald and R. Meyers, Diffusions on graphs, poisson problems and spectral geometry, Transactions of the American Mathematical Society, vol.354, issue.12, pp.5111-5136, 2002.
DOI : 10.1090/S0002-9947-02-02973-2

S. Osher and J. Shen, Digitized PDE for data restoration, Handbook of Analytic Computational Methods in Applied Mathematics, pp.751-771, 2000.
DOI : 10.1201/9781420036053.ch16

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2553

G. Peyré, Image processing with non-local spectral bases, 2007.

X. Ren and J. Malik, Learning a classification model for segmentation, Proceedings Ninth IEEE International Conference on Computer Vision, 2003.
DOI : 10.1109/ICCV.2003.1238308

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.1-4, 1992.
DOI : 10.1016/0167-2789(92)90242-F

S. Smith and . Brady, SUSAN -a new approach to low level image processing, International Journal of Computer Vision, vol.23, issue.1, pp.45-78, 1997.
DOI : 10.1023/A:1007963824710

C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), 1998.
DOI : 10.1109/ICCV.1998.710815

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.2091

Y. Tsai and S. Osher, Total variation and level set methods in image science, Acta Numerica, vol.14, pp.509-573, 2005.
DOI : 10.1017/S0962492904000273

D. Tschumperlé, Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's, International Journal of Computer Vision, vol.68, issue.1, pp.65-82, 2006.
DOI : 10.1007/s11263-006-5631-z

T. Viéville, An unbiased implementation of regularization mechanisms, Image and Vision Computing, vol.23, issue.11, pp.981-998, 2005.
DOI : 10.1016/j.imavis.2005.07.002

D. Zhou and B. Schölkopf, A regularization framework for learning from graph data, Proceedings of the ICML-2004 Workshop on Statistical Relational Learning and its Connections to Other Fields, 2004.

D. Zhou and B. Schölkopf, Regularization on Discrete Spaces, Patter Recognition-Proceedings of the 27th DAGM Symposium, 2005.
DOI : 10.1007/11550518_45

D. Zhou and B. Schölkopf, Discrete Regularization, Semi-Supervised Learning, section 3.13, Adaptive computation and machine learning, pp.221-232, 2006.