A Multiscale Approach to Optimal Transport
In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport pro...
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| Vydané v: | Computer graphics forum Ročník 30; číslo 5; s. 1583 - 1592 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Oxford, UK
Blackwell Publishing Ltd
01.08.2011
Wiley |
| Predmet: | |
| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth‐mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart. |
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| AbstractList | In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart. In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multi-scale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multi-scale counterpart. [PUBLICATION ABSTRACT] |
| Author | Mérigot, Quentin |
| Author_xml | – sequence: 1 givenname: Quentin surname: Merigot fullname: Merigot, Quentin |
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| Cites_doi | 10.1002/cpa.3160440402 10.1145/192115.192132 10.1007/978-3-540-71050-9 10.1007/PL00009187 10.1111/j.1467-8659.2010.01782.x 10.1016/j.crma.2004.12.018 10.1145/2010324.1964998 10.1137/090772708 10.2139/ssrn.1730684 10.1006/aima.1997.1634 10.1016/j.aim.2011.01.020 10.1007/BF02186476 10.1145/1531326.1531392 10.1007/s002110050002 10.1137/040608039 10.1007/978-3-662-05281-5_4 10.1023/A:1026543900054 10.1137/S0036141002410927 10.1111/j.1467-8659.2011.02033.x |
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| References | Brenier Y.: Polar factorization and monotone rearrangement of vector-valued functions. Communications on pure and applied mathematics 44, 4 (1991), 375-417. 3. Benamou J., Brenier Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik 84, 3 (2000), 375-393. 1. 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. 1. Loeper G., Rapetti F.: Numerical solution of the Monge-Ampère equation by a Newton's algorithm. Comptes Rendus Mathematique 340, 4 (2005), 319-324. 1. Aurenhammer F., Hoffmann F., Aronov B.: Minkowski-type theorems and least-squares clustering. Algorithmica 20, 1 (1998), 61-76. 2, 3, 4, 7, 9. Angenent S., Haker S., Tannenbaum A.: Minimizing flows for the monge-kantorovich problem. SIAM journal on mathematical analysis 35, 1 (2003), 61-97. 1. Mullen P., De Goes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets. Computer Graphics Forum 29, 5 (2010), 1733-1741. 1. Lachand-Robert T., Oudet É.: Minimizing within convex bodies using a convex hull method. SIAM Journal on Optimization 16, 2 (2006), 368-379. 9. 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. 1. Villani C.: Optimal transport: old and new. Springer Verlag, 2009. 1, 3, 6. Fletcher R.: Practical methods of optimization. John Wiley & Sons, 1987. 4, 7. Moré J., Thuente D.: Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software (TOMS) 20, 3 (1994), 286-307. 8. 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. 1, 2. Bertsekas D.: The auction algorithm: A distributed relaxation method for the assignment problem. Annals of Operations Research 14, 1 (1988), 105-123. 1. McCann R.: A Convexity Principle for Interacting Gases. Advances in Mathematics 128, 1 (1997), 153-179. 8, 10. 1997; 128 2005; 340 1781 2011 2010 2010; 29 1991; 44 1988; 14 2006; 16 2003; 35 1987 2009 2000; 84 2000; 40 2003 2010; 70 1998; 20 2009; 28 1994; 20 e_1_2_8_16_2 e_1_2_8_17_2 e_1_2_8_18_2 e_1_2_8_19_2 e_1_2_8_12_2 e_1_2_8_23_2 e_1_2_8_24_2 e_1_2_8_14_2 e_1_2_8_25_2 e_1_2_8_15_2 e_1_2_8_9_2 Fletcher R. (e_1_2_8_13_2) 1987 e_1_2_8_2_2 e_1_2_8_4_2 e_1_2_8_3_2 e_1_2_8_6_2 e_1_2_8_5_2 Machado Manhães de Castro P. (e_1_2_8_20_2) 2009 e_1_2_8_8_2 e_1_2_8_7_2 e_1_2_8_10_2 e_1_2_8_21_2 e_1_2_8_11_2 e_1_2_8_22_2 |
| References_xml | – reference: Loeper G., Rapetti F.: Numerical solution of the Monge-Ampère equation by a Newton's algorithm. Comptes Rendus Mathematique 340, 4 (2005), 319-324. 1. – reference: Fletcher R.: Practical methods of optimization. John Wiley & Sons, 1987. 4, 7. – reference: Villani C.: Optimal transport: old and new. Springer Verlag, 2009. 1, 3, 6. – reference: Angenent S., Haker S., Tannenbaum A.: Minimizing flows for the monge-kantorovich problem. SIAM journal on mathematical analysis 35, 1 (2003), 61-97. 1. – reference: McCann R.: A Convexity Principle for Interacting Gases. Advances in Mathematics 128, 1 (1997), 153-179. 8, 10. – reference: 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. 1. – reference: Benamou J., Brenier Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik 84, 3 (2000), 375-393. 1. – reference: Mullen P., De Goes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets. Computer Graphics Forum 29, 5 (2010), 1733-1741. 1. – reference: Aurenhammer F., Hoffmann F., Aronov B.: Minkowski-type theorems and least-squares clustering. Algorithmica 20, 1 (1998), 61-76. 2, 3, 4, 7, 9. – reference: Bertsekas D.: The auction algorithm: A distributed relaxation method for the assignment problem. Annals of Operations Research 14, 1 (1988), 105-123. 1. – reference: Brenier Y.: Polar factorization and monotone rearrangement of vector-valued functions. Communications on pure and applied mathematics 44, 4 (1991), 375-417. 3. – reference: Lachand-Robert T., Oudet É.: Minimizing within convex bodies using a convex hull method. SIAM Journal on Optimization 16, 2 (2006), 368-379. 9. – reference: Moré J., Thuente D.: Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software (TOMS) 20, 3 (1994), 286-307. 8. – reference: 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. 1, 2. – reference: 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. 1. – year: 2011 – volume: 84 start-page: 375 issue: 3 year: 2000 end-page: 393 article-title: A computational fluid mechanics solution to the Monge‐Kantorovich mass transfer problem publication-title: Numerische Mathematik – volume: 340 start-page: 319 issue: 4 year: 2005 end-page: 324 article-title: Numerical solution of the Monge‐Ampère equation by a Newton's algorithm publication-title: Comptes Rendus Mathematique – year: 2009 – volume: 20 start-page: 286 issue: 3 year: 1994 end-page: 307 article-title: Line search algorithms with guaranteed sufficient decrease publication-title: ACM Transactions on Mathematical Software (TOMS) – volume: 28 start-page: 86:1 year: 2009 end-page: 86:8 article-title: Capacity‐constrained point distributions: a variant of Lloyd's method publication-title: ACM Trans. Graph. – volume: 29 start-page: 1733 issue: 5 year: 2010 end-page: 1741 article-title: Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets publication-title: Computer Graphics Forum – volume: 20 start-page: 61 issue: 1 year: 1998 end-page: 76 article-title: Minkowski‐type theorems and least‐squares clustering publication-title: Algorithmica – volume: 128 start-page: 153 issue: 1 year: 1997 end-page: 179 article-title: A Convexity Principle for Interacting Gases publication-title: Advances in Mathematics – volume: 35 start-page: 61 issue: 1 year: 2003 end-page: 97 article-title: Minimizing flows for the monge‐kantorovich problem publication-title: SIAM journal on mathematical analysis – year: 1987 – start-page: 193 year: 2003 – volume: 40 start-page: 99 issue: 2 year: 2000 end-page: 121 article-title: The earth mover's distance as a metric for image retrieval publication-title: International Journal of Computer Vision – start-page: 666 year: 1781 end-page: 704 – volume: 14 start-page: 105 issue: 1 year: 1988 end-page: 123 article-title: The auction algorithm: A distributed relaxation method for the assignment problem publication-title: Annals of Operations Research – volume: 44 start-page: 375 issue: 4 year: 1991 end-page: 417 article-title: Polar factorization and monotone rearrangement of vector‐valued functions publication-title: Communications on pure and applied mathematics – volume: 70 start-page: 2239 issue: 7 year: 2010 end-page: 2258 article-title: Fast Transport Optimization for Monge Costs on the Circle publication-title: SIAM Journal on Applied Mathematics – volume: 16 start-page: 368 issue: 2 year: 2006 end-page: 379 article-title: Minimizing within convex bodies using a convex hull method publication-title: SIAM Journal on Optimization – volume: 28 start-page: 1465 year: 2009 end-page: 1474 – year: 2010 – ident: e_1_2_8_7_2 doi: 10.1002/cpa.3160440402 – ident: e_1_2_8_22_2 doi: 10.1145/192115.192132 – ident: e_1_2_8_25_2 doi: 10.1007/978-3-540-71050-9 – ident: e_1_2_8_21_2 – ident: e_1_2_8_2_2 doi: 10.1007/PL00009187 – ident: e_1_2_8_18_2 doi: 10.1111/j.1467-8659.2010.01782.x – ident: e_1_2_8_15_2 doi: 10.1016/j.crma.2004.12.018 – ident: e_1_2_8_19_2 doi: 10.1145/2010324.1964998 – start-page: 1465 volume-title: Computer Graphics Forum year: 2009 ident: e_1_2_8_20_2 – ident: e_1_2_8_12_2 doi: 10.1137/090772708 – ident: e_1_2_8_6_2 doi: 10.2139/ssrn.1730684 – ident: e_1_2_8_17_2 doi: 10.1006/aima.1997.1634 – ident: e_1_2_8_14_2 doi: 10.1016/j.aim.2011.01.020 – volume-title: Practical methods of optimization year: 1987 ident: e_1_2_8_13_2 – ident: e_1_2_8_5_2 doi: 10.1007/BF02186476 – ident: e_1_2_8_8_2 doi: 10.1145/1531326.1531392 – ident: e_1_2_8_4_2 doi: 10.1007/s002110050002 – ident: e_1_2_8_9_2 – ident: e_1_2_8_16_2 doi: 10.1137/040608039 – ident: e_1_2_8_23_2 doi: 10.1007/978-3-662-05281-5_4 – ident: e_1_2_8_24_2 doi: 10.1023/A:1026543900054 – ident: e_1_2_8_3_2 doi: 10.1137/S0036141002410927 – ident: e_1_2_8_10_2 – ident: e_1_2_8_11_2 doi: 10.1111/j.1467-8659.2011.02033.x |
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| Title | A Multiscale Approach to Optimal Transport |
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