EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 64 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 64
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2024008
Published online 12 September 2024
  1. C. de Boor, Best approximation properties of spline functions of odd degree. J. Math. Mech. 12 (1963) 747–749. [MathSciNet] [Google Scholar]
  2. L. Noakes, G. Heinzinger and B. Paden, Cubic splines on curved spaces. IMA J. Math. Control Inform. 6 (1989) 465–473. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [Google Scholar]
  4. F. Otto, The geometry of dissipative evolution equations: the porous medium equation (2001). [Google Scholar]
  5. N. Gigli, Second order analysis on (p-2(m), w-2). Mem. Am. Math. Soc. 216 (2012) VII. [Google Scholar]
  6. J.-D. Benamou, T. O. Gallouët and F.-X. Vialard, Second-order models for optimal transport and cubic splines on the Wasserstein space. Found. Comput. Math. 19 (2019) 1113–1143. [CrossRef] [MathSciNet] [Google Scholar]
  7. Y. Chen, G. Conforti and T. T. Georgiou, Measure-valued spline curves: an optimal transport viewpoint. SIAM J. Numer. Anal. 50 (2018) 5947–5968. [CrossRef] [Google Scholar]
  8. S. Chewi, J. Clancy, T. Le Gouic, P. Rigollet, G. Stepaniants and A. Stromme. Fast and smooth interpolation on Wasserstein space, in International Conference on Artificial Intelligence and Statistics. PMLR (2021) 3061–3069. [Google Scholar]
  9. A. Trouvé and F.-X. Vialard, Shape splines and stochastic shape evolutions: a second order point of view. Quart. Appl. Math. 70 (2012) 219–251. [CrossRef] [MathSciNet] [Google Scholar]
  10. N. Singh, F.-X. Vialard and M. Niethammer, Splines for diffeomorphisms. Med. Image Anal. 25 (2015) 56–71. [CrossRef] [Google Scholar]
  11. R. Tahraoui and F.-X. Vialard, Minimizing acceleration on the group of diffeomorphisms and its relaxation. ESAIM Control Optim. Calc. Var. 25 (2019). [Google Scholar]
  12. F.-X. Vialard, Variational second-order interpolation on the group of diffeomorphisms with a right-invariant metric, in Mathematics Of Shapes and Applications. World Scientific (2020) 1–14. [Google Scholar]
  13. Y. Chen and J. Karlsson, State tracking of linear ensembles via optimal mass transport. IEEE Control Syst. Lett. 2 (2018) 260–265. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Clancy. Interpolating Spline Curves of Measures. PhD thesis, Massachusetts Institute of Technology, 2021. [Google Scholar]
  15. A. Karimi and T.T. Georgiou, Regression analysis of distributional data through multi-marginal optimal transport. ArXiv preprint arXiv:2106.15031, 2021. [Google Scholar]
  16. E. Zhang and L. Noakes, Riemannian cubics and elastica in the manifold spd(n) of all n × n symmetric positivedefinite matrices. J. Geom. Mech. 11 (2019) 277–299. [CrossRef] [MathSciNet] [Google Scholar]
  17. D. Bures, An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras. Trans. Am. Math. Soc. 135 (1969) 199–212. [Google Scholar]
  18. P.J. Forrester and M. Kieburg, Relating the bures measure to the cauchy two-matrix model. Commun. Math. Phys. 342 (2016) 151–187. [CrossRef] [Google Scholar]
  19. R. Bhatia, T. Jain and Y. Lim, On the Bures–Wasserstein distance between positive definite matrices, 2017. [Google Scholar]
  20. L. Malagò, L. Montrucchio and G. Pistone, Wasserstein Riemannian geometry of Gaussian densities. Inform. Geom. 1 (2018) 137–179. [CrossRef] [Google Scholar]
  21. J. Justiniano, M. Rajković and M. Rumpf, Consistent approximation of interpolating splines in image metamorphosis. J. Math. Imaging Vis. 65 (2023) 29–52. [CrossRef] [Google Scholar]
  22. U. Mosco, Convergence of convex sets and of solutions of variational inequalities. Adv. Math. 3 (1969) 510–585. [CrossRef] [Google Scholar]
  23. B. Heeren, M. Rumpf and B. Wirth, Variational time discretization of Riemannian splines. IMA J. Numer. Anal. 39 (2018) 61–104. [Google Scholar]
  24. B. Heeren, M. Rumpf, P. Schröder, M. Wardetzky and B. Wirth, Splines in the space of shells, in Computer Graphics Forum, Vol. 35. Wiley Online Library (2016) 111–120. [CrossRef] [Google Scholar]
  25. Y. Nesterov, Smooth minimization of non-smooth functions. Math. Program. 103 (2005) 127–152. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Villani, Optimal Transport: Old and New, Vol. 338. Springer (2009). [CrossRef] [Google Scholar]
  27. Y.V. Prokhorov, Convergence of random processes and limit theorems in probability theory. Theory Prob. Applic. 1 (1956) 157–214. [CrossRef] [Google Scholar]
  28. J. Lott, Some geometric calculations on Wasserstein space. ArXiv preprint math/0612562 (2006). [Google Scholar]
  29. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows: In Metric Spaces and In the Space of Probability Measures. Springer Science & Business Media (2005). [Google Scholar]
  30. L. Ambrosio and N. Gigli. A user’s guide to optimal transport. In Modelling and optimisation of flows on networks, pages 1–155. Springer, 2013. [Google Scholar]
  31. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44 (1991) 375–417. [Google Scholar]
  32. R.J. McCann, Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal. 11 (2001) 589–608. [CrossRef] [MathSciNet] [Google Scholar]
  33. G. Peyré, M. Cuturi, et al., Computational optimal transport: With applications to data science. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  34. M. Rumpf and B. Wirth, Variational time discretization of geodesic calculus. IMA J. Numer. Anal. 35 (2015) 1011–1046. [Google Scholar]
  35. A. Braides, Local Minimization, Variational Evolution and Γ-convergence, Vol. 2094. Springer (2014). [CrossRef] [Google Scholar]
  36. M. Cuturi. Sinkhorn distances: lightspeed computation of optimal transport. Adv. Neural Information Process. Syst. 26 (2013). [Google Scholar]
  37. M. Cuturi and A. Doucet, Fast computation of wasserstein barycenters, in International Conference on Machine Learning. PMLR (2014) 685–693. [Google Scholar]
  38. B. Schmitzer, Stabilized sparse scaling algorithms for entropy regularized transport problems. SIAM J. Sci. Comput. 41 (2019) A1443–A1481. [Google Scholar]
  39. B. Charlier, J. Feydy, J.A. Glaunès, F.-D. Collin and G. Durif, Kernel operations on the gpu, with autodiff, without memory overflows. J. Mach. Learn. Res. 22 (2021) 1–6. [Google Scholar]
  40. J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna and G. Peyré, Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37 (2015) A1111–A1138. [CrossRef] [Google Scholar]
  41. A. Houdard, A. Leclaire, N. Papadakis and J. Rabin. Wasserstein generative models for patch-based texture synthesis. CoRR, abs/2007.03408, 2020. [Google Scholar]
  42. D. Ulyanov, V. Lebedev, A. Vedaldi and V. Lempitsky, Texture networks: Feed-forward synthesis of textures and stylized images. ArXiv preprint arXiv:1603.03417 (2016). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.