Minimum effective dimension for mixtures of subspaces: A robust GPCA algorithm and its applications

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

Volumn 2, Issue , 2004, Pages

  Huang, Kun ^a   Ma, Yi ^a   Vidal, René ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN INFORMATION CRITERION (BIC); EXPECTATION MINIMIZATION (EM) ALGORITHMS; MINIMUM EFFECTIVE DIMENSION (MED); MINIMUM MESSAGE LENGTH (MML);

ALGORITHMS; COMPUTER VISION; ERROR ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION; METADATA; PATTERN RECOGNITION; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING;

IMAGE SEGMENTATION;

EID: 5044226698     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (16)

1. H. Akaike. A new look at the statistical model selection. IEEE Transactions on Automatic Control, 16(6):716-723, 1977.
2. T.E. Boult and L.G. Brown. Factorization-based segmentation of motions. In Proc. of the IEEE Workshop on Motion Understanding, pages 179-186, 1991.
3. M. Collins, S. Dasgupta, and R. Schapire. A generalization of principal component analysis to the exponential family. In Neural Information Processing Systems, volume 14, 2001.
4. J. Costeira and T. Kanade. A multibody factorization method for independently moving objects. International Journal of Computer Vision, 29(3): 159-179, 1998.
5. M. Effros and P.A. Chou. Weighted universal transform coding: Universal image compression with the Karhunen-Loeve transform. In ICIP, volume II, pages 61-64, 1995.
6. M.H. Hansen and B. Yu. Model selection and the principle of minimum description length. Journal of American Statistical Association, 96:746-774, 2001.
7. K. Kanatani. Motion segmentation by subspace separation and model selection. In ICCV, volume 2, pages 586-91, 2001.
8. J.J. Rissanen. Modeling by shortest data description. Automatica, 14:465-471, 1978.
9. B. Scholkopf, A. Smola, and K.-R. Muller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998.
10. M. Tipping and C. Bishop. Mixtures of probabilistic principal component analyzers. Neural Computation, 11(2), 1999.
11. P. H. S. Torr. Geometric motion segmentation and model selection. Phil. Trans. Royal Society of London, 356(1740):1321-1340, 1998.
12. R. Vidal. Generalized Principal Component Analysis (GPCA): an Algebraic Geometric Approach to Subspace Clustering and Motion Segmentation. Ph.D. Dissertation, UC Berkeley, 2003.
13. R. Vidal and Y. Ma. A unified algebraic approach to 2-D and 3-D motion segmentation. In ECCV, 2004.
14. R. Vidal, Y. Ma, and J. Piazzi. A new GPCA algorithm for clustering subspaces by fitting, differentiating and dividing polynomials. In CVPR, 2004.
15. R. Vidal, Y. Ma, and S. Sastry. Generalized Principal Component Analysis (GPCA). In CVPR, 2003.
16. C.S. Wallace and D.M. Boulton. An information measure for classification. The Computer Journal, 11:185194, 1968.