Rolling riemannian manifolds to solve the multi-class classification problem

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

Volumn , Issue , 2013, Pages 41-48

  Caseiro, Rui ^a   Martins, Pedro ^a   Henriques, Joao F ^a   Leite, Fatima Silva ^a,b   Batista, Jorge ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Object Classification; Riemannian Manifolds; Rolling motions

Indexed keywords

BINARY CLASSIFICATION; MATHEMATICAL CONCEPTS; MULTI-CLASS CLASSIFICATION; MULTICLASS CLASSIFICATION PROBLEMS; OBJECT CLASSIFICATION; RIEMANNIAN MANIFOLD; ROLLING MOTION; SUPERVISED CLASSIFICATION;

CLASSIFIERS; LEARNING SYSTEMS; PATTERN RECOGNITION;

GEOMETRY;

EID: 84887398616     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2013.13     Document Type: Conference Paper

References (31)

1. V. Arsigny, P. Fillard, X. Pennec, and N. Ayache. Geometric means in a vector space structure on symmetric positive-definite matrices. Journal Matrix Analysis Applications, 29(1):328-347, 2007. 1, 2
2. J. Carreira, R. Caseiro, J. Batista, and C. Sminchisescu. Semantic segmentation with second-order pooling. In ECCV, 2012. 1, 2
3. R. Caseiro, J. F. Henriques, and J. Batista. Using directional statistics to learn cast shadows from a multi-spectral light sources physical model. In ICIP, 2010. 1
4. R. Caseiro, J. F. Henriques, P. Martins, and J. Batista. A nonparametric riemannian framework on tensor field application to foreground segmentation. In ICCV, 2011. 1
5. R. Caseiro, J. F. Henriques, P. Martins, and J. Batista. Semi-intrinsic mean shift on riemannian manifolds. In ECCV, 2012. 1, 2
6. H. Cetingul and R. Vidal. Intrinsic mean shift for clustering on stiefel and grassmann manifolds. In CVPR, 2009. 1, 2, 6
7. J. Friedman, T. Hastie, and R. Tibshirani. Additive logistic regression: A statistical view of boosting. The Annals of Statistics, 28(2):337-407, 2000. 2, 5, 6
8. A. S. Georghiades, P. N. Belhumeur, and D. J. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. TPAMI, 23(6):643-660, 2001. 7
9. B. Gong, Y. Shi, F. Sha, and K. Grauman. Geodesic flow kernel for unsupervised domain adaptation. In CVPR, 2012. 8
10. V. Guillemin and A. Pollack. Differential Topology. Prentice-Hall, 1974. 3
11. J. Hamm. Subspace-based Learning with Grassmann Kernels. Thesis PhD-University Pennsylvania, 2008. 2, 7, 8
12. J. Hamm and D. Lee. Grassmann discriminant analysis: a unifying view on subspace-based learning. In ICML, 2008. 2, 7, 8
13. M. T. Harandi, C. Sanderson, R. Hartley, and B. C. Lovell. Sparse coding and dictionary learning for symmetric positive definite matrices: A kernel approach. In ECCV, 2012. 2
14. M. Hein. Robust nonparametric regression with metric-space valued output. In NIPS, 2009. 8
15. K. Hupper and F. S. Leite. Smoothing interpolation curves on manifolds with applications to path planning. In Mediterranean Conference on Control and Automation, 2002. 2
16. K. Hupper and F. S. Leite. On the geometry of rolling and interpolation curves on Sn, SOn, Grassmann manifolds. J. Dynamical Control Systems, 13(4):467-502, 2007. 1, 2, 3, 4, 5
17. A. Krizhevsky. Learning multiple features from tiny images. In Technical Report, 2009. 6
18. B. Leibe and B. Schiele. Analyzing appearance and contour based methods object categorization. In CVPR, 2003. 6, 7, 8
19. Y. M. Lui. Advances in matrix manifolds for computer vision. Image Vision Computing, 30(6-7):380-388, 2012. 1
20. X. Pennec. Statistical Computing on Manifolds for Computational Anatomy. Habilitation à Diriger Recherche, 2006. 1
21. R. Sharpe. Differential Geometry. Springer, 1996. 1, 2, 3
22. Y. Shen, K. Hupper, and F. S. Leite. Smooth interpolation of orientation by rolling and wrapping for robot motion planning. In IEEE Int. Conf. Robotics Automation, 2006. 2, 3
23. T. Sim, S. Baker, and M. Bsat. Cmu pose, illumination, and expression database. TPAMI, 25(12):1615-1618, 2003. 7
24. A. Srivastava and E. Klassen. Bayesian and geometric subspace tracking. Advances Applied Probability, 36(1):43-56, 2004. 2, 5
25. R. Subbarao and P. Meer. Nonlinear mean shift over riemannian manifolds. IJCV, 84(1):1-20, 2009. 1, 2
26. S. Taheri, P. Turaga, and R. Chellappa. Towards view-invariant expression analysis using analytic shape manifolds. In FG, 2011. 8
27. D. Tosato, M. Farenzena, M. Cristani, M. Spera, and V. Murino. Multi-class classification on riemannian manifolds for video surveillance. In ECCV, 2010. 1, 2, 5, 6, 7
28. P. Turaga, A. Veeraraghavan, A. Srivastava, and R. Chellappa. Statistical analysis on manifolds and its applications to video analysis. in Video Search and Mining, Studies in Computational Intelligence, Springer-Verlag, 2010. 1, 2
29. P. Turaga, A. Veeraraghavan, A. Srivastava, and R. Chellappa. Statistical computations on grassmann and stiefel manifolds for image and video-based recognition. TPAMI, 33(11):2273-2286, 2011. 1, 2
30. O. Tuzel, F. Porikli, and P. Meer. Region covariance: A fast descriptor for detection and classification. In ECCV, 2006. 1
31. O. Tuzel, F. Porikli, and P. Meer. Pedestrian detection via classification on riemannian manifolds. TPAMI, 30(10):1713-1727, 2008. 1, 2, 6