R. Achanta, A. Shaji, K. Smith, P. Lucchi, S. Fua et al., SLIC Superpixels Compared to State-of-the-Art Superpixel Methods, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.34, issue.11, pp.2274-2282, 2012.
DOI : 10.1109/TPAMI.2012.120

S. Agarwal, Y. Furukawa, N. Snavely, B. Curless, S. M. Seitz et al., Reconstructing Rome, Computer, vol.43, issue.6, pp.40-47, 2010.
DOI : 10.1109/MC.2010.175

M. Agueh and G. Carlier, Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis, vol.43, issue.2, pp.904-924, 2011.
DOI : 10.1137/100805741

URL : https://hal.archives-ouvertes.fr/hal-00637399

H. A. Almohamad and S. O. Duffuaa, A linear programming approach for the weighted graph matching problem, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, issue.5, pp.522-525, 1993.
DOI : 10.1109/34.211474

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures, 2006.

S. Angenent, S. Haker, and A. Tannenbaum, Minimizing Flows for the Monge--Kantorovich Problem, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.61-97, 2003.
DOI : 10.1137/S0036141002410927

URL : http://iie.fing.edu.uy/investigacion/grupos/gti/seminario/simposio/tannembaum/mk_final.pdf

K. Arrow, L. Hurwicz, and H. Uzawa, Studies in linear and non-linear programming, 1958.

H. Attouch, J. Bolte, and B. Svaiter, Convergence of descent methods for semialgebraic and tame problems: proximal algorithms, forward?backward splitting, and regularized gauss?seidel methods, Mathematical Programming, pp.91-129, 2013.
DOI : 10.1007/s10107-011-0484-9

URL : https://hal.archives-ouvertes.fr/hal-00790042

G. Aubert, M. Barlaud, O. Faugeras, and S. Jehan-besson, Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?, SIAM Journal on Applied Mathematics, vol.63, issue.6, pp.2128-2154, 2003.
DOI : 10.1137/S0036139902408928

URL : https://hal.archives-ouvertes.fr/hal-00964649

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, Applied Mathematical Sciences, vol.147, 2002.

J. Aujol, G. Aubert, and L. Blanc-féraud, Wavelet-based level set evolution for classification of textured images, IEEE Transactions on Image Processing, vol.12, issue.12, pp.1634-1641, 2003.
DOI : 10.1109/TIP.2003.819309

URL : https://hal.archives-ouvertes.fr/hal-00202004

F. Aurenhammer, F. Hoffmann, and B. Aronov, Minkowski-type theorems and least-squares partitioning, Proceedings of the eighth annual symposium on Computational geometry , SCG '92, pp.350-357, 1992.
DOI : 10.1145/142675.142747

I. Ayed, H. Chen, K. Punithakumar, I. Ross, and S. Li, Graph cut segmentation with a global constraint: Recovering region distribution via a bound of the Bhattacharyya measure, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.3288-3295, 2010.
DOI : 10.1109/CVPR.2010.5540045

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011.
DOI : 10.1007/978-1-4419-9467-7

URL : https://hal.archives-ouvertes.fr/hal-01517477

A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009.
DOI : 10.1137/080716542

URL : http://ie.technion.ac.il/%7Ebecka/papers/finalicassp2009.pdf

S. Belongie, J. Malik, and J. Puzicha, Shape matching and object recognition using shape contexts, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.4, pp.509-522, 2002.
DOI : 10.1109/34.993558

URL : http://www.isi.uu.nl/Meetings/../TGV/Belo01a.pdf

J. Benamou and Y. Brenier, Weak Existence for the Semigeostrophic Equations Formulated as a Coupled Monge--Amp??re/Transport Problem, SIAM Journal on Applied Mathematics, vol.58, issue.5, pp.1450-1461, 1998.
DOI : 10.1137/S0036139995294111

J. Benamou, A Domain Decomposition Method for the Polar Factorization of Vector-Valued Mappings, SIAM Journal on Numerical Analysis, vol.32, issue.6, pp.1808-1838, 1995.
DOI : 10.1137/0732082

J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.
DOI : 10.1007/s002110050002

J. Benamou and Y. Brenier, Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions, Journal of Optimization Theory and Applications, vol.44, issue.2, pp.255-271, 2001.
DOI : 10.1002/9781118032954

J. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.1111-1138, 2015.
DOI : 10.1137/141000439

URL : https://hal.archives-ouvertes.fr/hal-01096124

J. Benamou, G. Carlier, Q. Mérigot, and E. Oudet, Discretization of functionals involving the Monge-Amp\'ere operator, 2014.

J. Benamou, B. D. Froese, and O. A. , Numerical solution of the optimal transportation problem via viscosity solutions for the Monge-Ampère equation, 2012.

J. Benamou, B. D. Froese, and A. M. Oberman, Numerical solution of the Optimal Transportation problem using the Monge???Amp??re equation, Journal of Computational Physics, vol.260, pp.107-126, 2014.
DOI : 10.1016/j.jcp.2013.12.015

D. Bertsekas, The auction algorithm: A distributed relaxation method for the assignment problem, Annals of Operations Research, vol.5, issue.1, pp.105-123, 1988.
DOI : 10.1007/BF02186476

S. Beyou, A. Cuzol, S. S. Gorthi, and E. Mémin, Weighted ensemble transform kalman filter for image assimilation. Tellus A: Dynamic Meteorology and Oceanography, 2013.
DOI : 10.3402/tellusa.v65i0.18803

URL : https://hal.archives-ouvertes.fr/hal-00793804

J. Bigot, R. Gouet, T. Klein, and A. López, Geodesic PCA in the Wasserstein space, 2013.
DOI : 10.1214/15-aihp706

URL : https://hal.archives-ouvertes.fr/hal-01581699

J. Bigot and T. Klein, Consistent estimation of a population barycenter in the wasserstein space, 2012.

A. Blake, C. Rother, M. Brown, P. Perez, and P. Torr, Interactive Image Segmentation Using an Adaptive GMMRF Model, European Conference on Computer Vision, 2004.
DOI : 10.1007/978-3-540-24670-1_33

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, pp.459-494, 2014.
DOI : 10.1007/BF01584660

URL : https://hal.archives-ouvertes.fr/hal-00916090

N. Bonneel, Faster and specialized c++ implementation of "optimal transport with proximal splitting, 2013.

N. Bonneel, J. Rabin, G. Peyré, and H. Pfister, Sliced and Radon Wasserstein Barycenters of Measures, Journal of Mathematical Imaging and Vision, vol.11, issue.1, pp.22-45, 2015.
DOI : 10.1023/A:1018366000512

URL : https://hal.archives-ouvertes.fr/hal-00881872

N. Bonneel, K. Sunkavalli, S. Paris, and H. Pfister, Example-based video color grading, ACM Transactions on Graphics, vol.32, issue.4, pp.1-3912, 2013.
DOI : 10.1145/2461912.2461939

URL : http://people.seas.harvard.edu/~nbonneel/videostyle.pdf

N. Bonneel, M. Van-de-panne, S. Paris, and W. Heidrich, Displacement interpolation using Lagrangian mass transport, Proceedings of SIGGRAPH Asia, p.30, 2011.
DOI : 10.1145/2070781.2024192

URL : https://hal.archives-ouvertes.fr/hal-00763270

F. Bornemann and C. Rasch, Finite-element Discretization of Static Hamilton-Jacobi Equations based on a Local Variational Principle, Computing and Visualization in Science, vol.40, issue.9, pp.57-69, 2006.
DOI : 10.1515/9781400873173

R. I. Bot, E. R. Csetnek, and A. Heinrich, On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems, 2013.

A. Bouharguane, A. Iollo, and L. Weynans, Numerical solution of the
URL : https://hal.archives-ouvertes.fr/hal-00946252

A. Bouharguane, E. Maitre, E. Oudet, and N. Papadakis, Multiphysics optimal transportation and image analysis, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00740671

Y. Boykov and M. Jolly, Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, pp.105-112, 2001.
DOI : 10.1109/ICCV.2001.937505

Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991.
DOI : 10.1002/cpa.3160440402

E. Brown, T. F. Chan, and X. Bresson, Completely Convex Formulation of the Chan-Vese Image Segmentation Model, International Journal of Computer Vision, vol.26, issue.2, pp.103-121, 2012.
DOI : 10.1007/BF02592050

T. Brox, M. Rousson, R. Deriche, and J. Weickert, Unsupervised Segmentation Incorporating Colour, Texture, and Motion, Computer Analysis of Images and Patterns, pp.353-360, 2003.
DOI : 10.1007/978-3-540-45179-2_44

URL : https://hal.archives-ouvertes.fr/inria-00071826

T. Brox and J. Weickert, Level Set Segmentation With Multiple Regions, IEEE Transactions on Image Processing, vol.15, issue.10, pp.3213-3218, 2006.
DOI : 10.1109/TIP.2006.877481

URL : http://www.cs.berkeley.edu/%7Ebrox/pub/brox_pp145.pdf

C. Brune, 4D imaging in tomography and optical nanoscopy, 2010.

M. Burger, M. Franek, and C. Schönlieb, Regularized Regression and Density Estimation based on Optimal Transport, Applied Mathematics Research eXpress, 2011.
DOI : 10.1093/amrx/abs007

G. Buttazzo, C. Jimenez, and E. Oudet, An Optimization Problem for Mass Transportation with Congested Dynamics, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.1961-1976, 2009.
DOI : 10.1137/07070543X

URL : https://hal.archives-ouvertes.fr/hal-00385145

P. Cardaliaguet, G. Carlier, and B. Nazaret, Geodesics for a class of distances in the space of probability measures, Calculus of Variations and Partial Differential Equations, vol.39, issue.1, pp.1-26, 2012.
DOI : 10.2140/pjm.1971.39.439

URL : https://hal.archives-ouvertes.fr/hal-00686908

G. Carlier, A. Oberman, and E. Oudet, Numerical methods for matching for teams and Wasserstein barycenters, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, 2014.
DOI : 10.1007/978-3-540-71050-9

URL : https://hal.archives-ouvertes.fr/hal-00987292

J. Carrillo and J. Moll, Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms, SIAM Journal on Scientific Computing, vol.31, issue.6, pp.314305-4329, 2010.
DOI : 10.1137/080739574

V. Chabot, M. Nodet, N. Papadakis, and A. Vidard, Accounting for observation errors in image data assimilation. Tellus A: Dynamic Meteorology and Oceanography , 67:19, 2015. [53] A. Chambolle. An algorithm for mean curvature motion. Interfaces and Free Boundaries, Mathematical Modelling, Analysis and Computation, vol.6, issue.2, pp.195-218, 2004.
DOI : 10.3402/tellusa.v67.23629

URL : https://hal.archives-ouvertes.fr/hal-00984508

A. Chambolle and J. Darbon, On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows, International Journal of Computer Vision, vol.40, issue.9, pp.288-307, 2009.
DOI : 10.1006/jctb.2000.1989

URL : https://link.springer.com/content/pdf/10.1007%2Fs11263-009-0238-9.pdf

A. Chambolle and C. Dossal, On the Convergence of the Iterates of the ???Fast Iterative Shrinkage/Thresholding Algorithm???, Journal of Optimization Theory and Applications, vol.155, issue.2, pp.968-982, 2015.
DOI : 10.1007/978-1-4419-9467-7

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 : 10.1007/978-3-540-74936-3_22

URL : https://hal.archives-ouvertes.fr/hal-00490826

A. Chambolle and T. Pock, On the ergodic convergence rates of a first-order primal???dual algorithm, Mathematical Programming, pp.1-35, 2015.
DOI : 10.1007/s10444-011-9254-8

URL : https://hal.archives-ouvertes.fr/hal-01151629

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

URL : http://www.math.ucla.edu/~lvese/PAPERS/IEEEIP2001.pdf

Y. Chen and X. Ye, Projection onto a simplex, 2011.

L. Chizat, B. Schmitzer, G. Peyré, and F. Vialard, An Interpolating Distance between Optimal Transport and Fischer-Rao, 2015.
DOI : 10.1007/s10208-016-9331-y

L. Chizat, B. Schmitzer, G. Peyré, and F. Vialard, Unbalanced Optimal Transport: Geometry and Kantorovich Formulation, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01271981

E. Chouzenoux, J. Pesquet, and A. Repetti, A block coordinate variable metric forward???backward algorithm, Journal of Global Optimization, vol.6, issue.3, 2014.
DOI : 10.1137/120887795

URL : https://hal.archives-ouvertes.fr/hal-00945918

P. Clarysse, B. Delhay, M. Picq, and J. Pousin, Optimal extended optical flow subject to a statistical constraint, Journal of Computational and Applied Mathematics, vol.234, issue.4, pp.1291-1302, 2010.
DOI : 10.1016/j.cam.2009.10.014

URL : https://hal.archives-ouvertes.fr/hal-00443196

P. L. Combettes and J. Pesquet, A Douglas???Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.564-574, 2007.
DOI : 10.1109/JSTSP.2007.910264

URL : https://hal.archives-ouvertes.fr/hal-00621820

P. L. Combettes and J. Pesquet, Proximal Splitting Methods in Signal Processing, Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011.
DOI : 10.1007/978-1-4419-9569-8_10

URL : https://hal.archives-ouvertes.fr/hal-00643807

L. Condat, A Primal???Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms, Journal of Optimization Theory and Applications, vol.23, issue.1???2, pp.460-479, 2013.
DOI : 10.1081/NFA-120003674

URL : https://hal.archives-ouvertes.fr/hal-00609728

D. Cordero-erausquin, B. Nazaret, and C. Villani, A mass-transportation approach to sharp Sobolev and Gagliardo???Nirenberg inequalities, Advances in Mathematics, vol.182, issue.2, pp.307-332, 2004.
DOI : 10.1016/S0001-8708(03)00080-X

URL : https://hal.archives-ouvertes.fr/hal-00157943

T. Corpetti, P. Héas, E. Mémin, and N. Papadakis, Pressure image assimilation for atmospheric motion estimation. Tellus A: Dynamic Meteorology and Oceanography, pp.160-178, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00273838

T. Corpetti, É. Mémin, and P. Pérez, Dense estimation of fluid flows, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.3, pp.365-380, 2002.
DOI : 10.1109/34.990137

URL : https://hal.archives-ouvertes.fr/hal-00329724

N. Courty, R. Flamary, and D. Tuia, Domain Adaptation with Regularized Optimal Transport, Machine Learning and Knowledge Discovery in Databases, pp.274-289, 2014.
DOI : 10.1007/978-3-662-44848-9_18

URL : https://hal.archives-ouvertes.fr/hal-01018698

D. Cremers, M. Rousson, and R. Deriche, A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape, International Journal of Computer Vision, vol.18, issue.9, p.215, 2007.
DOI : 10.1090/conm/313/05378

A. Criminisi, T. Sharp, C. Rother, and P. Pérez, Geodesic image and video editing, ACM Transactions on Graphics, vol.29, issue.5, pp.1-134, 2010.
DOI : 10.1145/1857907.1857910

URL : http://research.microsoft.com/pubs/81528/Criminisi_ACM_TOG2010.pdf

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Conference on Neural Information Processing Systems (NIPS'13), pp.2292-2300, 2013.

M. Cuturi and D. Avis, Ground metric learning, Journal of Machine Learning Research, vol.15, issue.1, pp.533-564, 2014.

M. Cuturi and A. Doucet, Fast computation of wasserstein barycenters, International Conference on Machine Learning (ICML'14), pp.685-693, 2014.

M. Cuturi, G. Peyré, and A. Rolet, A Smoothed Dual Approach for Variational Wasserstein Problems, SIAM Journal on Imaging Sciences, vol.9, issue.1, 2015.
DOI : 10.1137/15M1032600

URL : https://hal.archives-ouvertes.fr/hal-01188954

G. B. Dantzig, Linear Programming and Extensions, 1963.
DOI : 10.1515/9781400884179

F. De-goes, D. Cohen-steiner, P. Alliez, and M. Desbrun, An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes, Computer Graphics Forum, vol.26, issue.3, pp.1593-1602, 2011.
DOI : 10.1007/s00371-009-0395-4

URL : https://hal.archives-ouvertes.fr/hal-00758019

E. J. Dean and R. Glowinski, An augmented Lagrangian approach to the numerical solution of the dirichlet problem for the elliptic Monge-Ampère equation in two dimensions, Electronic Transactions on Numerical Analysis, vol.22, pp.71-96, 2006.

M. C. Delfour and J. Zolésio, Shapes and geometries: analysis, differential calculus , and optimization, Society for Industrial and Applied Mathematics, 2001.
DOI : 10.1137/1.9780898719826

J. Delon, Midway Image Equalization, Journal of Mathematical Imaging and Vision, vol.21, issue.2, pp.119-134, 2004.
DOI : 10.1023/B:JMIV.0000035178.72139.2d

URL : https://hal.archives-ouvertes.fr/hal-01338124

J. Delon, J. Delon, J. Salomon, and A. Sobolevski, Movie and video scale-time equalization application to flicker reduction, IEEE Transactions on Image Processing, vol.15, issue.1, pp.241-248, 2006.
DOI : 10.1109/TIP.2005.860328

J. Delon, J. Salomon, and A. Sobolevskii, Local Matching Indicators for Transport Problems with Concave Costs, SIAM Journal on Discrete Mathematics, vol.26, issue.2, pp.801-827, 2012.
DOI : 10.1137/110823304

URL : https://hal.archives-ouvertes.fr/hal-00525994

J. Digne, D. Cohen-steiner, P. Alliez, F. De-goes, and M. Desbrun, Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets, Journal of Mathematical Imaging and Vision, vol.40, issue.2, pp.369-382, 2014.
DOI : 10.1023/A:1026543900054

URL : https://hal.archives-ouvertes.fr/hal-00706712

J. Dolbeault, B. Nazaret, and G. Savaré, A new class of transport distances between measures, Calculus of Variations and Partial Differential Equations, vol.25, issue.9, pp.193-231, 2009.
DOI : 10.2140/pjm.1968.25.597

URL : https://hal.archives-ouvertes.fr/hal-00262455

Y. Drori, S. Sabach, and M. Teboulle, A simple algorithm for a class of nonsmooth convex???concave saddle-point problems, Operations Research Letters, vol.43, issue.2, pp.209-214, 2015.
DOI : 10.1016/j.orl.2015.02.001

B. During, D. Matthes, and J. Milisic, A gradient flow scheme for nonlinear fourth order equations. Discrete and Continuous Dynamical Systems -Series B, pp.935-959, 2010.

J. Eckstein and D. P. Bertsekas, On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, pp.293-318, 1992.
DOI : 10.2140/pjm.1970.33.209

A. A. Efros and T. K. Leung, Texture synthesis by non-parametric sampling, Proceedings of the Seventh IEEE International Conference on Computer Vision, pp.1033-1038, 1999.
DOI : 10.1109/ICCV.1999.790383

URL : http://http.cs.berkeley.edu/projects/vision/papers/efros-iccv99.pdf

A. Elmoataz, O. Lezoray, 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, pp.1047-060, 2008.
DOI : 10.1109/TIP.2008.924284

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

S. Ferradans, N. Papadakis, G. Peyré, and J. Aujol, Regularized discrete optimal transport, SIAM Journal on Imaging Science, vol.7, issue.1, pp.212-238, 2014.
DOI : 10.1007/978-3-642-38267-3_36

URL : https://hal.archives-ouvertes.fr/hal-01188963

S. Ferradans, N. Papadakis, J. Rabin, G. Peyré, and J. Aujol, Regularized discrete optimal transport, Scale Space and Variational Methods in Computer Vision (SSVM'13), pp.428-439, 2013.
DOI : 10.1007/978-3-642-38267-3_36

URL : https://hal.archives-ouvertes.fr/hal-01188963

S. Ferradans, G. Xia, G. Peyré, and J. Aujol, Static and Dynamic Texture Mixing Using Optimal Transport, Proc. SSVM'13, pp.137-148, 2013.
DOI : 10.1007/978-3-642-38267-3_12

L. Ferragut and I. Asensio, Mixed finite element methods for a class of nonlinear reaction diffusion problems, Neural, Parallel, and Scientific Computations, pp.91-112, 2002.

N. Feyeux, M. Nodet, and A. Vidard, Application of optimal transport to data assimilation. Special semester on new trends in calculus of variation, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01097190

J. H. Fitschen, F. Laus, and G. Steidl, Dynamic optimal transport with mixed boundary condition for color image processing, 2015 International Conference on Sampling Theory and Applications (SampTA), 2015.
DOI : 10.1109/SAMPTA.2015.7148953

O. Frigo, N. Sabater, J. Delon, and P. Hellier, Motion Driven Tonal Stabilization, 2015.
DOI : 10.1109/icip.2015.7351429

URL : https://hal.archives-ouvertes.fr/hal-01256874

O. Frigo, N. Sabater, V. Demoulin, and P. Hellier, Optimal Transportation for Example-Guided Color Transfer, Asian Conference on Computer Vision (ACCV'14), pp.655-670, 2014.
DOI : 10.1007/978-3-319-16811-1_43

U. Frisch, R. Matarrese, A. Mohayaee, and . Sobolevski, A reconstruction of the initial conditions of the Universe by optimal mass transportation, Nature, vol.34, issue.6886, pp.260-262, 2002.
DOI : 10.1007/978-1-4757-1693-1

B. D. Froese, A Numerical Method for the Elliptic Monge--Amp??re Equation with Transport Boundary Conditions, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.1432-1459, 2012.
DOI : 10.1137/110822372

C. Frogner, C. Zhang, H. Mobahi, M. Araya-polo, and T. Poggio, Learning with a wasserstein loss, 2015.

D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, vol.2, issue.1, pp.17-40, 1976.
DOI : 10.1016/0898-1221(76)90003-1

W. Gangbo and R. Mccann, The geometry of optimal transportation, Acta Mathematica, vol.177, issue.2, pp.113-161, 1996.
DOI : 10.1007/BF02392620

W. Gangbo and R. J. Mccann, Shape recognition via Wasserstein distance, Quarterly of Applied Mathematics, vol.58, issue.4, pp.705-737, 2000.
DOI : 10.1090/qam/1788425

URL : http://www.ams.org/qam/2000-58-04/S0033-569X-2000-1788425-X/S0033-569X-2000-1788425-X.pdf

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

R. Glowinski and A. Marroco, Sur l'approximation, par ??l??ments finis d'ordre un, et la r??solution, par p??nalisation-dualit?? d'une classe de probl??mes de Dirichlet non lin??aires, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.9, issue.R2, pp.41-76, 1975.
DOI : 10.1051/m2an/197509R200411

L. Gorelick, F. R. Schmidt, Y. Boykov, A. Delong, and A. Ward, Segmentation with Non-linear Regional Constraints via Line-Search Cuts, European Conference on Computer Vision (ECCV'12), pp.583-597, 2012.
DOI : 10.1007/978-3-642-33718-5_42

URL : http://lmb.informatik.uni-freiburg.de/Publications/2012/Sch12/GSBDW-eccv12.pdf

K. Guittet, On the Time-Continuous Mass Transport Problem and Its Approximation by Augmented Lagrangian Techniques, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.382-399, 2004.
DOI : 10.1137/S0036142901386069

E. Haber, T. Rehman, and A. Tannenbaum, An Efficient Numerical Method for the Solution of the $L_2$ Optimal Mass Transfer Problem, SIAM Journal on Scientific Computing, vol.32, issue.1, pp.197-211, 2010.
DOI : 10.1137/080730238

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Optimal Mass Transport for Registration and Warping, International Journal of Computer Vision, vol.60, issue.3, pp.225-240, 2004.
DOI : 10.1023/B:VISI.0000036836.66311.97

URL : http://www.ee.technion.ac.il/courses/048831/downloads/monge_ijcv.pdf

F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.149, issue.12, pp.2182-2189, 1965.
DOI : 10.1098/rsta.1952.0006

B. He and X. Yuan, Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective, SIAM Journal on Imaging Sciences, vol.5, issue.1, pp.119-149, 2012.
DOI : 10.1137/100814494

M. Henry, E. Maitre, and V. Perrier, Optimal transport using Helmholtz-Hodge decomposition and first-order primal-dual algorithms, 2015 IEEE International Conference on Image Processing (ICIP), 2015.
DOI : 10.1109/ICIP.2015.7351708

URL : https://hal.archives-ouvertes.fr/hal-01134194

A. Herbulot, S. Jehan-besson, S. Duffner, M. Barlaud, and G. Aubert, Segmentation of Vectorial Image Features Using Shape Gradients and Information Measures, Journal of Mathematical Imaging and Vision, vol.18, issue.1, pp.365-386, 2006.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

URL : https://hal.archives-ouvertes.fr/hal-00418217

A. Hertzmann, C. E. Jacobs, N. Oliver, B. Curless, and D. H. Salesin, Image analogies, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.327-340, 2001.
DOI : 10.1145/383259.383295

R. Horst and N. Thoai, DC Programming: Overview, Journal of Optimization Theory and Applications, vol.1, issue.1, pp.1-43, 1999.
DOI : 10.1287/moor.1.3.251

R. Hug, E. Maitre, and N. Papadakis, Mathematical and numerical analysis of the dynamic optimal transport problem, 2015.

R. Hug, E. Maitre, and N. Papadakis, Multi-physics optimal transportation and image interpolation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, pp.1671-1692, 2015.
DOI : 10.1007/978-1-4419-9467-7

URL : https://hal.archives-ouvertes.fr/hal-00998370

T. Hurtut, Y. Gousseau, and F. Schmitt, Adaptive image retrieval based on the spatial organization of colors, Computer Vision and Image Understanding, vol.112, issue.2, pp.101-113, 2008.
DOI : 10.1016/j.cviu.2007.12.006

URL : https://hal.archives-ouvertes.fr/hal-00430456

A. Iollo and D. Lombardi, A lagrangian scheme for the solution of the optimal mass transfer problem, Journal of Computational Physics, vol.230, issue.9, pp.3430-3442, 2011.
DOI : 10.1016/j.jcp.2011.01.037

URL : https://hal.archives-ouvertes.fr/hal-00664718

H. Jégou, F. Perronnin, M. Douze, J. Sánchez, P. Pérez et al., Aggregating Local Image Descriptors into Compact Codes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.34, issue.9, pp.1704-1716, 2012.
DOI : 10.1109/TPAMI.2011.235

R. Jordan, D. Kinderlehrer, and F. Otto, The Variational Formulation of the Fokker--Planck Equation, SIAM Journal on Mathematical Analysis, vol.29, issue.1, pp.1-17, 1998.
DOI : 10.1137/S0036141096303359

L. Kantorovitch, On the Translocation of Masses, Management Science, vol.5, issue.1, pp.1-4, 1958.
DOI : 10.1287/mnsc.5.1.1

J. Kim, J. W. Fisher, A. Yezzi, M. Cetin, and A. S. Willsky, A nonparametric statistical method for image segmentation using information theory and curve evolution, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1486-1502, 2005.

Y. Kim and B. Pass, Multi-marginal optimal transport on Riemannian manifolds, American Journal of Mathematics, vol.137, issue.4, 2013.
DOI : 10.1353/ajm.2015.0024

R. Kimmel and J. Sethian, Computing geodesic paths on manifolds, Proc. of the National Academy of Sciences, pp.8431-8435, 1998.
DOI : 10.1073/pnas.95.15.8431

URL : http://www.pnas.org/content/95/15/8431.full.pdf

M. Kowalski, Thresholding RULES and iterative shrinkage/thresholding algorithm: A convergence study, 2014 IEEE International Conference on Image Processing (ICIP), p.2014
DOI : 10.1109/ICIP.2014.7025843

URL : https://hal.archives-ouvertes.fr/hal-01102810

H. W. Kuhn, The Hungarian method for the assignment problem, Naval Research Logistics Quarterly, vol.3, issue.1-2, pp.83-97, 1955.
DOI : 10.2140/pjm.1953.3.369

URL : http://www.eecs.umich.edu/%7Epettie/matching/Kuhn-hungarian-assignment.pdf

J. Lellmann, D. A. Lorenz, C. Schönlieb, and T. Valkonen, Imaging with Kantorovich--Rubinstein Discrepancy, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.2833-2859, 2014.
DOI : 10.1137/140975528

URL : http://arxiv.org/pdf/1407.0221.pdf

B. Levy, A numerical algorithm for $l_2$ semi-discrete optimal transport in 3d, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01105021

H. Ling and K. Okada, An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.5, pp.840-853, 2007.
DOI : 10.1109/TPAMI.2007.1058

URL : http://www.cs.umd.edu/~hbling/publication/emd_pami_O.pdf

P. L. Lions and B. Mercier, Splitting Algorithms for the Sum of Two Nonlinear Operators, SIAM Journal on Numerical Analysis, vol.16, issue.6, pp.964-979, 1979.
DOI : 10.1137/0716071

G. Loeper and F. Rapetti, Numerical solution of the Monge???Amp??re equation by a Newton's algorithm, Comptes Rendus Mathematique, vol.340, issue.4, pp.319-324, 2005.
DOI : 10.1016/j.crma.2004.12.018

D. Lombardi and E. Maitre, Eulerian models and algorithms for unbalanced optimal transport, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, pp.1717-1744, 2015.
DOI : 10.1090/gsm/058

URL : https://hal.archives-ouvertes.fr/hal-00976501

D. Lorenz and T. Pock, An Inertial Forward-Backward Algorithm for Monotone Inclusions, Journal of Mathematical Imaging and Vision, vol.23, issue.3, pp.311-325, 2015.
DOI : 10.1137/110844805

URL : http://arxiv.org/pdf/1403.3522.pdf

J. Louet and F. Santambrogio, A sharp inequality for transport maps in <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> via approximation, Applied Mathematics Letters, vol.25, issue.3, pp.648-653, 2012.
DOI : 10.1016/j.aml.2011.10.006

J. Maas, M. Rumpf, C. Schönlieb, and S. Simon, A generalized model for optimal transport of images including dissipation and density modulation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, 2015.
DOI : 10.1007/978-3-540-39903-2_35

S. Mallat and I. Waldspurger, Phase Retrieval for the Cauchy Wavelet Transform, Journal of Fourier Analysis and Applications, vol.10, issue.3, 2014.
DOI : 10.1080/713817747

URL : http://arxiv.org/pdf/1404.1183

R. Mccann, Polar factorization of maps on Riemannian manifolds, Geometric and Functional Analysis, vol.11, issue.3, pp.589-608, 2001.
DOI : 10.1007/PL00001679

R. J. Mccann, A convexity principle for interacting gases. advances in mathematics, pp.153-179, 1997.

C. Mendoza, J. Perez-carrasco, A. Saez, B. Acha, and C. Serrano, Linearized Multidimensional Earth-Mover's-Distance Gradient Flows, IEEE Transactions on Image Processing, vol.22, issue.12, pp.5322-5335, 2013.
DOI : 10.1109/TIP.2013.2279952

Q. Mérigot, A Multiscale Approach to Optimal Transport, Computer Graphics Forum, vol.40, issue.2, pp.1583-1592, 2011.
DOI : 10.1007/978-3-540-71050-9

G. Monge, Mémoire sur la théorie des déblais et de remblais, Académie Royale des Sciences de Paris, pp.666-704

J. Morovic and P. Sun, Accurate 3D image colour histogram transformation, Pattern Recognition Letters, vol.24, issue.11, pp.1725-1735, 2003.
DOI : 10.1016/S0167-8655(02)00328-8

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 : 10.1109/TPAMI.1984.4767596

T. Möllenhoff, E. Strekalovskiy, M. Moeller, and D. Cremers, The Primal-Dual Hybrid Gradient Method for Semiconvex Splittings, SIAM Journal on Imaging Sciences, vol.8, issue.2, pp.827-857, 2015.
DOI : 10.1137/140976601

G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, 1988.
DOI : 10.1002/9781118627372

Y. E. Nesterov and A. S. Nemirovsky, Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms, 1993.
DOI : 10.1137/1.9781611970791

K. Ni, X. Bresson, T. F. Chan, and S. Esedoglu, Local Histogram Based Segmentation Using the Wasserstein Distance, International Journal of Computer Vision, vol.18, issue.9, pp.97-111, 2009.
DOI : 10.1090/gsm/058

URL : https://link.springer.com/content/pdf/10.1007%2Fs11263-009-0234-0.pdf

M. Nikolova, S. Esedoglu, and T. F. Chan, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, vol.66, issue.5, pp.1632-1648, 2006.

M. Nikolova, Y. Wen, and R. H. Chan, Exact Histogram Specification for Digital Images Using a Variational Approach, Journal of Mathematical Imaging and Vision, vol.51, issue.4, pp.309-325, 2013.
DOI : 10.1109/TCE.2005.1561863

URL : https://hal.archives-ouvertes.fr/hal-00723448

A. M. Oberman, Wide stencil finite difference schemes for the elliptic Monge- Ampere equation and functions of the eigenvalues of the hessian. Discrete and Continuous Dynamical Systems -Series B, pp.221-238, 2008.

A. M. Oberman and Y. Ruan, An efficient linear programming method for Optimal Transportation, 2015.

P. Ochs, Y. Chen, T. Brox, and T. Pock, iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, SIAM Journal on Imaging Sciences, vol.7, issue.2, pp.1388-1419, 2014.
DOI : 10.1137/130942954

URL : http://lmb.informatik.uni-freiburg.de/Publications/2014/OB14/ipiano.pdf

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://www.ann.jussieu.fr/~frey/papers/levelsets/Osher S., Fronts propagating with curvature dependent speed.pdf

N. Papadakis, V. Chabot, A. Makris, M. Nodet, and A. Vidard, Assimilation d'images et de structures, Colloque du Groupe d'Etudes du Traitement du Signal et des Images (GRETSI'13), 2013.
URL : https://hal.archives-ouvertes.fr/hal-00836062

N. Papadakis, G. Peyré, and E. Oudet, Optimal Transport with Proximal Splitting, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.212-238, 2014.
DOI : 10.1137/130920058

URL : https://hal.archives-ouvertes.fr/hal-00918460

N. Papadakis, E. Provenzi, and V. Caselles, A Variational Model for Histogram Transfer of Color Images, IEEE Transactions on Image Processing, vol.20, issue.6, pp.1682-1695, 2011.
DOI : 10.1109/TIP.2010.2095869

URL : https://hal.archives-ouvertes.fr/hal-00596053

O. Pele and M. Werman, A Linear Time Histogram Metric for Improved SIFT Matching, European Conference on Computer Vision (ECCV'08), pp.495-508, 2008.
DOI : 10.1109/CVPR.1997.609451

URL : http://www.cs.huji.ac.il/~werman/Papers/ECCV2008.pdf

O. Pele and M. Werman, Fast and robust Earth Mover's Distances, 2009 IEEE 12th International Conference on Computer Vision, pp.460-467, 2009.
DOI : 10.1109/ICCV.2009.5459199

URL : http://www.cs.huji.ac.il/~werman/Papers/ICCV2009.pdf

P. Pérez, M. Gangnet, and A. Blake, Poisson image editing, ACM Transactions on Computer Graphics and Interactive Techniques (SIGGRAPH'03), pp.313-331, 2003.

G. Peyré, J. Fadili, and J. Rabin, Wasserstein active contours, 2012 19th IEEE International Conference on Image Processing, p.2012
DOI : 10.1109/ICIP.2012.6467416

B. Piccoli and F. Rossi, Generalized wasserstein distance and its application to transport equations with source. Archive for Rational Mechanics and Analysis, pp.335-358, 2014.
DOI : 10.1007/s00205-013-0669-x

URL : http://arxiv.org/pdf/1206.3219.pdf

F. Pierre, J. Aujol, A. Bugeau, N. Papadakis, and V. Ta, Luminance-Chrominance Model for Image Colorization, SIAM Journal on Imaging Sciences, vol.8, issue.1, pp.536-563, 2015.
DOI : 10.1137/140979368

URL : https://hal.archives-ouvertes.fr/hal-01166919

F. Pitié and A. Kokaram, The linear Monge-Kantorovitch linear colour mapping for example-based colour transfer, IET 4th European Conference on Visual Media Production (CVMP 2007), pp.1-9, 2007.
DOI : 10.1049/cp:20070055

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

URL : http://gpu4vision.icg.tugraz.at/papers/2009/pock_convex.pdf

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, vol.40, issue.1, pp.49-71, 2000.
DOI : 10.1023/A:1026553619983

T. Pouli and E. Reinhard, Progressive color transfer for images of arbitrary dynamic range, Computers & Graphics, vol.35, issue.1, pp.67-80, 2011.
DOI : 10.1016/j.cag.2010.11.003

K. Punithakumar, J. Yuan, I. B. Ayed, S. Li, and Y. Boykov, A Convex Max-Flow Approach to Distribution-Based Figure-Ground Separation, SIAM Journal on Imaging Sciences, vol.5, issue.4, pp.1333-1354, 2012.
DOI : 10.1137/110850372

J. Rabin, J. Delon, and Y. Gousseau, Removing Artefacts From Color and Contrast Modifications, IEEE Transactions on Image Processing, vol.20, issue.11, pp.3073-3085, 2011.
DOI : 10.1109/TIP.2011.2142318

J. Rabin, S. Ferradans, and N. Papadakis, Adaptive color transfer with relaxed optimal transport, 2014 IEEE International Conference on Image Processing (ICIP), p.2014
DOI : 10.1109/ICIP.2014.7025983

URL : https://hal.archives-ouvertes.fr/hal-01002830

J. Rabin and N. Papadakis, Convex Color Image Segmentation with Optimal Transport Distances, Scale Space and Variational Methods in Computer Vision (SSVM'15), pp.241-252, 2015.
DOI : 10.1007/978-3-319-18461-6_21

URL : https://hal.archives-ouvertes.fr/hal-01133447

J. Rabin and N. Papadakis, Cosegmentation d'images non-supervisée utilisant les distances de sinkhorn, Colloque du Groupe d'Etudes du Traitement du Signal et des Images (GRETSI'15), 2015.

J. Rabin and N. Papadakis, Non-convex relaxation of optimal transport for color transfer, Conference on Geometric Science of Information (GSI'15, p.2015
DOI : 10.1007/978-3-319-25040-3_10

J. Rabin and G. Peyré, Wasserstein regularization of imaging problem, 2011 18th IEEE International Conference on Image Processing, pp.1541-1544, 2011.
DOI : 10.1109/ICIP.2011.6115740

J. Rabin, G. Peyré, J. Delon, and M. Bernot, Wasserstein Barycenter and Its Application to Texture Mixing, Scale Space and Variational Methods in Computer Vision (SSVM'11), pp.435-446, 2011.
DOI : 10.1109/18.119725

J. Rabin, G. Peyré, and L. Cohen, Geodesic Shape Retrieval via Optimal Mass Transport, European Conference on Computer Vision (ECCV'10), pp.771-784, 2010.
DOI : 10.1007/978-3-642-15555-0_56

URL : https://hal.archives-ouvertes.fr/hal-00498607

H. Raguet, J. Fadili, and G. Peyré, A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1199-1226, 2013.
DOI : 10.1137/120872802

URL : https://hal.archives-ouvertes.fr/hal-00613637

A. Rangarajan, A. L. Yuille, S. Gold, and E. Mjolsness, A convergence proof for the softassign quadratic assignment algorithm, Neural Information Processing Systems (NIPS'96), pp.620-626, 1996.
DOI : 10.1162/089976699300016313

URL : http://www.cis.ufl.edu/~anand/ps/nc.ps.gz

E. Reinhard, M. Adhikhmin, B. Gooch, and P. Shirley, Color transfer between images, IEEE Computer Graphics and Applications, vol.21, issue.4, pp.34-41, 2001.
DOI : 10.1109/38.946629

C. Rother, T. Minka, A. Blake, and V. Kolmogorov, Cosegmentation of Image Pairs by Histogram Matching - Incorporating a Global Constraint into MRFs, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Volume 1 (CVPR'06), pp.993-1000, 2006.
DOI : 10.1109/CVPR.2006.91

M. Rousson, T. Brox, and R. Deriche, Active unsupervised texture segmentation on a diffusion based feature space, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings., 2003.
DOI : 10.1109/CVPR.2003.1211535

URL : https://hal.archives-ouvertes.fr/inria-00071891

Y. Rubner, C. Tomasi, and L. Guibas, A metric for distributions with applications to image databases, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.59-66, 1998.
DOI : 10.1109/ICCV.1998.710701

URL : http://vision.stanford.edu/public/publication/rubner/rubnerIccv98.pdf

C. Schellewald, S. Roth, and C. Schnörr, Evaluation of a convex relaxation to a quadratic assignment matching approach for relational object views, Image and Vision Computing, vol.25, issue.8, pp.251301-1314, 2007.
DOI : 10.1016/j.imavis.2006.08.005

B. Schmitzer, A sparse algorithm for dense optimal transport, Scale Space and Variational Methods in Computer Vision (SSVM'15), pp.629-641, 2015.
DOI : 10.1007/978-3-319-18461-6_50

URL : https://hal.archives-ouvertes.fr/hal-01385274

B. Schmitzer and C. Schnörr, A Hierarchical Approach to Optimal Transport, Scale Space and Variational Methods in Computer Vision (SSVM'13), pp.452-464, 2013.
DOI : 10.1007/978-3-642-38267-3_38

B. Schmitzer and C. Schnörr, Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance, Journal of Mathematical Imaging and Vision, vol.123, issue.1, pp.143-159, 2013.
DOI : 10.1007/978-3-540-71050-9

B. Schmitzer and C. Schnörr, Globally Optimal Joint Image Segmentation and Shape Matching Based on Wasserstein Modes, Journal of Mathematical Imaging and Vision, vol.9, issue.1, pp.436-458, 2015.
DOI : 10.1007/978-3-642-12055-8

URL : http://arxiv.org/pdf/1407.3956

A. Schrijver, Theory of linear and integer programming, 1986.

V. Seguy and M. Cuturi, An Algorithmic Approach to Compute Principal Geodesics in the Wasserstein Space, 2015.

J. A. Sethian, A fast marching level set method for monotonically advancing fronts., Proc. of the National Academy of Sciences, pp.1591-1595, 1996.
DOI : 10.1073/pnas.93.4.1591

URL : http://www.pnas.org/content/93/4/1591.full.pdf

G. Sharma, F. Jurie, and C. Schmid, Expanded Parts Model for Human Attribute and Action Recognition in Still Images, 2013 IEEE Conference on Computer Vision and Pattern Recognition, pp.652-659, 2014.
DOI : 10.1109/CVPR.2013.90

URL : https://hal.archives-ouvertes.fr/hal-00816144

S. Shirdhonkar and D. Jacobs, Approximate earth mover's distance in linear time, IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08), pp.1-8, 2008.
DOI : 10.1109/cvpr.2008.4587662

R. Sinkhorn, Diagonal Equivalence to Matrices with Prescribed Row and Column Sums, The American Mathematical Monthly, vol.74, issue.4, pp.402-405, 1967.
DOI : 10.2307/2314570

J. Solomon, F. De-goes, G. Peyré, M. Cuturi, A. Butscher et al., Convolutional wasserstein distances, ACM Transactions on Graphics, vol.34, issue.4, p.2015
DOI : 10.1145/563858.563893

URL : https://hal.archives-ouvertes.fr/hal-01188953

J. Solomon, R. Rustamov, L. Guibas, and A. Butscher, Wasserstein propagation for semi-supervised learning, International Conference on machine Learning (ICML'14), pp.306-314, 2014.

G. Strang, Linear Algebra and Its Applications, 1988.

E. Strekalovskiy, A. Chambolle, and D. Cremers, Convex Relaxation of Vectorial Problems with Coupled Regularization, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.294-330, 2014.
DOI : 10.1137/130908348

Z. Su, K. Zeng, L. Liu, B. Li, and X. Luo, Corruptive Artifacts Suppression for Example-Based Color Transfer, IEEE Transactions on Multimedia, vol.16, issue.4, pp.988-999, 2014.
DOI : 10.1109/TMM.2014.2305914

URL : http://doi.org/10.1109/tmm.2014.2305914

M. Sulman, J. F. Williams, and R. D. Russell, Optimal mass transport for higher dimensional adaptive grid generation, Journal of Computational Physics, vol.230, issue.9, pp.3302-3330, 2011.
DOI : 10.1016/j.jcp.2011.01.025

P. Swoboda and C. Schnörr, Convex Variational Image Restoration with Histogram Priors, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1719-1735, 2013.
DOI : 10.1137/120897535

P. Swoboda and C. Schnörr, Variational Image Segmentation and Cosegmentation with the Wasserstein Distance, International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'13), pp.321-334, 2013.
DOI : 10.1007/978-3-642-40395-8_24

Y. Tai, J. Jia, and C. Tang, Local color transfer via probabilistic segmentation by expectation-maximization, IEEE Conference on Computer Vision and Pattern Recognition (CVPR'05), pp.747-754, 2005.

J. B. Tenenbaum, V. De-silva, and J. C. Langford, A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, vol.290, issue.5500, pp.2902319-2323, 2000.
DOI : 10.1126/science.290.5500.2319

O. Titaud, A. Vidard, I. Souopgui, and F. Dimet, Assimilation of Image Sequences in Numerical Models. Tellus A: Dynamic Meteorology and Oceanography, pp.30-47, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00391876

P. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

J. Tsitsiklis, Efficient algorithms for globally optimal trajectories, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1528-1538, 1995.
DOI : 10.1109/9.412624

URL : http://www.mit.edu/people/jnt/Papers/J058-95-jnt-traj.pdf

B. V?uv?u, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Advances in Computational Mathematics, vol.38, issue.3, pp.667-681, 2013.

L. A. Vese and T. F. Chan, A multiphase level set framework for image segmentation using the mumford and shah model, International Journal of Computer Vision, vol.50, issue.3, pp.271-293, 2002.
DOI : 10.1023/A:1020874308076

S. Vicente, V. Kolmogorov, and C. Rother, Joint optimization of segmentation and appearance models, 2009 IEEE 12th International Conference on Computer Vision, pp.755-762, 2009.
DOI : 10.1109/ICCV.2009.5459287

S. Vicente, V. Kolmogorov, and C. Rother, Cosegmentation Revisited: Models and Optimization, European Conference on Computer Visio (ECCV'10), pp.465-479, 2010.
DOI : 10.1007/978-3-642-15552-9_34

URL : http://www0.cs.ucl.ac.uk/staff/S.Vicente/papers/ECCV2010.pdf

C. Villani, Topics in Optimal Transportation, 2003.
DOI : 10.1090/gsm/058

C. Villani, Optimal Transport: Old and New. Grundlehren der mathematischen Wissenschaften, 2008.
DOI : 10.1007/978-3-540-71050-9

A. G. Wilson, The Use of Entropy Maximising Models, in the Theory of Trip Distribution, Mode Split and Route Split, Journal of Transport Economics and Policy, vol.3, issue.1, pp.108-126, 1969.

G. Xia, S. Ferradans, G. Peyré, and J. Aujol, Synthesizing and Mixing Stationary Gaussian Texture Models, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.476-508, 2014.
DOI : 10.1137/130918010

URL : https://hal.archives-ouvertes.fr/hal-00816342

X. Xiao and L. Ma, Color transfer in correlated color space, Proceedings of the 2006 ACM international conference on Virtual reality continuum and its applications, VRCIA '06, pp.305-309, 2006.
DOI : 10.1145/1128923.1128974

URL : http://cgm.cs.ntust.edu.tw/kay/2007-01-04 abstract/color transfer in correlated color space.pdf

R. Y?ld?zo?lu, J. Aujol, and N. Papadakis, Active contours without level sets, IEEE International Conference on Image Processing (ICIP'12), pp.2549-2552, 2012.

R. Y?ld?zo?lu, J. Aujol, and N. Papadakis, A Convex Formulation for Global Histogram Based Binary Segmentation, International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'13), pp.335-349, 2013.
DOI : 10.1007/978-3-642-40395-8_25

J. Yuan, C. Schnörr, and E. Mémin, Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation, Journal of Mathematical Imaging and Vision, vol.34, issue.2, pp.67-80, 2007.
DOI : 10.1137/1.9780898718003

Y. Yuan, E. Ukwatta, X. Tai, A. Fenster, and C. Schnörr, A fast global optimization-based approach to evolving contours with generic shape prior, UCLA Tech. Report CAM, pp.12-38, 2012.

M. Zaslavskiy, F. Bach, and J. Vert, A Path Following Algorithm for the Graph Matching Problem, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.12, pp.312227-2242, 2009.
DOI : 10.1109/TPAMI.2008.245

URL : https://hal.archives-ouvertes.fr/hal-00433567

M. Zaslavskiy, F. Bach, and J. Vert, Many-to-Many Graph Matching: A Continuous Relaxation Approach, European Conference on Machine Learning and Practice of Knowledge Discovery in Databases (ECML PKDD'10), pp.515-530, 2010.
DOI : 10.1007/978-3-642-15939-8_33

URL : https://hal.archives-ouvertes.fr/hal-00465916

Y. Zheng and D. Doermann, Robust point matching for nonrigid shapes by preserving local neighborhood structures, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.4, pp.643-649, 2006.
DOI : 10.1109/TPAMI.2006.81

S. Zhu, T. Lee, and A. Yuille, Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation, Proceedings of IEEE International Conference on Computer Vision, pp.416-423, 1995.
DOI : 10.1109/ICCV.1995.466909