Efficient similarity search for covariance matrices via the Jensen-Bregman LogDet Divergence

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2011, Pages 2399-2406

  Cherian, Anoop ^a   Sra, Suvrit ^b   Banerjee, Arindam ^a   Papanikolopoulos, Nikolaos ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVITY RECOGNITION; COMPUTATIONAL COSTS; COMPUTER VISION APPLICATIONS; COVARIANCE MATRICES; DIFFUSION TENSOR; DISSIMILARITY MEASURES; FEATURE DESCRIPTORS; GRADIENT BASED ALGORITHM; NEAREST-NEIGHBORS; RIEMANNIAN METRICS; SIMILARITY FUNCTIONS; SIMILARITY SEARCH;

COMPUTER APPLICATIONS; DIFFUSION TENSOR IMAGING; IMAGE PROCESSING;

COVARIANCE MATRIX;

EID: 84856635207     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2011.6126523     Document Type: Conference Paper

References (34)

1. D. Alexander, C. Pierpaoli, P. Basser, and J. Gee. Spatial transformations of diffusion tensor magnetic resonance images. IEEE Tran. Med. Imaging, 20(11):1131-1139, 2002. 1
2. V. Arsigny, P. Fillard, X. Pennec, and N. Ayache. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine, 56(2):411-421, 2006. 2
3. A. Banerjee, D. Boley, and S. Acharyya. Symmetrized Bregman Divergences and Metrics. The Learning Workshop, 2009. 2
4. A. Banerjee, S. Merugu, I. Dhillon, and J. Ghosh. Clustering with Bregman divergences. JMLR, 6:1705-1749, 2005. 2
5. R. Bhatia. Positive definite matrices. Princeton Univ Press, 2007. 2, 4
6. L. Bregman. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 7(3):200-217, 1967. 2
7. L. Cayton. Fast nearest neighbor retrieval for bregman divergences. In ICML, pages 112-119, 2008. 3, 4, 5
8. Y. Censor and S. A. Zenios. Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, 1997. 2
9. R. Chaudhry and Y. Ivanov. Fast approximate nearest neighbor methods for non-Euclidean manifolds with applications to human activity analysis in videos. ECCV, pages 735-748, 2010. 2
10. P. Chen. Bregman metrics and their applications. PhD thesis, University of Florida, 2007. 2
11. I. Dryden, A. Koloydenko, and D. Zhou. Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Annals, 3(3):1102-1123, 2009. 2
12. F. Porikli, and O. Tuzel. Covariance tracker. CVPR, 2006. 1
13. G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, MD, third edition, 1996. 3
14. Q. Gu and J. Zhou. A similarity measure under Log-Euclidean metric for stereo matching. In ICPR, pages 1-4, 2009. 2
15. B. Kulis, M. Sustik, and I. Dhillon. Low-rank Kernel Learning with Bregman Matrix Divergences. Journal of Machine Learning Research, 10:341-376, 2009. 2
16. H. Lee and Y. Lim. Invariant metrics, contractions and nonlinear matrix equations. Nonlinearity, 21:857-878, 2008. 4
17. N. Lepore, C. Brun, Y. Chou, M. Chiang, R. Dutton, K. Hayashi, E. Luders, O. Lopez, H. Aizenstein, A. Toga, et al. Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors. IEEE Tran. Med. Imaging, 27(1):129-141, 2007. 1
18. X. Li,W. Hu, Z. Zhang, X. Zhang,M. Zhu, and J. Cheng. Visual tracking via incremental log-euclidean riemannian subspace learning. In CVPR, 2008. 2
19. C. Liu. Gabor-based kernel PCA with fractional power polynomial models for face recognition. IEEE PAMI, 26(5):572-581, 2004. 7
20. M. Moakher, and P. Batchelor. Symmetric positive-definite matrices: From geometry to applications and visualization. Springer Berlin Heidelberg, Chapter 17, isbn-978-3-540-31272-7, 2006. 2
21. E. Maggio, E. Piccardo, C. Regazzoni, and A. Cavallaro. Particle PHD filtering for multi-target visual tracking. In ICASSP, volume 1, 2007. 5
22. F. Nielsen and R. Nock. On the centroids of symmetrized bregman divergences. Arxiv preprint arXiv:0711.3242, 2007. 2, 5
23. F. Nielsen and R. Nock. Jensen-Bregman Voronoi diagrams and centroidal tessellations. In Int. Symp. Voronoi Diagrams in Science and Engineering, pages 56-65, 2010. 2
24. F. Nielsen, P. Piro, and M. Barlaud. Tailored Bregman ball trees for effective nearest neighbors. In Eur. Work. Comput. Geo., pages 16-18, 2009. 5
25. O. Tuzel, F. Porikli, and P. Meer. Covariance Tracking using model update based on Lie Algebra. CVPR, 2006. 1, 7
26. O. Tuzel, F.Porikli, and P. Meer. Region covariance: A fast descriptor for detection and classification. ECCV, 2006. 1, 6
27. Y. Pang, Y. Yuan, and X. Li. Gabor-based region covariance matrices for face recognition. IEEE Tran. Circuits and Sys. for Video Tech., 18(7):989-993, 2008. 1
28. X. Pennec, P. Fillard, and N. Ayache. A Riemannian framework for tensor computing. IJCV, 66(1):41-66, 2006. 2
29. R. T. Rockafellar and R. J.-B. Wets. Variational Analysis. Springer, 1997. 4
30. P. Turaga and R. Chellappa. Nearest-neighbor search algorithms on non-Euclidean manifolds for computer vision applications. In Indian Conf. Comp. Vis. Graph. and Img. Proc., pages 282-289, 2010. 2
31. C. Ye, J. Liu, C. Chen, M. Song, and J. Bu. Speech emotion classification on a Riemannian manifold. Adv. Multimedia Inf. Proc., pages 61-69, 2008. 1
32. C. Yuan, W. Hu, X. Li, S. Maybank, and G. Luo. Human action recognition under log-Euclidean Riemannian metric. ACCV, pages 343-353, 2010. 1
33. W. Zheng, H. Tang, Z. Lin, and T. Huang. motion ecognition from arbitrary view facial images. ECCV, ages 490-503, 2010. 1
34. H. Zhu, H. Zhang, J. Ibrahim, and B. Peterson. Statistical analysis of diffusion tensors in diffusion-weighted magnetic resonance imaging data. Journal of the American Statistical Association, 102(480):1085-1102, 2007. 1