Geometric modeling in shape space

ACM Transactions on Graphics

Volumn 26, Issue 3, 2007, Pages

  Kilian, Martin ^a   Mitra, Niloy J ^a   Pottmann, Helmut ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Geodesic; Isometric deformation; Parallel transport; Riemannian geometry; Shape exploration; Shape space

Indexed keywords

EXPONENTIAL MAPS; GEODESICS; PARALLEL TRANSPORT; RIEMANNIAN GEOMETRY; SHAPE EXPLORATION; SHAPE SPACES;

BOUNDARY VALUE PROBLEMS; GEOMETRY; INTERPOLATION; USER INTERFACES;

COMPUTER GRAPHICS;

EID: 34547679824     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1276377.1276457     Document Type: Article

References (39)

1. ALEXA, M., COHEN-OR, D., AND LEVIN, D. 2000. As-rigid-as-possible shape interpolation. In Proc. SIGGRAPH '00, 157-164.
2. ALLEN, B., CURLESS, B., AND POPOVIĆ, Z. 2003. The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans. Graphics 22, 3, 587-594.
3. ANGUELOV, D., SRINIVASAN, P., KOLLER, D., THRUN, S., RODGERS, J., AND DAVIS, J. 2005. SCAPE: shape completion and animation of people. ACM Trans. Graphics 24, 3, 408-416.
4. BERGER, M. 1987. Geometry I, II. Springer.
5. BOTSCH, M., PAULY, M., GROSS, M., AND KOBBELT, L. 2006. Primo: coupled prisms for intuitive surface modeling. In Symp. Geom. Processing, 11-20.
6. BOTTEMA, O., AND ROTH, B. 1990. Theoretical kinematics. Dover Publ.
7. 3. In Proc. of Scale-Space, 622-631.
8. CECIL, T. 1992. Lie Sphere Geometry. Springer.
9. CHARPIAT, G., FAUGERAS, O., AND KERIVEN, R. 2005. Approximations of shape metrics and application to shape warping and empirical statistics. Foundations of Comp. Math., 5, 1-58.
10. CHARPIAT, G., KERIVEN, R., PONS, J.-P., AND FAUGERAS, O. 2005. Designing spatially coherent minimizing flows for variational problems based on active contours. In Proc. ICCV 2005, vol. 2, 1403-1408.
11. CHENG, H.-L., EDELSBRUNNER, H., AND FU, P. 1998. Shape space from deformation. In Proc. Pacific Graphics, 104-113.
12. COX, T., AND COX, M. 2001. Multidimensional Scaling. CRC/Chapman and Hall.
13. DO CARMO, M. P. 1992. Riemannian Geometry. Birkhäuser.
14. FUNCK, W., THEISEL, H., AND SEIDEL, H. 2006. Vector field based shape deformations. ACM Trans. Graphics 25, 3, 1118-1125.
15. GARLAND, M., AND HECKBERT, P. 1997. Surface simplification using quadric error metrics. In ACM SIGGRAPH, 209-216.
16. GELFAND, I. M., AND FOMIN, S.V. 1963. Calculus of Variations. Prentice Hall.
17. HOPPE, H. 1996. Progressive meshes. In ACM SIGGRAPH, 99-108.
18. HUANG, J., SHI, X., LIU, X., ZHOU, K., WEI, L., TENG, S., BAO, H., GUO, B., AND SHUM, H. 2006. Subspace gradient domain mesh deformation. ACM Trans. Graphics 25, 3, 1126-1134.
19. IGARASHI, T., MOSCOVICH, T., AND HUGHES, J. F. 2005. As-rigid-as-possible shape manipulation. ACM Trans. Graphics 24, 3, 1134-1141.
20. JU, T., SCHAEFER, S., AND WARREN, J. 2005. Mean value coordinates for closed triangular meshes. ACM Trans. Graphics 24, 3, 561-566.
21. KENDALL, D. G. 1984. Shape manifolds, procrustean metrics and complex projective spaces. Bull. London Math. Soc. 18, 81-121.
22. KILIAN, M. 2007. Shapes, metrics, and their geodesics. Tech. Rep. 178, Vienna University of Technology.
23. KIMMEL, R., AND SETHIAN, J. 1998. Computing geodesic paths on manifolds. Proc. Natl. Acad. Sci. 95, 8431-8435.
24. KLASSEN, E., SRIVASTAVA, A., MIO, W., AND JOSHI, S. H. 2004. Analysis of planar shapes using geodesic paths on shape spaces. IEEE PAMI 26, 3, 372-383.
25. KRAEVOY, V., AND SHEFFER, A. 2004. Cross-parameterization and compatible remeshing of 3D models. ACM Trans. Graphics 23, 3, 861-869.
26. KRAEVOY, V., AND SHEFFER, A. 2007. Mean-value geometry encoding. International Journal of Shape Modeling 12, 1.
27. LIPMAN, Y., SORKINE, O., LEVIN, D., AND COHEN-OR, D. 2005. Linear rotation-invariant coordinates for meshes. ACM Trans. Graphics 24, 3, 479-487.
28. LIPMAN, Y., COHEN-OR, D., GAL, R., AND LEVIN, D. 2007. Volume and shape preservation vai moving frame manipulation. ACM Trans. Graphics 26, 1.
29. LIU, D. C., AND NOCEDAL, J. 1989. On the limited memory BFGS method for large scale optimization. Math. Program. 45, 3, 503-528.
30. MEMOLI, F., AND SAPIRO, G. 2001. Fast computation of weighted distance functions and geodesics on implicit hypersurfaces. J. Comput. Phys. 173, 730-764.
31. MEMOLI, F., AND SAPIRO, G. 2004. Comparing point clouds. In Symp. Geometry Processing, 32-40.
32. MICHOR, P. W., AND MUMFORD, D. 2006. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc. 8, 1-48.
33. POTTMANN, H., AND WALLNER, J. 2001. Computational Line Geometry. Springer.
34. SCHREINER, J., ASIRVATHAM, A., PRAUN, E., AND HOPPE, H. 2004. Inter-surface mapping. ACM Trans. Graphics 23, 3, 870-877.
35. SLOAN, P.-P. J., ROSE, C. F., AND COHEN, M. F. 2001. Shape by example. In Proc. of the 2001 symposium on interactive 3D graphics, 135-143.
36. SORKINE, O., LIPMAN, Y., COHEN-OR, D., ALEXA, M., RÖSSL, C., AND SEIDEL, H.-P. 2004. Laplacian surface editing. In Symp. Geom. Processing, 179-188.
37. SUMNER, R. W., AND POPOVIČ, J. 2004. Deformation transfer for triangle meshes. ACM Trans. Graphics 23, 3, 399-405.
38. XU, D., ZHANG, H., WANG, Q., AND BAO, H. 2005. Poisson shape interpolation. In SPM '05: Proc. ACM Symp. on Solid and Physical Modeling, 267-274.
39. YEZZI, A., AND MENNUCCI, A. 2005. Conformal metrics and true "gradient flows" for curves. In Proc. ICCV '05, 913-919.