Robust factorization methods using a Gaussian/uniform mixture model

International Journal of Computer Vision

Volumn 81, Issue 3, 2009, Pages 240-258

  Zaharescu, Andrei ^a   Horaud, Radu ^a  

^a INRIA RHÔNE ALPES   (France)

Author keywords

3 D reconstruction; Data clustering; EM; Expectation maximization; M estimators; Multiple camera calibration; Outlier rejection; Robust factorization

Indexed keywords

CALIBRATION; CAMERAS; CLUSTER ANALYSIS; CLUSTERING ALGORITHMS; FACTORIZATION; MAXIMUM PRINCIPLE; OPTIMIZATION; PARAMETER ESTIMATION; RESTORATION; VIDEO CAMERAS;

3-D RECONSTRUCTION; DATA CLUSTERING; EM; EXPECTATION-MAXIMIZATION; M-ESTIMATORS; MULTIPLE CAMERA CALIBRATION; OUTLIER REJECTION; ROBUST FACTORIZATION;

THREE DIMENSIONAL;

EID: 58149510648     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-008-0169-x     Document Type: Article

References (48)

1. H. Aanaes R. Fisker K. Astrom 2002 Robust factorization IEEE Transactions on Pattern Analysis and Machine Intelligence 24 9 1215 1225
2. P. Anandan M. Irani 2002 Factorization with uncertainty International Journal of Computer Vision 49 2/3 101 116
3. Bishop, C. M. (2006). Pattern recognition and machine learning. Berlin: Springer.
4. Bouguet, J.-Y. (2001). Pyramidal implementation of the affine lucas kanade feature tracker-description of the algorithm (Technical report). Intel Corporation.
5. Brant, S. (2002). Closed-form solutions for affine reconstruction under missing data. In Proceedings of statistical methods for video processing (ECCV '02 Workshop) (pp. 109-114).
6. S. Christy R. Horaud 1996 Euclidean shape and motion from multiple perspective views by affine iterations IEEE Transactions on Pattern Analysis and Machine Intelligence 18 11 1098 1104
7. A. P. Dempster N. M. Laird D. B. Rubin 1977 Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion) Journal of the Royal Statistical Society, Series B 39 1 38
8. Faugeras, O. (1993). Three dimensional computer vision: a geometric viewpoint. Cambridge: MIT Press.
9. M. A. Fischler R. C. Bolles 1981 Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography Communications of the ACM 24 6 381 395
10. C. Fraley A. E. Raftery 2002 Model-based clustering, discriminant analysis, and density estimation Journal of the American Statistical Association 97 611 631
11. Golub, G. H., & Van Loan, C. F. (1989). Matrix computations. Baltimore: The Johns Hopkins University Press.
12. Gruber, A., & Weiss, Y. (2003). Factorization with uncertainty and missing data: exploring temporal coherence. In Proceedings neural information processing systems (NIPS'2003).
13. Gruber, A., & Weiss, Y. (2004). Multibody factorization with uncertainty and missing data using the em algorithm. In Proceedings conference on computer vision and pattern recognition (pp. 707-714).
14. Hajder, L., & Chetverikov, D. (2004). Robust structure from motion under weak perspective. In Proc. of the second international symposium on 3d data processing, visualization, and transmission, September 2004.
15. Hartley, R., & Schaffalitzky, F. (2003). Powerfactorization: 3d reconstruction with missing or uncertain data (Technical report). Australian National University.
16. Hartley, R., & Zisserman, A. (2000). Multiple view geometry in computer vision. Cambridge: Cambridge University Press.
17. B. K. P. Horn 1987 Closed-form solution of absolute orientation using unit quaternions Journal of Optical Society of America A 4 4 629 642
18. Huynh, D. Q., Hartley, R., & Heyden, A. (2003). Outlier correction in image sequences for the affine camera. In Proceedings ICCV (Vol. 1, pp. 585-590).
19. Huynh, D. Q., & Heyden, A. (2002). Robust factorization for the affine camera: Analysis and comparison. In Proc. seventh international conference on control, automation, robotics, and vision, Singapore, December 2002.
20. K. Kanatani 1998 Geometric information criterion for model selection International Journal of Computer Vision 26 3 171 189
21. K. Kanatani 2004 Uncertainty modeling and model selection for geometric inference IEEE Transactions on Pattern Analysis and Machine Intelligence 26 10 1307 1319
22. Q. Luong O. Faugeras 1997 Self-calibration of a moving camera from point correspondences and fundamental matrices International Journal of Computer Vision 1 5 40
23. Luong, Q.-T., & Faugeras, O. D. (2001). The geometry of multiple images. Boston: MIT Press.
24. Mahamud, S., & Hebert, M. (2000). Iterative projective reconstruction from multiple views. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR '00) (Vol. 2, pp. 430-437). June 2000.
25. Mahamud, S., Hebert, M., Omori, Y., & Ponce, J. (2001). Provably-convergent iterative methods for projective structure from motion. In IEEE conf. on computer vision and pattern recognition (CVPR).
26. McLachlan, G. J., & Krishnan, T. (1997). The EM algorithm and extensions. New York: Wiley.
27. Meer, P. (2004). Robust techniques for computer vision. In Emerging topics in computer vision. Prentice Hall.
28. D. J. Miller J. Browning 2003 A mixture model and em-based algorithm for class discovery, robust classification and outlier rejection in mixed labeled/unlabeled data sets IEEE Transactions on Pattern Analysis and Machine Intelligence 25 11 1468 1483
29. I. Miyagawa K. Arakawa 2006 Motion and shape recovery based on iterative stabilization for modest deviation from planar motion IEEE Transactions on Pattern Analysis and Machine Intelligence 28 7 1176 1181
30. Morris, D., & Kanade, T. (1998). A unified factorization algorithm for points, line segments and planes with uncertainty models. In Proceedings of international conference of computer vision (pp. 696-702).
31. J. Oliensis R. Hartley 2007 Iterative extensions of the sturm/triggs algorithm: Convergence and nonconvergence IEEE Transactions on Pattern Analysis and Machine Intelligence 29 12 2217 2233
32. P. J. Rousseeuw 1984 Least median of squares regression Journal of the American Statistical Association 79 871 880
33. Rousseeuw, P. J., & Van Aelst, S. (1999). Positive-breakdown robust methods in computer vision. In Berk, & Pourahmadi (Eds.), Computing science and statistics (Vol. 31, pp. 451-460). Interface Foundation of North America.
34. S. Roweis 1997 EM algorithm for PCA and SPCA Proceedings NIPS 10 626 632
35. H. Shum K. Ikeuchi R. Reddy 1995 Principal component analysis with missing data and its application to polyhedral object modeling IEEE Transactions on Pattern Analysis and Machine Intelligence 17 9 855 867
36. C. V. Stewart 1999 Robust parameter estimation in computer vision SIAM Review 41 3 513 537
37. Sturm, P., & Triggs, W. (1996). A factorization based algorithm for multi-image projective structure and motion. In LNCS : Vol. 1065. Proceedings of the 4th European conference on computer vision (pp. 709-720). Cambridge, England. Berlin: Springer.
38. Tardif, J.P., Bartoli, A., Trudeau, M., Guilbert, N., & Roy, S. (2007). Algorithms for batch matrix factorization with application to structure-from-motion. In Proc. of IEEE conference on computer vision and pattern recognition, Minneapolis, USA, June 2007.
39. C. Tomasi T. Kanade 1992 Shape and motion from image streams under orthography: a factorization method International Journal of Computer Vision 9 2 137 154
40. Trajkovic, M., & Hedley, M. (2007). Robust recursive structure and motion recovery under affine projection. In Proc. of the British machine vision conference, September 1997.
41. Triggs, W., McLauchlan, P., Hartley, R., & Fitzgibbon, A. (2000). Bundle adjustment-a modern synthesis. In LNCS. Vision algorithms: theory and practice (pp. 298-375).
42. Vidal, R., & Hartley, R. (2004). Motion segmentation with missing data using powerfactorization and GPCA. In Proceedings CVPR (Vol. 2, pp. 310-316).
43. M. W. Walker L. Shao R. A. Volz 1991 Estimating 3-d location parameters using dual number quaternions CGVIP-Image Understanding 54 3 358 367
44. Wiberg, T. (1976). Computation of principal components when data are missing. In Proceedings symposium of computational statistics (pp. 229-326).
45. Zaharescu, A., Horaud, R., Ronfard, R., & Lefort, L. (2006). Multiple camera calibration using robust perspective factorization. In Proceedings of the 3rd international symposium on 3d data processing, visualization and transmission, Chapel Hill, USA. IEEE Computer Society Press.
46. Zaharescu, A., Boyer, E., & Horaud, R. P. (2007). Transformesh: a topology-adaptive mesh-based approach to surface evolution. In Proceedings of the eighth Asian conference on computer vision, LNCS, Tokyo, Japan, November 2007. Springer.
47. Z. Zhang 2000 A flexible new technique for camera calibration IEEE Transactions on Pattern Analysis and Machine Intelligence 22 11 1330 1334
48. Z. Zhang 2004 Camera calibration with one-dimensional objects IEEE Transactions on Pattern Analysis and Machine Intelligence 26 7 892 899