L. Ambrosio, N. N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

G. Aubert and J. Aujol, Optimal partitions, regularized solutions, and application to image classification, Applicable Analysis, vol.420, issue.1, pp.15-35, 2005.
DOI : 10.1023/A:1020874308076
URL : https://hal.archives-ouvertes.fr/hal-00202002

J. Aujol, S. Masnou, and S. Ladjal, Exemplar-Based Inpainting from a Variational Point of View, SIAM Journal on Mathematical Analysis, vol.42, issue.3, pp.1246-1285, 2010.
DOI : 10.1137/080743883
URL : https://hal.archives-ouvertes.fr/hal-00392011

E. Bae, J. Yuan, and X. Tai, Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach, International Journal of Computer Vision, vol.51, issue.11, pp.92-112, 2011.
DOI : 10.1007/s11263-010-0406-y

A. Baeza, P. Gargallo, V. Caselles, and N. Papadakis, A Narrow Band Method for the Convex Formulation of Discrete Multilabel Problems, Multiscale Modeling & Simulation, vol.8, issue.5, pp.2048-2078, 2010.
DOI : 10.1137/090780936
URL : https://hal.archives-ouvertes.fr/hal-00596060

J. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Archive for Rational Mechanics and Analysis, pp.337-403, 1976.

E. S. Brown, X. Chan, and . Bresson, Completely Convex Formulation of the Chan-Vese Image Segmentation Model, International Journal of Computer Vision, vol.26, issue.2, pp.98-103, 2012.
DOI : 10.1007/s11263-011-0499-y

A. Chambolle, An algorithm for mean curvature motion, Interfaces and Free Boundaries, pp.1-24, 2004.

A. Chambolle, D. Cremers, and T. Pock, A convex approach for computing minimal partitions, 2008.

A. Chambolle, T. Cremers, and . Pock, A Convex Approach to Minimal Partitions, SIAM Journal on Imaging Sciences, vol.5, issue.4, 2011.
DOI : 10.1137/110856733
URL : https://hal.archives-ouvertes.fr/hal-00630947

A. Chambolle and T. Pock, A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011.
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826

T. F. Chan and L. A. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.266-277, 2001.
DOI : 10.1109/83.902291

Y. Chen and X. Ye, Projection onto a simplex, 1208.

P. L. Combettes and V. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, 2005.
DOI : 10.1137/050626090
URL : https://hal.archives-ouvertes.fr/hal-00017649

B. Goldluecke and D. Cremers, Convex Relaxation for Multilabel Problems with Product Label Spaces, European conference on Computer vision (ECCV'10), pp.225-238, 2010.
DOI : 10.1007/978-3-642-15555-0_17

B. Goldluecke, E. Strekalovskiy, and D. Cremers, Tight convex relaxations for vectorvalued labeling, To appear in SIAM, Journal on Imaging Science, 2013.

T. Goldstein, X. Bresson, and S. Osher, Global minimization of Markov random fields with applications to optical flow, Inverse Problems and Imaging, vol.6, issue.4, pp.623-644, 2012.
DOI : 10.3934/ipi.2012.6.623

K. Kolev, M. Klodt, T. Brox, and D. Cremers, Continuous Global Optimization in Multiview 3D Reconstruction, International Journal of Computer Vision, vol.29, issue.12, pp.80-96, 2009.
DOI : 10.1007/s11263-009-0233-1

P. Maurel, J. Aujol, and G. Peyré, Locally Parallel Texture Modeling, SIAM Journal on Imaging Sciences, vol.4, issue.1, pp.413-447, 2011.
DOI : 10.1137/090770795
URL : https://hal.archives-ouvertes.fr/hal-00415779

J. J. Moreau, Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, p.93, 1965.
DOI : 10.24033/bsmf.1625

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1002/cpa.3160420503

M. Nikolova, S. Esedoglu, and T. F. Chan, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, pp.66-1632, 2006.

N. Papadakis, A. Baeza, P. Gargallo, and V. Caselles, Polyconvexification of the multilabel optical flow problem, Proc. IEEE Int. Conf. on Image Processing (ICIP'10), 2010.
URL : https://hal.archives-ouvertes.fr/hal-00596186

T. Pock and A. Chambolle, Diagonal preconditioning for first order primal-dual algorithms in convex optimization, 2011 International Conference on Computer Vision, pp.1762-1769, 2011.
DOI : 10.1109/ICCV.2011.6126441

T. Pock, D. Cremers, H. Bischof, and A. Chambolle, Global Solutions of Variational Models with Convex Regularization, SIAM Journal on Imaging Sciences, vol.3, issue.4, pp.1122-1145, 2010.
DOI : 10.1137/090757617

T. Pock, T. Schoenemann, G. Graber, H. Bischof, and D. Cremers, A Convex Formulation of Continuous Multi-label Problems, Proceedings of the 10th European Conference on Computer Vision (ECCV'08): Part III, pp.792-805, 2008.
DOI : 10.1007/978-3-540-88690-7_59

L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

E. Strekalovskiy, B. Goldluecke, and D. Cremers, Tight convex relaxations for vectorvalued labeling problems, IEEE International Conference on Computer Vision (ICCV'11), 2011.

R. Yildizoglu, J. Aujol, and N. Papadakis, Active contours without level sets, 2012 19th IEEE International Conference on Image Processing, 2012.
DOI : 10.1109/ICIP.2012.6467418
URL : https://hal.archives-ouvertes.fr/hal-00696065

C. Zach, T. Pock, and H. Bischof, A duality based approach for realtime tv-l1 optical flow, DAGM conference on Pattern recognition, pp.214-223, 2007.