Maximum likelihood robust regression by mixture models

Journal of Mathematical Imaging and Vision

Volumn 25, Issue 1, 2006, Pages 25-48

  Brandt, Sami S ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Epipolar geometry; Model selection; Robust regression; Statistical modelling

Indexed keywords

EPIPOLAR GEOMETRY; MODEL SELECTION; ROBUST REGRESSION; STATISTICAL MODELLING;

COMPUTATION THEORY; DATA REDUCTION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBLEM SOLVING; REGRESSION ANALYSIS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 33749626297     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-4386-4     Document Type: Article

References (41)

1. H. Akaike, "On entropy maximization principle," in (ed.), Applications of Statistics, P.R. Krishnaiah, North Holland, Amsterdam, pp. 27-41, 1977.
2. R. Beran, "Asymptotically efficient adaptive rank estimates in location models," Ann. Stat. Vol. 2, No. 1, pp. 63-74, 1974.
3. C. Biernacki, G. Celeux, and G. Govaert, "Strategies for getting the largest likelihood in mixture models," Presented at the invited session in Joint Statistical Meetings 2000, Indianapolis. Presentation available at http://www.inrialpes.fr/is2/people/celeux/, 2000.
4. S. Brandt, "Maximum likelihood robust regression with known and unknown residual models," in Proc of the Statistical Methods in Video Proc Workshop, in conjunction with ECCV 2002, Copenhagen, Denmark, 2002a, pp. 97-102.
5. S. Brandt, "Theorems and algorithms for multiple view geometry with applications to electron tomography," Doctoral thesis, Helsinki University of Technology, 2002b.
6. S. Brandt and J. Heikkonen, "A Bayesian weighting principle for the fundamental matrix estimation," Pattern Recognit. Lett. Vol. 21, No. 12, pp. 1081-1092, 2000.
7. S. Brandt and J. Heikkonen, "Optimal method for the affine F-matrix and its uncertainty estimation in the sense of both noise and outliers," in Proc. of the Eighth International Conference on Computer Vision, Vol. 2, Vancouver, Canada, 2001, pp. 166-173.
8. G. Celeux and J. Diebolt, "The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem," Computat. Stat. Quart, Vol. 2, pp. 73-82, 1985.
9. G. Celeux and G. Govaert, "A classification EM algorithm for clustering and two stochastic versions," Computat. Stat. Data Anal, Vol. 14, pp. 315-332, 1992
10. G. Csurka, C. Zeller, Z. Zhang, and O.D. Faugeras, "Characterizing the uncertainty of the fundamental matrix," Comput. Vis. Image Underst, Vol. 68, No. 1, pp. 18-36, 1997
11. A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum likelihood form incomplete data via the EM algorithm (with discussion)," J.R. Statist. Soc. Ser. B-Stat. Methodol, Vol. 39, pp. 1-38, 1977.
12. M. Fischler and L. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography," Commun. ACM, Vol. 24, pp. 381-385, 1981.
13. C. Fraley and A.E. Raftery, "How many clusters? which clustering method? answers via model-based cluster analysis," Comput. J, Vol. 41, pp. 578-588, 1998.
14. G.H. Golub and C.F.V. Loan, Matrix Computations, Second edn. The John Hopkins University Press, Chap. 7, 1989, pp. 345-346.
15. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge University Press, 2000.
16. R.V. Hogg, "Adaptive robust procedures: A partial review and some suggestions for future applications and theory," J. Am. Stat. Assoc, Vol. 69, No. 348, pp. 909-927, 1974.
17. P.J. Huber, Robust Statistics, Wiley, 1981.
18. INRIA Syntim Project, http://www-syntim.inria.fr/ syntim/analyse/paires- eng.html. 1999.
19. H. Longuet-Higgins, "A computer algorithm for reconstructing a scene from two projections," Nature, Vol. 293, pp. 133-135, 1981.
20. Q.-T. Luong and O. Faugeras, "The fundamental matrix: Theory, algorithms, and stability analysis," Int. J. Comput. Vis., Vol. 17, No. 1, pp. 43-76, 1996.
21. G. McLachlan and T. Krishnan, The EM Algorithm and Extensions, Wiley, 1996.
22. J. Rissanen, "Modeling by shortest data description," Automatica, Vol. 14, pp. 465-471, 1978.
23. J. Rissanen, "A universal prior for integers and estimation by minimum description length," Ann. Stat., Vol. 11, No. 2, pp. 416-431, 1983.
24. J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 of Series in Computer Science, World Scientific, Singapore, 1989.
25. P.J. Rousseeuw, "Least median of squares regression," J. Am. Stat. Assoc., Vol. 79, pp. 871-880, 1984.
26. P.J. Rousseeuw and A.M. Leroy, Robust Regression and Outlier Detection, Wiley, 1987.
27. J. Sacks, "An asymptotically efficient sequence of estimators of a location parameter," Ann. Stat., Vol. 3, No. 2, pp. 285-298, 1975.
28. Y. Sakamoto, M. Ishiguro, and G. Kitagawa, Akaike Information Criterion Statistics, KTK Scientific Publishers, 1986.
29. G. Schwarz, "Estimating the dimension of a model," Ann. Stat., Vol. 6, No. 2, pp. 461-464, 1978.
30. L. Shapiro and J. Brady, "Rejecting outliers and estimating errors in an orthogonal regression framework," Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., Vol. 350, 1995.
31. L. Shapiro, A. Zisserman, and M. Brady, "Motion from point matches using affine epipolar geometry," in Proceedings of the Third European Conference on Computer Vision, 1994.
32. M. Srinath, P. Rajasekaran, and R. Viswanathan, Introduction to Statistical Signal Processing with Applications, Prentice Hall, Chap. 5, 1996, pp. 146-149.
33. C.J. Stone, "Adaptive maximum likelihood estimators," Ann. Stat., Vol. 3, No. 2, pp. 267-284, 1975.
34. P. Torr and D. Murray, "The development and comparison of robust methods for estimating the fundamental matrix," Int. J. Comput. Vis., Vol. 24, No. 3, pp. 271-300, 1997.
35. P. Torr and A. Zisserman, "MLESAC: A new robust estimator with application to estimating image geometry," Comput. Vis. Image Underst, Vol. 78, No. 1, pp. 138-156, 2000.
36. V.N. Vapnik, The Nature of Statistical Learning Theory, Second edn., Springer-Verlag, New York, 2000.
37. J. Weng, T.S. Huang, and N. Ahuja, "Motion and structure from two perspective views: Algorithms, error analysis, and error estimation," IEEE Trans. Pattern Anal. Mach. Intell., Vol. 11, No. 5, pp. 451-476, 1989.
38. C.J. Wu, "On the convergence properties of the EM algorithm," Ann. Stat, Vol. 11, No. 1, pp. 95-103, 1983.
39. G. Xu and Z. Zhang, Epipolar Geometry in Stereo, Motion and Object Recognition, Vol. 6 of Computational Imaging and Vision, Kluwer Academic Publishers, 1996.
40. Z. Zhang, R. Deriche, O. Faugeras, and Q. Luong, "A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry," Artif. Intell., Vol. 78, pp. 87-119, 1994.
41. Z. Zhang and C. Loop, "Estimating the fundamental matrix by transforming image points in protective space," Comput. Vis. Image Underst, Vol. 82, pp. 174-180, 2001.