A multiscale approach to optimal transport

Computer Graphics Forum

Volumn 30, Issue 5, 2011, Pages 1583-1592

  Mérigot, Quentin ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; PROBABILITY DENSITY FUNCTION;

LEAST SQUARE MATCHING; LLOYD'S ALGORITHMS; MASS CONSTRAINTS; MULTI-SCALE APPROACHES; MULTISCALE NATURE; OPTIMAL TRANSPORT; PROBABILITY DENSITIES; WASSERSTEIN DISTANCE;

ITERATIVE METHODS;

EID: 84880847393     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2011.02032.x     Document Type: Article

References (24)

1. AURENHAMMER F., HOFFMANN F., ARONOV B.: Minkowski-type theorems and least-squares clustering. Algorithmica 20, 1 (1998), 61-76.
2. ANGENENT S., HAKER S., TANNENBAUM A.: Minimizing flows for the monge-kantorovich problem. SIAM journal on mathematical analysis 35, 1 (2003), 61-97.
3. BENAMOU J., BRENIER Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik 84, 3 (2000), 375-393.
4. BERTSEKAS D.: The auction algorithm: A distributed relaxation method for the assignment problem. Annals of Operations Research 14, 1 (1988), 105-123.
5. BOSC D.: Numerical approximation of optimal transport maps. Preprint, 2010.
6. BRENIER Y.: Polar factorization and monotone rearrangement of vector-valued functions. Communications on pure and applied mathematics 44, 4 (1991), 375-417.
7. BALZER M., SCHLÖMER T., DEUSSEN O.: Capacity-constrained point distributions: a variant of Lloyd's method. ACM Trans. Graph. 28 (2009), 86:1-86:8.
8. CHAZAL F. COHEN-STEINER D. MÉRIGOT Q.: Geometric inference for probability measures. Foundation of Computational Mathematics (2010). to appear.
9. CGAL Computational Geometry Algorithms Library. http://www.cgal.org.
10. DE GOES F. COHEN-STEINER D. ALLIEZ P. DESBRUN. M.: An optimal transport approach to robust reconstruction and simplification of 2D shapes. Preprint, 2011.
11. DELON J. SALOMON J. SOBOLEVSKI A.: Fast Transport Optimization for Monge Costs on the Circle. SIAM Journal on Applied Mathematics 70 7 (2010) 2239-2258.
12. FLETCHER R.: Practical methods of optimization. John Wiley & Sons 1987.
13. LIPMAN Y., DAUBECHIES I.: Conformal Wasserstein distances: comparing surfaces in polynomial time. Advances in Mathematics (2011).
14. LOEPER G., RAPETTI F.: Numerical solution of the Monge-Ampère equation by a Newton's algorithm. Comptes Rendus Mathematique 340, 4 (2005), 319-324.
15. LACHAND-ROBERT T., OUDET É.: Minimizing within convex bodies using a convex hull method. SIAM Journal on Optimization 16, 2 (2006), 368-379.
16. MCCANN R.: A Convexity Principle for Interacting Gases. Advances in Mathematics 128, 1 (1997), 153-179.
17. MULLEN P., DE GOES F., DESBRUN M., COHENSTEINER D., ALLIEZ P.: Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets. Computer Graphics Forum 29, 5 (2010), 1733-1741.
18. MULLEN P., MEMARI DE GOES F., DESBRUN M.: Hodge-Optimized Triangulations. In Proceedings of ACM SIGGRAPH 2011 (2011).
19. MACHADO MANHÃES DE CASTRO P., TOURNOIS J., ALLIEZ P., DEVILLERS O.: Filtering relocations on a Delaunay triangulation. In Computer Graphics Forum (2009), Vol. 28, Wiley Online Library, pp. 1465-1474.
20. MONGE G.: Mémoire sur la théorie des déblais et de remblais. In Histoire de l'Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique etde Physique pour la même année (1781), pp. 666-704.
21. MORÉ J., THUENTE D.: Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software (TOMS) 20, 3 (1994), 286-307.
22. OLIKER V.: Mathematical aspects of design of beam shaping surfaces in geometrical optics. In Trends in Nonlinear Analysis. Springer Verlag, 2003, p. 193.
23. RUBNER Y., TOMASI C., GUIBAS L.: The earth mover's distance as a metric for image retrieval. International Journal of Computer Vision 40, 2 (2000), 99-121.
24. VILLANI C.: Optimal transport: old and new. Springer Verlag, 2009.