The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Convolutional wasserstein distances: efficient optimal transportation on geometric domains
Open accessAbstract
This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images and triangle meshes, improving performance by orders of magnitude compared to previous work. To this end, we approximate optimal transportation distances using entropic regularization. The resulting objective contains a geodesic distance-based kernel that can be approximated with the heat kernel. This approach leads to simple iterative numerical schemes with linear convergence, in which each iteration only requires Gaussian convolution or the solution of a sparse, pre-factored linear system. We demonstrate the versatility and efficiency of our method on tasks including reflectance interpolation, color transfer, and geometry processing.
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Cites
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 36,808
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2005) · doi:10.1002/047174882x · Cited by 13,791
The Earth Mover's Distance as a Metric for Image Retrieval
Rubner, Y., Tomasi, C., & Guibas, L. J. (2000) · International Journal of Computer Vision · doi:10.1023/a:1026543900054 · Cited by 4,568
Self-citationTopics in Optimal Transportation
Villani, C. (2003) · Graduate Studies in Mathematics · doi:10.1090/gsm/058 · Cited by 4,412
Bregman, L. M. (1967) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(67)90040-7 · Cited by 2,618
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Benamou, J.-D., & Brenier, Y. (2000) · Numerische Mathematik · doi:10.1007/s002110050002 · Cited by 1,609
Implicit fairing of irregular meshes using diffusion and curvature flow
Desbrun, M., Meyer, M., Schröder, P., & Barr, A. H. (1999) · Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 · doi:10.1145/311535.311576 · Cited by 1,538
Deming, W. E., & Stephan, F. F. (1940) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177731829 · Cited by 1,537
Direct Methods for Sparse Linear Systems
Davis, T. A. (2006) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718881 · Cited by 1,443
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Cited by
Scaling algorithms for unbalanced optimal transport problems
Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F.-X. (2018) · Mathematics of Computation · doi:10.1090/mcom/3303 · Cited by 336
Self-citationCharacterMixer: Rig-Aware Interpolation of 3D Characters
Zhan, X., Fu, R., & Ritchie, D. (2024) · Computer Graphics Forum · doi:10.1111/cgf.15047
“We evaluate CharacterMixer by comparing to a state-of-the-art optimal transport approach for shape interpolation [SdGP ∗ 15] and a mesh-based data-driven method for shape correspondence and interpolation [ENK ∗ 21], showing that CharacterMixer generates intermediate shapes with higher visual…”
BackgroundMethodResultInfluential
Metadata
- Authors
- Solomon, J., de Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A., Du, T., & Guibas, L.
- Venue
- ACM Transactions on Graphics
- Published
- 2015-07-27
- Volume
- 34
- Issue
- 4
- Pages
- 1-11
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2009172320
- Cited by
- 481
- References
- 36
- FWCI
- 63.73
- Type
- journal article
- Language
- en
- Open access
- green
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