Dirichlet energy for analysis and synthesis of soft maps

Computer Graphics Forum

Volumn 32, Issue 5, 2013, Pages 197-206

  Solomon, Justin ^a   Guibas, Leonidas ^a   Butscher, Adrian ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS;

ANALYSIS AND SYNTHESIS; COMBINATORIAL COMPLEXITY; DIRICHLET ENERGY; DISCRETIZATIONS; OTHER PROPERTIES; POINT TO POINT; SURFACE MAPPING;

PROBABILITY DISTRIBUTIONS;

EID: 84882751286     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/cgf.12186     Document Type: Article

References (39)

1. Ambrosio L., Gigli N., Savaré G.,: Gradient flows: in metric spaces and in the space of probability measures. Springer, 2005. 4.
2. Aubry M., Schlickewei U., Cremers D.,: The wave kernel signature: A quantum mechanical approach to shape analysis. In Computer Vision Workshops (ICCV) (2011), pp. 1626-1633. 7.
3. Anguelov D., Srinivasan P., Pang H.-C., Koller D., Thrun S., Davis J.,: The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In NIPS (2004). 1.
4. Bartels S.,: Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces. Math. Computation 79, 271 (2010), 1263-1301. 2.
5. Benamou J.-D., Brenier Y.,: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik 84, 3 (2000), 375-393. 4.
6. Berg A., Berg T., Malik J.,: Shape matching and object recognition using low distortion correspondences. In CVPR (2005), vol. 1, pp. 26-33. 2.
7. Ben-Chen M., Butscher A., Solomon J., Guibas L.,: On discrete Killing vector fields and patterns on surfaces. CGF 29, 5 (2010), 1701-1711. 9.
8. Ben-Chen M., Weber O., Gotsman C.,: Variational harmonic maps for space deformation. TOG 28, 3 (2009), 34:1-34:11. 2.
9. Chao I., Pinkall U., Sanan P., Schröder P.,: A simple geometric model for elastic deformations. TOG 29, 4 (July 2010), 38:1-38:6. 2.
10. De Goes F., Cohen-Steiner D., Alliez P., Desbrun M.,: An optimal transport approach to robust reconstruction and simplification of 2d shapes. In CGF (2011), vol. 30, pp. 1593-1602. 3.
11. Desbrun M., Meyer M., Alliez P.,: Intrinsic parameterizations of surface meshes. In CGF (2003), vol. 21, pp. 209-218. 2.
12. Eck M., DeRose T., Duchamp T., Hoppe H., Lounsbery M., Stuetzle W.,: Multiresolution analysis of arbitrary meshes. In SIGGRAPH (1995), pp. 173-182. 2.
13. Floater M., Hormann K.,: Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling, Dodgson N., Floater M., Sabin M., (Eds.), Mathematics and Visualization. Springer, 2005, pp. 157-186. 2.
14. GU X., YAU S.-T.,: Computing conformal structures of surfaces. 121-146. 2.
15. Hirani A.,: Discrete Exterior Calculus. PhD thesis, Caltech, 2003. 8.
16. Hélein F., Wood J.,: Harmonic maps. In Handbook of global analysis. Elsevier Science, 2008, pp. 417-491. 2.
17. Huang Q.-X., Zhang G.-X., Gao L., Hu S.-M., Butscher A., Guibas L.,: An optimization approach for extracting and encoding consistent maps in a shape collection. TOG 31, 6 (2012), 167:1-167:11. 2.
18. Jost J.,: Equilibrium maps between metric spaces. Calc. Var. and PDE 2 (1994), 173-204. 3.
19. Kim V. G., Lipman Y., Funkhouser T.,: Blended intrinsic maps. TOG 30, 4 (2011), 79:1-79:12. 2.
20. Kim V. G., Li W., Mitra N. J., DiVerdi S., Funkhouser T.,: Exploring collections of 3d models using fuzzy correspondences. TOG 31, 4 (2012), 54:1-54:11. 1, 2.
21. Lipman Y., Daubechies I.,: Conformal Wasserstein distances: Comparing surfaces in polynomial time. Advances in Mathematics 227, 3 (2011), 1047-1077. 3.
22. Lipman Y., Funkhouser T.,: Möbius voting for surface correspondence. TOG 28, 3 (July 2009), 72:1-72:12. 2.
23. Ling H., Okada K.,: Diffusion distance for histogram comparison. In CVPR (2006), vol. 1, pp. 246-253. 3. (Pubitemid 44931337)
24. Lipman Y., Puente J., Daubechies I.,: Conformal Wasserstein distance: Ii. computational aspects and extensions. arXiv preprint:1103.4681 (2011). 3.
25. Mémoli F.,: Gromov-Wasserstein distances and the metric approach to object matching. Foundations of Computational Mathematics 11, 4 (2011), 417-487. 3.
26. Monge G.,: Mémoire sur la théorie des déblais et remblais, mémoires acad. Royale Sci. Paris (1781). 3.
27. Nocedal J., Wright S.,: Numerical Optimization, 2 ed. Springer, 2006. 8.
28. Ovsjanikov M., Ben-Chen M., Solomon J., Butscher A., Guibas L.,: Functional maps: A flexible representation of maps between shapes. TOG 31, 4 (2012). 2, 5.
29. Ovsjanikov M., Mérigot Q., Mémoli F., Guibas L.,: One point isometric matching with the heat kernel. In CGF (2010), vol. 29, pp. 1555-1564. 2.
30. Pilanci M., El Ghaoui L., Chandrasekaran V.,: Recovery of sparse probability measures via convex programming. In NIPS (Dec. 2012). 9.
31. Rubner Y., Tomasi C., Guibas L. J.,: A metric for distributions with applications to image databases. In ICCV (1998), pp. 59-66. 3.
32. Solomon J., Nguyen A., Butscher A., Ben-Chen M., Guibas L.,: Soft maps between surfaces. In CGF (2012), vol. 31, pp. 1617-1626. 1, 2, 3, 4, 5, 7, 9.
33. Sun J., Ovsjanikov M., Guibas L.,: A concise and provably informative multi-scale signature based on heat diffusion. In SGP (2009), pp. 1383-1392. 7.
34. Tevs A., Berner A., Wand M., Ihrke I., Seidel H.-P.,: Intrinsic shape matching by planned landmark sampling. CGF 30, 2 (2011), 543-552. 2.
35. Villani C.,: Topics in optimal transportation, vol. 58. American Mathematical Soc., 2003. 4, 10.
36. Witte F. P., Lucas D.,: Probabilistic tracking in a multitarget environment. In IEEE Conf. on Decision and Control (1978), vol. 17, pp. 1212-1216. 2.
37. Windheuser T., Schlickwei U., Schimdt F. R., Cremers D.,: Large-scale integer linear programming for orientation preserving 3d shape matching. CGF 30, 5 (2011), 1471-1480. 2.
38. Yan W., Wang Q., Liu Q., Lu H., Ma S.,: Topology-preserved diffusion distance for histogram comparison. In British Machine Vision Conf. (2007). 3.
39. Zhang H., Sheffer A., Cohen-Or D., Zhou Q., Van Kaick O., Tagliasacchi A.,: Deformation-driven shape correspondence. In SGP (2008), pp. 1431-1439. 2.