Highly-expressive spaces of well-behaved transformations: Keeping it simple

Proceedings of the IEEE International Conference on Computer Vision

Volumn 2015 International Conference on Computer Vision, ICCV 2015, Issue , 2015, Pages 2911-2919

  Freifeld, Oren ^a   Hauberg, Soren ^b   Batmanghelich, Kayhan ^a   Fisher, John W ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTION FUNCTIONS; OPTIMIZATION; VELOCITY;

CUMULATIVE DISTRIBUTION FUNCTION; DIFFEOMORPHISMS; FINITE DIMENSIONAL SPACE; ITS APPLICATIONS; MONOTONIC FUNCTIONS; PIECEWISE AFFINES; UNCONSTRAINED OPTIMIZATION; VOLUME PRESERVATION;

COMPUTER VISION;

EID: 84973902150     PISSN: 15505499     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2015.333     Document Type: Conference Paper

References (45)

1. S. Allassonnière, A. Trouvé, and L. Younes. Geodesic shooting and diffeomorphic matching via textured meshes. In EMMCVPR. Springer, 2005. 3, 4
2. N. Arad, N. Dyn, D. Reisfeld, and Y. Yeshurun. Image warping by radial basis functions: Application to facial expressions. CVGIP, 1994. 4
3. V. Arsigny, O. Commowick, X. Pennec, and N. Ayache. A log-euclidean polyaffine framework for locally rigid or affine registration. In BIR. Springer, 2006. 3, 4, 8
4. M. F. Beg, M. I. Miller, A. Trouvé, and L. Younes. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV, 2005. 3
5. F. L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. TPAMI, 1989. 4
6. T.-L. Chen and S. Geman. Image warping using radial basis functions. JAS, 2014. 4
7. T. F. Cootes, C. J. Twining, V. Petrovic, R. Schestowitz, and C. J. Taylor. Groupwise construction of appearance models using piecewise affine deformations. In BMVC, 2005. 3
8. P. Dupuis, U. Grenander, and M. I. Miller. Variational problems on flows of diffeomorphisms for image matching. QAM, 1998. 3
9. S. Durrleman, S. Allassonnière, and S. Joshi. Sparse adaptive parameterization of variability in image ensembles. IJCV, 2013. 3
10. P. Fletcher. Geodesic regression and the theory of least squares on Riemannian manifolds. IJCV, 2012. 4
11. P. Fletcher, C. Lu, and S. Joshi. Statistics of shape via principal geodesic analysis on Lie groups. In CVPR, 2003. 4
12. P. Fletcher, C. Lu, S. Pizer, and S. Joshi. Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE TMI, 2004. 4
13. O. Freifeld and M. Black. Lie bodies: A manifold representation of 3D human shape. In ECCV. Springer, 2012. 4
14. O. Freifeld, S. Hauberg, and M. Black. Model transport: Towards scalable transfer learning on manifolds. In CVPR, 2014. 4
15. U. Grenander. General pattern theory: A mathematical study of regular structures. Clarendon Press, 1993. 3
16. U. Grenander and M. Miller. Representations of knowledge in complex systems. JRSS, Series B, 1994. 3
17. U. Grenander and M. Miller. Pattern theory: from representation to inference. Oxford University Press, 2007. 3
18. H. Guo, A. Rangarajan, and S. Joshi. Diffeomorphic point matching. In Handbook of Mathematical Models in Computer Vision. Springer, 2006. 3, 8
19. M. T. Harandi, M. Salzmann, and R. Hartley. From manifold to manifold: geometry-aware dimensionality reduction for SPD matrices. In ECCV. Springer, 2014. 4
20. S. Hauberg, O. Freifeld, and M. Black. A geometric take on metric learning. In NIPS, 2012. 4
21. J. Hinkle, P. T. Fletcher, and S. Joshi. Intrinsic polynomials for regression on riemannian manifolds. JMIV, 2014. 4
22. C. Ionescu, D. Papava, V. Olaru, and C. Sminchisescu. Human3. 6m: Large scale datasets and predictive methods for 3d human sensing in natural environments. TPAMI, 2014. 8
23. S. Jayasumana, R. Hartley, M. Salzmann, H. Li, and M. Harandi. Kernel methods on the riemannian manifold of symmetric positive definite matrices. In CVPR, 2013. 4
24. S. C. Joshi and M. I. Miller. Landmark matching via large deformation diffeomorphisms. IEEE TIP, 2000. 3, 8
25. J. Kim, C. Liu, F. Sha, and K. Grauman. Deformable spatial pyramid matching for fast dense correspondences. In CVPR, 2013. 3
26. D. Lin, E. Grimson, and J. Fisher. Modeling and estimating persistent motion with geometric flows. In CVPR, 2010. 3
27. C. Liu, H.-Y. Shum, and C.-S. Zhang. A two-step approach to hallucinating faces: global parametric model and local nonparametric model. In CVPR, 2001. 4
28. M. Lorenzi and X. Pennec. Geodesics, parallel transport & one-parameter subgroups for diffeomorphic image registration. IJCV, 2012. 4
29. E. G. Miller and C. Chefd'hotel. Practical non-parametric density estimation on a transformation group for vision. In CVPR, 2003. 4
30. D. Mumford and A. Desolneux. Pattern theory: the stochastic analysis of real-world signals. AK Peters, 2010. 3
31. T. Nir, A. M. Bruckstein, and R. Kimmel. Overparameterized variational optical flow. IJCV, 2008. 2
32. X. Pennec. Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements. JMIV, 2006. 4
33. Y. Rubner, C. Tomasi, and L. Guibas. Metric for distributions with applications to image databases. In CVPR, 1998. 4
34. S. Sommer, F. Lauze, S. Hauberg, and M. Nielsen. Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximation. ECCV, 2010. 4
35. A. Srivastava, I. Jermyn, and S. Joshi. Riemannian analysis of probability density functions with applications in vision. In CVPR, 2007. 4
36. A. Srivastava, S. H. Joshi, W. Mio, and X. Liu. Statistical shape analysis: Clustering, learning, and testing. TPAMI, 2005. 4
37. M. B. Stegmann and D. D. Gomez. A brief introduction to statistical shape analysis, 2002. 8
38. R. Subbarao and P. Meer. Nonlinear mean shift over riemannian manifolds. IJCV, 2009. 4
39. D. Sun, S. Roth, and M. J. Black. Secrets of optical flow estimation and their principles. In CVPR, 2010. 8
40. R. Szeliski. Computer vision: Algorithms and applications. Springer Science & Business Media, 2010. 2, 3
41. S. Taheri, P. Turaga, and R. Chellappa. Towards viewinvariant expression analysis using analytic shape manifolds. In AFGR, 2011. 4
42. M. Vaillant, M. I. Miller, L. Younes, and A. Trouvé. Statistics on diffeomorphisms via tangent space representations. NeuroImage, 2004. 3, 4
43. T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache. Diffeomorphic demons: Efficient non-parametric image registration. NeuroImage, 2009. 3, 4, 8
44. Q. Xie, S. Kurtek, H. Le, and A. Srivastava. Parallel transport of deformations in shape space of elastic surfaces. In ICCV, 2013. 4
45. L. Younes. Spaces and manifolds of shapes in computer vision: An overview. IVC, 2012. 3