A condition number for non-rigid shape matching

Computer Graphics Forum

Volumn 30, Issue 5, 2011, Pages 1503-1512

  Ovsjanikov, Maks ^a   Huang, Qi Xing ^a   Guibas, Leonidas ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER GRAPHICS;

CONDITION NUMBERS; DEFORMABLE SHAPES; DISTORTION MEASURES; LARGE AMOUNTS; NON-RIGID SHAPES; PRACTICAL METHOD; SHAPE CONDITIONS; SHAPE MATCHING;

NUMBER THEORY;

EID: 84866662712     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2011.02024.x     Document Type: Article

References (34)

1. BRONSTEIN A. M., BRONSTEIN M. M., BUSTOS B., CASTELLANI U., CRISTANI M., FALCIDIENO B., GUIBAS L. J., ET AL.: SHREC'10 Track: Feature detection and description. In Proc. 3DOR (2010), pp. 79-86.
2. BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. PNAS 103, 5 (2006), 1168-1172.
3. BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Numerical Geometry of Non-Rigid Shapes. Springer, 2008.
4. BURKARD R., CELA E., PARDALOS P., PITSOULIS L.: The quadratic assignment problem. Handbook of Combinatorial Optimization (1998), 241-338.
5. BOYER R. S., MOORE J. S.: A fast string searching algorithm. Commun. ACM 20 (October 1977).
6. CHERTOK M., KELLER Y.: Spectral symmetry analysis. IEEE Trans. PAMI 32, 7 (2010), 1227-1238.
7. CHEN Y., MEDIONI G.: Object modelling by registration of multiple range images. Image Vision Comput. 10 (1992), 145-155.
8. GELFAND N., GUIBAS L.: Shape segmentation using local slippage analysis. In Proc. SGP (2004), pp. 219-228.
9. GELFAND N., IKEMOTO L., RUSINKIEWICZ S., LEVOY M.: Geometrically stable sampling for the ICP algorithm. In 3DIM (2003).
10. HUANG Q.-X., ADAMS B., WICKE M., GUIBAS L. J.: Non-rigid registration under isometric deformations. CGF (Proc. SGP) 27, 5 (2008), 1449-1457.
11. HILDEBRANDT K., SCHULZ C., VON TYCOWICZ C., POLTHIER K.: Eigenmodes of surface energies for shape analysis. In Advances in Geometric Modeling and Processing (2010), Vol. 6130 of Lecture Notes in Computer Science, Springer, pp. 296-314.
12. HUANG Q., WICKE M., ADAMS B., GUIBAS L.: Shape decomposition using modal analysis. Computer Graphics Forum 28, 2 (2009), 407-416.
13. KNUTH D. E., MORRIS J., PRATT V. R.: Fast pattern matching in strings. SIAM Journal of Computing 6, 2 (1977), 323-350.
14. KILIAN M., MITRA N. J., POTTMANN H.: Geometric modeling in shape space. In Proc. SIGGRAPH (2007), pp. 64:1-64:8.
15. KRAEVOY V., SHEFFER A.: Cross-parameterization and compatible remeshing of 3d models. In Proc. of SIGGRAPH (2004), pp. 861-869.
16. LIPMAN Y., FUNKHOUSER T.: Möbius voting for surface correspondence. In Proc. of SIGGRAPH (2009), Vol. 28:3, pp. 72:1-72:12.
17. LEORDEANU M., HEBERT M.: A spectral technique for correspondence problems using pairwise constraints. In Proc. of ICCV (2005), pp. 1482-1489.
18. LEVOY M., PULLI K., CURLESS B., RUSINKIEWICZ S., KOLLER D., PEREIRA L., GINZTON M., ANDERSON S., DAVIS J., GINSBERG J., SHADE J., FULK D.: The digital Michelangelo project: 3D scanning of large statues. In Proc. SIGGRAPH (2000), pp. 131-144.
19. LI H., SUMNER R. W., PAULY M.: Global correspondence optimization for non-rigid registration of depth scans. CGF (Proc. SGP'08) 27, 5 (2008).
20. MÉMOLI F.: On the use of Gromov-Hausdorff Distances for Shape Comparison. In Symposium on Point Based Graphics (2007), pp. 81-90.
21. MITRA N. J., GELFAND N., POTTMANN H., GUIBAS L.: Registration of point cloud data from a geometric optimization perspective. In Proc. SGP (2004), pp. 23-31.
22. MÉMOLI F., SAPIRO G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. Found. Comput. Math. 5, 3 (2005).
23. MAINTZ J., VIERGEVER M. A.: A survey of medical image registration. Medical Image Analysis 2 (1998), 1-36.
24. OVSJANIKOV M., MERIGOT Q., MEMOLI F., GUIBAS L.: One point isometric matching with the heat kernel. CGF 29, 5 (2010), 1555-1564.
25. RAVIV D., BRONSTEIN A., BRONSTEIN M., KIMMEL R.: Symmetries of non-rigid shapes. In Proc. NRTL (ICCV) (2007), pp. 1-7.
26. RUGGERI M. R., PATANÈ G., SPAGNUOLO M., SAUPE D.: Spectral-driven isometry-invariant matching of 3d shapes. IJCV (2010), 248-265.
27. SUN J., CHEN X., FUNKHOUSER T.: Fuzzy geodesics and consistent sparse correspondences for deformable shapes. CGF (Proc. SGP) 29, 5 (2010).
28. SUN J., OVSJANIKOV M., GUIBAS L.: A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion. CGF (Proc. SGP) 28, 5 (2009).
29. TREFETHEN L. N., BAU D.: Numerical Linear Algebra. SIAM: Society for Industrial and Applied Mathematics, 1997.
30. TEVS A., BOKELOH M., WAND M., SCHILLING A., SEIDEL H.-P.: Isometric registration of ambiguous and partial data. In Proc. CVPR (2009), pp. 1185-1192.
31. TEVS A., BERNER A., WAND M., IHRKE I., SEIDEL H.-P.: Intrinsic shape matching by planned landmark sampling. In Proc. Eurographics (2011), p. to appear.
32. WAND M., ADAMS B., OVSJANIKOV M., BERNER A., BOKELOH M., JENKE P., GUIBAS L., SEIDEL H.-P.,SCHILLING A.: Efficient reconstruction of nonrigid shape and motion from real-time 3d scanner data. ACM Trans. Graph. 28 (May 2009), 15:1-15:15.
33. WAINWRIGHT M. J., JAAKKOLA T., WILLSKY A. S.: Map estimation via agreement on trees: message-passing and linear programming. IEEE Transactions on Information Theory 51, 11 (2005), 3697-3717.
34. ZHANG H., SHEFFER A., COHEN-OR, ZHOU Q., VAN KAICK O., TAGLIASACCHI A.: Deformation-driven shape correspondence. In Proc. SGP (2008), pp. 1431-1439.