Model transport: Towards scalable transfer learning on manifolds

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Volumn , Issue , 2014, Pages 1378-1385

  Freifeld, Oren ^a   Hauberg, Søren ^b   Black, Michael J ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Computer Vision; Manifold Valued Data; PGA; Riemannian Manifolds; Scalable; Statistics on Manifolds; Transfer Learning

Indexed keywords

COMPUTER VISION; LARGE DATASET; LEARNING SYSTEMS; LOGISTIC REGRESSION;

LOGISTIC REGRESSION MODELS; MANIFOLD STRUCTURES; MANIFOLD-VALUED DATUM; MODELING TRANSPORT; PARALLEL TRANSPORT; RIEMANNIAN MANIFOLD; SCALABLE; STATISTICS ON MANIFOLDS;

TRANSFER LEARNING;

EID: 84911412369     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2014.179     Document Type: Conference Paper

References (44)

1. V. Arsigny, P. Fillard, X. Pennec, and N. Ayache. Log-euclidean metrics for fast and simple calculus on diffusion tensors. MR in medicine, 56(2):411-421, 2006.
2. M. F. Beg, M. I. Miller, A. Trouvé, and L. Younes. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV, 61(2):139-157, 2005.
3. E. Begelfor and M. Werman. Affine invariance revisited. CVPR, 2:2087-2094, 2006.
4. A. Bhattacharya and R. Bhattacharya. Nonparametric inference on manifolds: with applications to shape spaces. Cambridge University Press, 2012.
5. H. Daumé III. Frustratingly easy domain adaptation. In ACL, 256-263, 2007.
6. H. Daumé III and D. Marcu. Domain adaptation for statistical classifiers. JAIR, 26(1):101-126, 2006.
7. M. Do Carmo. Riemannian geometry. Birkhäuser Boston, 1992.
8. J. Du, A. Goh, S. Kushnarev, and A. Qiu. Geodesic regression on orientation distribution functions with its application to an aging study. NeuroImage, 2013.
9. A. Edelman, T. Arias, and S. Smith. The geometry of algorithms with orthogonality constraints. SIMAX, 20(2):303-353, 1998.
10. P. Fletcher. Geodesic regression and the theory of least squares on Riemannian manifolds. IJCV, 1-15, 2012
11. P. Fletcher, C. Lu, S. Pizer, and S. Joshi. Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE TMI, 23(8):995-1005, 2004.
12. O. Freifeld and M. Black. Lie bodies: A manifold representation of 3D human shape. ECCV, 1-14, 2012.
13. O. Freifeld, S. Hauberg, and M. Black. Model Transport: Towards Scalable Transfer Learning on Manifolds-Supplemental material. MPI-IS-TR-009, 2014.
14. B. Gong, Y. Shi, F. Sha, and K. Grauman. Geodesic flow kernel for unsupervised domain adaptation. CVPR, 2066-2073, 2012.
15. U. Grenander and M. Miller. Computational anatomy: An emerging discipline. QAM, 56(4):617-694, 1998.
16. J. Ham, D. Lee, and L. Saul. Semisupervised alignment of manifolds. In UAI, 10:120-127, 2005.
17. S. Hauberg, F. Lauze, and K. Pedersen. Unscented Kalman filtering on Riemannian manifolds. JMIV, 1-18, 2012.
18. S. Hauberg, S. Sommer, and K. S. Pedersen. Natural metrics and least-committed priors for articulated tracking. IVC, 30(6-7):453-461, 2012.
19. S. Huckemann, T. Hotz, and A. Munk. Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions. Stat. Sinica, 20:1-100, 2010.
20. Y. Ke and R. Sukthankar. PCA-SIFT: A more distinctive representation for local image descriptors. CVPR, 2:506-513, 2004.
21. D. Kendall. Shape manifolds, Procrustean metrics, and complex projective spaces. BLMS, 16(2):81-121, 1984.
22. X. Li and J. Bilmes. A bayesian divergence prior for classifier adaptation. In AISTATS, 2007.
23. D. Lin, E. Grimson, and J. Fisher III. Learning visual flows: A Lie algebraic approach. CVPR 747-754, 2009.
24. M. Lorenzi, N. Ayache, and X. Pennec. Schild's ladder for the parallel transport of deformations in time series of images. In IPMI, 463-474, 2011.
25. M. Lorenzi and X. Pennec. Geodesics, parallel transport & one-parameter subgroups for diffeomorphic image registration. IJCV, 1-17, 2012.
26. A. Makadia and K. Daniilidis. Direct 3d-rotation estimation from spherical images via a generalized shift theorem. CVPR, 2003.
27. R. Murray, Z. Li, and S. Sastry. A mathematical introduction to robotic manipulation. CRC, 1994.
28. X. Pennec. Probabilities and statistics on Riemannian manifolds: Basic tools for geometric measurements. In NSIP, 194-198, 1999.
29. X. Pennec, P. Fillard, and N. Ayache. A riemannian framework for tensor computing. IJCV, 66(1):41-66, 2006.
30. X. Pennec and M. Lorenzi. Which parallel transport for the statistical analysis of longitudinal deformations? In Colloque GRETSI'11, 2011.
31. K. Robinette, S. Blackwell, H. Daanen, M. Boehmer, S. Fleming, T. Brill, D. Hoeferlin, and D. Burnsides. Civilian American and European Surface Anthropometry Resource. AFRL-HE-WP-TR-2002-0169, US AFRL, 2002.
32. J. Schäfer and K. Strimmer. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. SAGMB, 4(1), 2005.
33. S. Sommer, F. Lauze, S. Hauberg, and M. Nielsen. Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximation. ECCV, 43-56, 2010.
34. G. Sparr. Structure and motion from kinetic depth. In The Sophus Lie International Workshop on CVAM, 1995.
35. A. Srivastava, I. Jermyn, and S. Joshi. Riemannian analysis of probability density functions with applications in vision. CVPR, 1-8, 2007.
36. A. Srivastava, S. H. Joshi, W. Mio, and X. Liu. Statistical shape analysis: Clustering, learning, and testing. IEEE PAMI, 27(4):590-602, 2005.
37. J. Straub, G. Rosman, O. Freifeld, J. Leonard, and J. Fisher III. A mixture of Manhattan frames: Beyond the Manhattan world. CVPR, 2014.
38. R. Subbarao and P. Meer. Nonlinear mean shift over rieman-nian manifolds. IJCV, 84(1):1-20, 2009.
39. S. Taheri, P. Turaga, and R. Chellappa. Towards viewinvariant expression analysis using analytic shape manifolds. In AFGR, 306-313, 2011.
40. O. Tuzel, F. Porikli, and P. Meer. Region covariance: A fast descriptor for detection and classification. ECCV, 589-600, 2006.
41. M. Vaillant, M. I. Miller, L. Younes, and A. Trouvé. Statistics on diffeomorphisms via tangent space representations. NeuroImage, 23:S161-S169, 2004.
42. D. Wei, D. Lin, and J. Fisher III. Learning deformations with parallel transport. ECCV, 287-300, 2012.
43. Q. Xie, S. Kurtek, H. Le, and A. Srivastava. Parallel transport of deformations in shape space of elastic surfaces. ICCV, 2013.
44. L. Younes. Spaces and manifolds of shapes in computer vision: An overview. IVC, 30(6):389-397, 2012.