Lie bodies: A manifold representation of 3D human shape

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7572 LNCS, Issue PART 1, 2012, Pages 1-14

  Freifeld, Oren ^a   Black, Michael J ^b  

^a BROWN UNIVERSITY   (United States)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Lie group; Shape deformation; Statistics on manifolds

Indexed keywords

BODY SHAPES; EUCLIDEAN; GROUP STRUCTURE; LINEAR COMBINATIONS; MANIFOLD STRUCTURES; MEASURING DISTANCES; ON-BODY; PRINCIPAL GEODESIC ANALYSIS; RIEMANNIAN STRUCTURE; SHAPE DEFORMATION; SHAPE REPRESENTATION; SHAPE VARIATIONS; THREE-DIMENSIONAL OBJECT; TRIANGULAR MESHES;

COMPUTER VISION; DEFORMATION; LIE GROUPS; PRINCIPAL COMPONENT ANALYSIS;

THREE DIMENSIONAL;

EID: 84867842930     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-33718-5_1     Document Type: Conference Paper

References (28)

1. Balan, A., Sigal, L., Black, M., Davis, J., Haussecker, H.: Detailed human shape and pose from images. In: CVPR, pp. 1-8 (2007)
2. Hasler, N., Ackermann, H., Rosenhahn, B., Thormahlen, T., Seidel, H.: Multilinear pose and body shape estimation of dressed subjects from image sets. In: CVPR, pp. 1823-1830 (2010)
3. Salzmann, M., Fua, P.: Linear local models for monocular reconstruction of deformable surfaces. PAMI 33, 931-944 (2011)
4. Weiss, A., Hirshberg, D., Black, M.: Home 3D body scans from noisy image and range data. In: ICCV, pp. 1951-1958 (2011)
5. Anguelov, D., Srinivasan, P., Koller, D., Thrun, S., Rodgers, J., Davis, J.: SCAPE: Shape completion and animation of people. ACM ToG 24, 408-416 (2005)
6. Sumner, R., Popović, J.: Deformation transfer for triangle meshes. ACM ToG 23, 399-405 (2004)
7. Hasler, N., Stoll, C., Sunkel, M., Rosenhahn, B., Seidel, H.: A statistical model of human pose and body shape. Computer Graphics Forum 28, 337-346 (2009)
8. Chao, I., Pinkall, U., Sanan, P., Schröder, P.: A simple geometric model for elastic deformations. ACM ToG 29, 38:1-38:6 (2010)
9. Grenander, U.: General pattern theory: A mathematical study of regular structures. Clarendon Press (1993)
10. Grenander, U., Miller, M.: Pattern theory: From representation to inference. Oxford University Press, USA (2007)
11. Fletcher, P., Lu, C., Joshi, S.: Statistics of shape via principal geodesic analysis on Lie groups. In: CVPR, vol. 1, pp. 95-101 (2003)
12. Fletcher, P.T., Joshi, S.: Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors. In: Sonka, M., Kakadiaris, I.A., Kybic, J. (eds.) CVAMIA/MMBIA 2004. LNCS, vol. 3117, pp. 87-98. Springer, Heidelberg (2004)
13. Balan, A.: Detailed Human Shape and Pose from Images. PhD thesis, Brown Univ., Providence, RI (2010)
14. Robinette, K., Blackwell, S., Daanen, H., Boehmer, M., Fleming, S., Brill, T., Hoeferlin, D., Burnsides, D.: Civilian American and European Surface Anthropometry Resource (CAESAR) final report. AFRL-HE-WP-TR-2002-0169, US AFRL (2002)
15. Grenander, U., Miller, M.: Representations of knowledge in complex systems. J. Royal Stat. Soc. B (Methodological), 549-603 (1994)
16. Freifeld, O.,Weiss, A., Zuffi, S., Black, M.: Contour people: A parameterized model of 2D articulated human shape. In: CVPR, pp. 639-646 (2010)
17. Miller, M., Christensen, G., Amit, Y., Grenander, U.: Mathematical textbook of deformable neuroanatomies. PNAS 90, 11944-11948 (1993)
18. Grenander, U., Miller, M.: Computational anatomy: An emerging discipline. Quarterly of Applied Math. 56, 617-694 (1998)
19. Fletcher, P.T., Joshi, S., Lu, C., Pizer, S.M.: Gaussian Distributions on Lie Groups and Their Application to Statistical Shape Analysis. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 450-462. Springer, Heidelberg (2003)
20. Alexa, M.: Linear combination of transformations. ACMToG 21(3), 380-387 (2002)
21. Kilian, M., Mitra, N., Pottmann, H.: Geometric modeling in shape space. ACM ToG 26(3), 64:1-64:8 (2007)
22. Kendall, D.: Shape manifolds, Procrustean metrics, and complex projective spaces. Bull. London Math. Soc. 16, 81-121 (1984)
23. Lee, J.: Introduction to smooth manifolds, vol. 218. Springer (2003)
24. Freifeld, O., Black, M.: Lie bodies: Supplemental material. MPI-IS-TR-005, Max Planck Institute for Intelligent Systems (2012)
25. Murray, R., Li, Z., Sastry, S.: A mathematical introduction to robotic manipulation. CRC Press (1994)
26. Higham, N.: The scaling and squaring method for the matrix exponential revisited. SIAM J. Matrix Analysis and Applications 26(4), 1179-1193 (2005)
27. Karcher, H.: Riemannian center of mass and mollifier smoothing. Comm. Pure and Applied Math. 30, 509-541 (1977)
28. Sommer, S., Lauze, F., Hauberg, S., Nielsen, M.: Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part VI. LNCS, vol. 6316, pp. 43-56. Springer, Heidelberg (2010)