Volume 49, Number 6, November-December 2015
Special Issue - Optimal Transport
Page(s) 1745 - 1769
Published online 05 November 2015
  1. L. Ambrosio, Lecture notes on optimal transport problems. Mathematical aspects of evolving interfaces, Lectures given at the C.I.M.-C.I.M.E. joint Euro-summer school, Madeira, Funchal, Portugal, July 3–9, 2000, edited by P. Colli. Vol. 1812 of Lect. Notes Math. Springer, Berlin (2003) 1–52. [Google Scholar]
  2. L. Ambrosio and G. Buttazzo, Weak lower semicontinuous envelope of functionals defined on a space of measures. Ann. Mat. Pura Appl. 150 (1988) 311–339. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Math. Monogr. The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  4. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows: in Metric Spaces and in the Space of Probability Measures. Springer (2006). [Google Scholar]
  5. S. Angenent, S. Haker and A. Tannenbaum, Minimizing flows for the Monge–Kantorovich problem. SIAM J. Math. Anal. 35 (2003) 61–97. [CrossRef] [MathSciNet] [Google Scholar]
  6. V. Arnold, Sur la géométrie différentielle des groupes de lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits. Ann. Institut Fourier 16 (1966) 319–361. [Google Scholar]
  7. V. Arnold and B. Khesin, Topological Methods in Hydrodynamics. Springer (1998). [Google Scholar]
  8. M.F. Beg, M.I. Miller, A. Trouvé and L. Younes, Computational anatomy: Computing metrics on anatomical shapes. In Proc. of 2002 IEEE ISBI (2002) 341–344. [Google Scholar]
  9. M.F. Beg, M.I. Miller, A. Trouvé and L. Younes, Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vision 61 (2005) 139–157. [CrossRef] [Google Scholar]
  10. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge−Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Berkels, Al. Effland and M. Rumpf, Time discrete geodesic paths in the space of images. SIAM J. Imag. Sci. 8 (2015) 1457–1488. [CrossRef] [Google Scholar]
  12. M. Burger, J.A. Carrillo and M.-T. Wolfram, A mixed finite element method for nonlinear diffusion equations. Kinet. Relat. Models 3 (2010) 59–83. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Burger, M. Franek and C.-B. Schönlieb, Regularized regression and density estimation based on optimal transport. Appl. Math. Res. Express 2012 (2012) 209–253. [Google Scholar]
  14. G. Buttazzo and F. Santambrogio, A model for the optimal planning of an urban area. SIAM J. Math. Anal. 37 (2005) 514–530. [CrossRef] [MathSciNet] [Google Scholar]
  15. T. Chan, S. Esedoglu and K. Ni, Histogram Based Segmentation Using Wasserstein Distances. Scale Space and Variational Methods in Computer Vision. Springer (2007) 697–708. [Google Scholar]
  16. R. Chartrand, B. Wohlberg, K. Vixie, and E. Bollt, A gradient descent solution to the Monge−Kantorovich problem. Appl. Math. Sci. 3 (2009) 1071–1080. [MathSciNet] [Google Scholar]
  17. Ph.G. Ciarlet, Mathematical Elasticity, I: Three-dimensional elasticity. Vol. 20 of Stud. Math. Appl. Elsevier (1988). [Google Scholar]
  18. E.J. Dean and R. Glowinski, Numerical methods for fully nonlinear elliptic equations of the Monge–Ampère type. Comput. Methods Appl. Mech. Eng. 195 (2006) 1344–1386. [Google Scholar]
  19. J. Dolbeault, B. Nazaret and G. Savaré, A new class of transport distances between measures. Calc. Var. Partial Differ. Equ. 34 (2009) 193–231. [Google Scholar]
  20. P. Dupuis, U. Grenander and M.I. Miller, Variational problems on flows of diffeomorphisms for image matching. Quart. Appl. Math. 56 (1998) 587. [MathSciNet] [Google Scholar]
  21. D. Dupuis, U. Grenander and M.I. Miller, Variational problems on flows of diffeomorphisms for image matching. Quart. Appl. Math. 56 (1998) 587–600. [MathSciNet] [Google Scholar]
  22. B. Düring, D. Matthes and J.P. Milišic, A gradient flow scheme for nonlinear fourth order equations. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 935–959. [CrossRef] [MathSciNet] [Google Scholar]
  23. L.C. Evans, Partial Differential Equations and Monge-Kantorovich Mass Transfer, Current Developments in Mathematics. Papers from the conference held in Cambridge, MA, USA, 1997. Edited by R. Bott et al. International Press, Boston, MA (1999) 65–126. [Google Scholar]
  24. S. Ferradans, N. Papadakis, J. Rabin, G. Peyré and J.-F. Aujol, Regularized Discrete Optimal Transport, Scale Space and Variational Methods in Computer Vision. In Lect. Notes Comput. Sci. Springer (2013) 428–439. [Google Scholar]
  25. P.T. Fletcher, C. Lu, S.M. Pizer and S. Joshi, Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Trans. Medical Imaging 23 (2004) 995–1005. [Google Scholar]
  26. K. Grauman and T. Darrell, Fast Contour Matching Using Approximate Earth Mover’s Distance. In Proc. of the 2004 IEEE Computer Society Conference on. Computer Vision and Pattern Recognition CVPR 2004. IEEE 1 (2004) I–220. [Google Scholar]
  27. U. Grenander, Lectures in Pattern Theory. Appl. Math. Sci. Springer-Verlag (1981). [Google Scholar]
  28. E. Haber, T. Rehman and A. Tannenbaum, An efficient numerical method for the solution of the L2 optimal mass transfer problem. SIAM J. Sci. Comput. 32 (2010) 197–211. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  29. S. Haker, L. Zhu, A. Tannenbaum and S. Angenent, Optimal mass transport for registration and warping. Int. J. Comput. Vision 60 (2004) 225–240. [Google Scholar]
  30. S.C. Joshi and M.I. Miller, Landmark matching via large deformation diffeomorphisms. IEEE Trans. Image Process. 9 (2000) 1357–1370. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  31. L.V. Kantorovitch, On the translocation of masses. Dokl. Akad. Nauk. USSR 37 (1942) 227–229. [Google Scholar]
  32. L.V. Kantorovich, On a problem of monge. Usp. Mat. Nauk 3 (1948) 225–226. [Google Scholar]
  33. M. Kilian, N.J. Mitra and H. Pottmann. Geometric modeling in shape space. In ACM Trans. Graph. 26 (2007) 1–8. [Google Scholar]
  34. H. Ling and K. Okada, An efficient earth mover’s distance algorithm for robust histogram comparison. IEEE Trans. Pattern Anal. Mach. Intelligence 29 (2007) 840–853. [CrossRef] [Google Scholar]
  35. Y. Lipman and I. Daubechies, Conformal Wasserstein distances: Comparing surfaces in polynomial time. Adv. Math. 227 (2011) 1047–1077. [CrossRef] [MathSciNet] [Google Scholar]
  36. G. Loeper and F. Rapetti, Numerical solution of the Monge–Ampère equation by a Newton’s algorithm. C. R. Math. 340 (2005) 319–324. [Google Scholar]
  37. F. Mémoli, On the use of Gromov-Hausdorff distances for shape comparison. In Eurographics symposium on point-based graphics. The Eurographics Association (2007) 81–90. [Google Scholar]
  38. F. Mémoli, Gromov–Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11 (2011) 417–487. [CrossRef] [MathSciNet] [Google Scholar]
  39. M.I. Miller and L. Younes, Group actions, homeomorphisms and matching: a general framework. Int. J. Comput. Vision 41 (2001) 61–84. [CrossRef] [Google Scholar]
  40. M.I. Miller, A. Trouvé and L. Younes, On the metrics and Euler−Lagrange equations of computational anatomy. Ann. Rev. Biomed. Eng. 4 (2002) 375–405. [CrossRef] [Google Scholar]
  41. G. Monge, Mémoire sur la théorie des déblais et des remblais. De l’Imprimerie Royale (1781). [Google Scholar]
  42. J. Moser, On the volume elements on a manifold. Tran. Amer. Math. Soc. 120 (1965) 286–294. [CrossRef] [MathSciNet] [Google Scholar]
  43. J. Nečas and M. Šilhavý, Multipolar viscous fluids. Quart. Appl. Math. 49 (1991) 247–265. [MathSciNet] [Google Scholar]
  44. K. Ni, X. Bresson, T. Chan and S. Esedoglu, Local histogram based segmentation using the Wasserstein distance. Int. J. Comput. Vision 84 (2009) 97–111. [Google Scholar]
  45. A.M. Oberman, Wide stencil finite difference schemes for the elliptic Monge-Ampere equation and functions of the eigenvalues of the Hessian. Discrete Contin. Dyn. Syst. Ser. B 10 (2008) 221–238. [CrossRef] [MathSciNet] [Google Scholar]
  46. L. Oudre, J. Jakubowicz, P. Bianchi and Ch. Simon, Classification of periodic activities using the Wasserstein distance. IEEE Trans. Biomed. Eng. 59 (2012) 1610–1619. [Google Scholar]
  47. N. Papadakis, G. Peyré and E. Oudet, Optimal transport with proximal splitting. SIAM J. Imaging Sci. 7 (2014) 212–238. [CrossRef] [MathSciNet] [Google Scholar]
  48. G. Peyré, M. Péchaud, R. Keriven and L.D. Cohen, Geodesic methods in computer vision and graphics. Found. Trends Comput. Graph. Vision 5 (2010) 197–397. [CrossRef] [Google Scholar]
  49. G. Peyré, J. Fadili and J. Rabin, Wasserstein active contours. In Image Proc. of 19th IEEE International Conference (2012) 2541–2544. [Google Scholar]
  50. J. Rabin and G. Peyré, Wasserstein Regularization of Imaging Problem. In 18th IEEE International Conf. of Image Processing ICIP (2011) 1541–1544. [Google Scholar]
  51. J. Rabin, G. Peyré and L.D. Cohen, Geodesic Shape Retrieval via Optimal Mass Transport. In Computer Vision–ECCV 2010. Springer (2010) 771–784. [Google Scholar]
  52. J. Rabin, G. Peyré, J. Delon and M. Bernot, Wasserstein Barycenter and its Application to Texture Mixing. In Scale Space and Variational Methods in Computer Vision. Springer (2012) 435–446. [Google Scholar]
  53. Y. Rubner, C. Tomasi and L.J. Guibas, The earth mover’s distance as a metric for image retrieval. Int. J. Comput. Vision 40 (2000) 99–121. [CrossRef] [Google Scholar]
  54. M. Rumpf and B. Wirth, Variational time discretization of geodesic calculus. IMA J. Numer. Anal. 35 (2015) 1011–1046. [CrossRef] [Google Scholar]
  55. L.-Ph. Saumier, M. Agueh and B. Khouider, An efficient numerical algorithm for the L2 optimal transport problem with applications to image processing. Preprint arXiv:1009.6039 (2010). [Google Scholar]
  56. B. Schmitzer and Ch. Schnörr, A Hierarchical Approach to Optimal Transport. In Scale Space and Variational Methods in Computer Vision. Springer (2013) 452–464. [Google Scholar]
  57. B. Schmitzer and Ch. Schnörr, Modelling convex shape priors and matching based on the Gromov-Wasserstein distance. J. Math. Imaging and Vision 46 (2013) 143–159. [CrossRef] [MathSciNet] [Google Scholar]
  58. B. Schmitzer and Ch. Schnörr, Object segmentation by shape matching with Wasserstein modes. In Energy Minimization Methods in Computer Vision and Pattern Recognition. Springer (2013) 123–136. [Google Scholar]
  59. J.W. Strutt. Theory of sound. Vol. 2. Dover Publications (1945). [Google Scholar]
  60. A. Trouvé and L. Younes, Metamorphoses through Lie group action. Found. Comput. Math. 5 (2005) 173–198. [CrossRef] [MathSciNet] [Google Scholar]
  61. C. Villani,Topics in optimal transportation. American Mathematical Soc. (2003) 58. [Google Scholar]
  62. C. Villani,Optimal transport: old and new. Vol. 338. Springer (2008). [Google Scholar]
  63. B. Wirth, L. Bar, M. Rumpf and G. Sapiro, A continuum mechanical approach to geodesics in shape space. Int. J. Comput. Vision 93 (2011) 293–318. [CrossRef] [Google Scholar]
  64. L. Zhu, S. Haker and A. Tannenbaum, Area-preserving mappings for the visualization of medical structures. Springer (2003). [Google Scholar]
  65. L. Zhu, Y. Yang, S. Haker and A. Tannenbaum, An image morphing technique based on optimal mass preserving mapping. IEEE Trans. Image Process. 16 (2007) 1481–1495. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]

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