Wasserstein barycenter and its application to texture mixing

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6667 LNCS, Issue , 2012, Pages 435-446

  Rabin, Julien ^a   Peyré, Gabriel ^b   Delon, Julie ^c   Bernot, Marc ^d  

^a Paris Descartes University   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c INSTITUT TELECOM   (France)

^d THALES ALENIA SPACE   (France)

Author keywords

barycenter of distributions; Optimal transport; texture synthesis and mixing

Indexed keywords

AS DISTRIBUTION; BARYCENTERS; COLOR TEXTURES; CONVEX DOMAINS; DISCRETE PROBABILITY DISTRIBUTION; GRADIENT DESCENT ALGORITHMS; MULTISCALES; OPTIMAL TRANSPORT; ORIENTED FILTER; POINT CLOUD; TEXTURE SYNTHESIS; TIME COMPLEXITY; WASSERSTEIN METRIC;

COMPUTER APPLICATIONS; COMPUTER VISION; FILTER BANKS; OPTIMIZATION; TEXTURES;

PROBABILITY DISTRIBUTIONS;

EID: 84855704498     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-24785-9_37     Document Type: Conference Paper

References (32)

1. Villani, C.: Topics in Optimal Transportation. American Math. Society (2003)
2. Rubner, Y., Tomasi, C., Guibas, L.J.: The Earth Mover's Distance as a Metric for Image Retrieval. International Journal of Computer Vision 40, 99-121 (2000)
3. Pitié, F., Kokaram, A.: The Linear Monge-Kantorovitch Colour Mapping for Example-Based Colour Transfer. In: Proc. of CVMP 2006 (2006)
4. Dominitz, A., Tannenbaum, A.: Texture mapping via optimal mass transport. IEEE Transactions on Visualization and Computer Graphics 16, 419-433 (2009)
5. Delon, J.: Movie and video scale-time equalization application to flicker reduction. IEEE Trans. Image Proc. 15, 241-248 (2006)
6. Ambrosio, L., Caffarelli, L.A., Brenier, Y., Buttazzo, G., Villani, C.: Optimal Transportation and Applications. Mathematics and statistics edn. Lecture Notes in Mathematics, vol. 1813. Springer, Heidelberg (2003)
7. Efros, A.A., Leung, T.K.: Texture synthesis by non-parametric sampling. In: Proc. of ICCV 1999, p. 1033 (1999)
8. Wei, L.Y., Levoy, M.: Fast texture synthesis using tree-structured vector quantization. In: Proc. Siggraph 2000, pp. 479-488 (2000)
9. Efros, A., Freeman, W.: Image quilting for texture synthesis and transfer. ACM Trans. on Graphics, 341-346 (2001)
10. Ashikhmin, M.: Synthesizing natural textures. In: SI3D 2001: Proceedings of the 2001 Symposium on Interactive 3D Graphics, pp. 217-226 (2001)
11. Lefebvre, S., Hoppe, H.: Parallel controllable texture synthesis. ACM Trans. on Graphics 24, 777-786 (2005)
12. Kwatra, V., Essa, I., Bobick, A., Kwatra, N.: Texture optimization for example-based synthesis. ACM Trans. on Graphics 24, 795-802 (2005)
13. Kwatra, V., Schdl, A., Essa, I., Turk, G., Bobick, A.: Graphcut textures: Image and video synthesis using graph cuts. ACM Trans. on Graphics 22, 277-286 (2003)
14. Perlin, K.: An image synthesizer. In: Proc. Siggraph 1985, pp. 287-296. ACM Press, New York (1985)
15. Bonet, J.S.D.: Multiresolution sampling procedure for analysis and synthesis of texture images. In: Proc. Siggraph 1997, pp. 361-368. ACM Press, New York (1997)
16. Paget, R., Longstaff, I.D.: Texture synthesis via a noncausal nonparametric multiscale markov random field. IEEE Trans. Image Proc. 7, 925-931 (1998)
17. Mumford, D., Gidas, B.: Stochastic models for generic images. Q. Appl. Math. LIV, 85-111 (2001)
18. Heeger, D.J., Bergen, J.R.: Pyramid-Based texture analysis/synthesis. In: Proc. Siggraph 1995. Annual Conference Series, ACM SIGGRAPH, pp. 229-238 (1995)
19. Cook, R., DeRose, T.: Wavelet noise. ACM Trans. on Graphics 24, 803-811 (2005)
20. Portilla, J., Simoncelli, E.P.: A parametric texture model based on joint statistics of complex wavelet coefficients. Int. Journal of Computer Vision 40, 49-70 (2000)
21. Bar-Joseph, Z., El-Yaniv, R., Lischinski, D., Werman, M.: Texture mixing and texture movie synthesis using statistical learning. IEEE Transactions on Visualization and Computer Graphics 7, 120-135 (2001)
22. Peyré, G.: Texture synthesis with grouplets. IEEE Trans. Patt. Anal. and Mach. Intell. 32, 733-746 (2010)
23. Hertzmann, A., Jacobs, C.E., Oliver, N., Curless, B., Salesin, D.H.: Image analogies. In: ACM (ed.) Proc. Siggraph 2001, pp. 327-340. ACM Press, New York (2001)
24. Liu, Z., Liu, C., Shum, H.Y., Yu, Y.: Pattern-based texture metamorphosis. In: Proc. Pacific Graphics 2002, pp. 184-193. IEEE Computer Society, Los Alamitos (2002)
25. Tonietto, L., Walter, M.: Texture metamorphosis driven by texton masks. Computers and Graphics 29, 697-703 (2005)
26. Tal, A., Elber, G.: Image morphing with feature preserving texture. Comput. Graph. Forum 18, 339-348 (1999)
27. Matusik, W., Zwicker, M., Durand, F.: Texture design using a simplicial complex of morphable textures. ACM Trans. on Graphics 24, 787-794 (2005)
28. Burkard, R., Dell'Amico, M., Martello, S.: Assignment Problems. SIAM, Philadelphia (2009)
29. Rabin, J., Peyré, G., Cohen, L.D.: Geodesic shape retrieval via optimal mass transport. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6315, pp. 771-784. Springer, Heidelberg (2010)
30. Dowson, D.C., Landau, B.V.: The Fréchet distance between multivariate normal distributions. Journal of Multivariate Analysis 12, 450-455 (1982)
31. Agueh, M., Carlier, G.: Barycenters in the Wasserstein space. To appear in SIAM Journal on Mathematical Analysis (2011)
32. Simoncelli, E.P., Freeman, W.T., Adelson, E.H., Heeger, D.J.: Shiftable multiscale transforms. IEEE Trans. Info. Theory 38, 587-607 (1992)