Soft maps between surfaces

Computer Graphics Forum

Volumn 31, Issue 5, 2012, Pages 1617-1626

  Solomon, Justin ^a   Nguyen, Andy ^a   Butscher, Adrian ^a   Ben Chen, Mirela ^a   Guibas, Leonidas ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX OPTIMIZATION; MAPPING; MATRIX ALGEBRA;

GLOBAL SCALE; ISOMETRIC SURFACES; LINEAR-ALGEBRAIC; LOW RANK APPROXIMATIONS; MAPPING PROCESS; POINT TO POINT; PROBABILISTIC RELAXATION; USING PROBABILITIES;

APPROXIMATION THEORY;

EID: 84870201932     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2012.03167.x     Document Type: Article

References (36)

1. AUBRY M., SCHLICKEWEI U., CREMERS D.: The wave kernel signature: A quantum mechanical approach to shape analysis. In ICCV Workshops (2011), pp. 1626-1633. 3, 4, 7
2. 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). 3
3. BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching. PNAS 103, 5 (2006), 1168- 1172. 2
4. BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Numerical Geometry of Non-Rigid Shapes. Springer, 2008. 2
5. BERG A., BERG T., MALIK J.: Shape matching and object recognition using low distortion correspondences. In CVPR (2005), vol. 1, IEEE, pp. 26-33. 3
6. BURKARD R., DELL'AMICO M., MARTELLO S.: Assignment problems. SIAM, 2009. 4
7. CHANG W., LI H., MITRA N., PAULY M., RUSINKIEWICZ S., WAND M.: Computing correspondences in geometric data sets. Eurographics tutorial (2011). 2
8. GEBAL K., BÆRENTZEN J., AANÆS H., LARSEN R.: Shape analysis using the auto diffusion function. In Comp. Graph. Forum (2009), vol. 28, pp. 1405-1413. 2
9. HAKER S., ZHU L., TANNENBAUM A., ANGENENT S.: Optimal mass transport for registration and warping. Int. J. Comp. Vision 60, 3 (Dec. 2004), 225-240. 3
10. IBM, INC: IBM ILOG CPLEX optimizer. See http://www-01.ibm.com/software/ integration/optimization/cplex-optimizer/. 5
11. KIM V. G., LIPMAN Y., CHEN X., FUNKHOUSER T.: Möbius transformations for global intrinsic symmetry analysis. Proc. SGP (2010). 2
12. KIM V., LIPMAN Y., FUNKHOUSER T.: Blended intrinsic maps. Proc. SIGGRAPH (2011). 2, 8
13. LIPMAN Y., DAUBECHIES I.: Conformal wasserstein distances: Comparing surfaces in polynomial time. Adv. Mathematics 227, 3 (2011), 1047-1077. 3
14. LIPMAN Y., FUNKHOUSER T.: Möbius voting for surface correspondence. Trans. Graph. 28 (2009), 72:1-72:12. 2, 3
15. MÉMOLI F.: On the use of Gromov-Hausdorff distances for shape comparison. In Point Based Graphics (2007), pp. 81-90. 3
16. MÉMOLI F.: Spectral Gromov-Wasserstein distances for shape matching. In Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (2009). 3
17. MÉMOLI F.: A spectral notion of Gromov-Wassersteindistance and related methods. Applied and Computational Harmonic Analysis 30, 3 (2011), 363-401. 3
18. MÉMOLI F., SAPIRO G., THOMPSON P.: Geometric surface and brain warping via geodesic minimizing lipschitz extensions. In MFCA-2006 Int. Workshop on Math. Found. of Comp. Anatomy (2006), pp. 58-67. 5
19. NGUYEN A., BEN-CHEN M., WELNICKA K., YE Y., GUIBAS L.: An optimization approach to improving collections of shape maps. Comp. Graph. Forum 30, 5 (2011), 1481-1491. 3, 9
20. OVSJANIKOV M., BEN-CHEN M., SOLOMON J., BUTSCHER A., GUIBAS L.: Functional maps: A flexible representation of maps between shapes. Proc. SIGGRAPH, to appear (2012). 9
21. OVSJANIKOV M., MÉRIGOT Q., MÉMOLI F., GUIBAS L.: One point isometric matching with the heat kernel. Comp. Graph. Forum 29, 5 (2010), 1555-1564. 2
22. OVSJANIKOV M., SUN J., GUIBAS L.: Global intrinsic symmetries of shapes. In Comp. Graph. Forum (2008), vol. 27, pp. 1341-1348. 2
23. PELE O., WERMAN M.: Fast and robust earth mover's distances. In ICCV (2009). 4
24. RAVIV D., BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Full and partial symmetries of non-rigid shapes. IJCV89, 1 (2010), 18-39. 2
25. RANGARAJAN A., CHUI H., BOOKSTEIN F.: The soft-assign procrustes matching algorithm. In Information Processing in Medical Imaging (1997), Springer, pp. 29-42. 3
26. SOLOMON J., BEN-CHEN M., BUTSCHER A., GUIBAS L.: Discovery of intrinsic primitives on triangle meshes. Comp. Graph. Forum 30, 2 (2011), 365-374. 6, 7
27. SUN J., OVSJANIKOV M., GUIBAS L.: A concise and provably informative multi-scale signature based on heat diffusion. In Proc. SGP (2009), pp. 1383-1392. 2
28. SCHEINERMAN E., ULLMAN D.: Fractional graph theory. Wiley, 1997. 3
29. TIKHONOV A., ARSENIN V.: Solutions of ill-posed problems. Scripta Series in Math. Winston, 1977. 5
30. TAKANO Y.: Metric-preserving reduction of earth mover's distance. Asia-Pac. J. Op. Res. 27, 1 (2010), 39-54. 5
31. TEVS A., BERNER A., WAND M., IHRKE I., SEIDEL H.: Intrinsic shape matching by planned landmark sampling. In Comp. Graph. Forum (2011), vol. 30, pp. 543-552. 3
32. VILLANI C.: Topics in optimal transportation, vol. 58. Amer Mathematical Society, 2003. 4
33. VAN KAICK O., ZHANG H., HAMARNEH G., COHEN-OR D.: A survey on shape correspondence. Eurographics STAR (2010). 2
34. WITTE F. P., LUCAS D.: Probabilistic tracking in a multitarget environment. In Decision and Control (January 1978), vol. 17, pp. 1212-1216. 3
35. WINDHEUSER T., SCHLICKWEI U., SCHIMDT F., CREMERS D.: Large-scale integer linear programming for orientation preserving 3d shape matching. Proc. SGP 30, 5 (2011), 1471-1480. 3
36. ZASS R., SHASHUA A.: Probabilistic graph and hypergraph matching. In CVPR (2008), pp. 1-8. 3