The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix

International Journal of Computer Vision

Volumn 24, Issue 3, 1997, Pages 271-300

  Torr, P H S ^a   Murray, D W ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Fundamental matrix; Matching; Robust methods

Indexed keywords

ALGORITHMS; FEATURE EXTRACTION; MATRIX ALGEBRA; MEASUREMENT ERRORS; REGRESSION ANALYSIS; VIDEO CAMERAS;

FUNDAMENTAL MATRIX;

COMPUTER VISION;

EID: 0031233843     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007927408552     Document Type: Article

References (63)

1. Ballard, D.H. and Brown, C.M. 1982. Computer Vision. Prentice-Hall: New Jersey.
2. Bar-Shalom, Y. and Fortmann, T.E. 1988. Tracking and Data Association. Academic Press.
3. Beardsley, P.A., Torr, P.H.S., and Zisserman, A.P. 1996. 3D model acquisition from extended image sequences. OUEL Report 2089/96, Department of Engineering Science, University of Oxford.
4. Bookstein, F. 1979. Fitting conic sections to scattered data. Computer Vision Graphics and Image Processing, 9:56-71.
5. Chaterjee, S. and Hadi, A.S. 1988. Sensitivity Analysis in Linear Regression. John Wiley: New York.
6. Cook, R.D. and Weisberg, S. 1980. Characterisations of an empirical influence function for detecting influential cases in regression. Technometrics, 22:337-344.
7. Critchley, F. 1985. Influence in principal component analysis. Biometrika, 72:627-636.
8. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood from incomplete data via the em algorithm. J. Roy. Statist. Soc., 39 B:1-38.
9. Devlin S.J., Gnanadesikan, R., and Kettering, J.R. 1981. Robust estimation of dispersion matrices and principal components. J. Amer. Stat. Assoc., 76:354-362.
10. Faugeras, O.D. 1992. What can be seen in three dimensions with an uncalibrated stereo rig? In Proc. 2nd European Conference on Computer Vision, G. Sandini (Ed.), Santa Margherita Ligure, Italy, Springer-Verlag, vol. LNCS 588, pp. 563-578.
11. Fischler, M.A. and Bolles, R.C. 1981. Random sample consensus: A paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach., 24:381-395.
12. Gill, P.E. and Murray, W. 1978. Algorithms for the solution of the nonlinear least-squares problem. SIAM J. Num. Anal., 15(5):977-992.
13. Golub, G.H. 1973. Some modified eigenvalue problems. SIAM Review, 15(2):318-335.
14. Golub, G.H. and van Loan, C.F. 1989. Matrix Computations. The John Hopkins University Press.
15. Gu, M. and Eisenstat, S.C. 1995. Downdating the singular value decomposition. SIAM J. Matrix Analysis and Applications, 16:793-810.
16. Hampel J.P., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. 1986. Robust Statistics: An Approach Based on Influence Functions. Wiley: New York.
17. Hartley, R.I. 1992. Estimation of relative camera positions for uncalibrated cameras. In Proc. 2nd European Conference on Computer Vision, G. Sandini (Ed.), Santa Margherita Ligure, Italy, Springer-Verlag, vol. LNCS 588, pp. 579-587.
18. Hartley, R.I. 1995. In defence of the 8-point algorithm. Proc. 5th Int. Conf. on Computer Vision, Boston, MA, pp. 1064-1070. IEEE Computer Society Press: Los Alamitos CA.
19. Hartley, R.I. and Sturm, Y. 1994. Triangulation. In Proc. ARPA Image Understanding Workshop, pp. 957-966. and see Proc. Computer Analysis of Images and Patterns, Prague, vol. LNCS 970, Springer Verlag, 1995, pp. 190-197.
20. Hartley, R.I. and Sturm, Y. 1994. Triangulation. In Proc. ARPA Image Understanding Workshop, pp. 957-966. and see Proc. Computer Analysis of Images and Patterns, Prague, vol. LNCS 970, Springer Verlag, 1995, pp. 190-197.
21. Hoaglin, D.C., Mosteller, F., and Tukey, J.W. (Eds.), 1985. Robust Regression. John Wiley and Sons.
22. Huber, P.J. 1981. Robust Statistics. John Wiley and Sons.
23. Kanatani, K. 1992. Geometric Computation for Machine Vision. Oxford University Press.
24. Kanatani, K. 1994. Statistical bias of conic fitting and renormalization. IEEE Trans. Pattern Analysis and Machine Intelligence, 16(3):320-326.
25. Kanatani, K. 1996. Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science: Amsterdam.
26. Kendall, M. and Stuart, A. 1983. The Advanced Theory of Statistics. Charles Griffin and Company: London.
27. Kumar, R. and Hanson, A.R. 1994. Robust methods for estimating pose and a sensitivity analysis. Computer Vision, Graphics and Image Processing, 60(3):313-342.
28. Li, G. 1985. Exploring data tables, trends and shapes. In Robust Regression, D.C. Hoaglin, F. Mosteller, and J.W. Tukey (Eds.), John Wiley and Sons, pp. 281-343.
29. Li, H., Lavin, M.A., and LeMaster, R.J. 1986. Fast Hough transforms: A hierarchical approach. Computer Vision, Graphics and Image Processing, 36:139-161.
30. Longuet-Higgins, H.C. 1981. A computer algorithm for reconstructing a scene from two projections. Nature, 293:133-135.
31. Luong, Q.T. 1992. Matrice Fondamentale et Calibration Visuelle sur l'environnement: Vers use plus grande autonomie des systemes robotiques. Ph.D. Thesis, Paris University.
32. Luong, Q.T., Deriche, R., Faugeras, O.D., and Papadopoulo, T. 1993. On determining the fundamental matrix: Analysis of different methods and experimental results. INRIA Technical Report 1894, INRIA-Sophia Antipolis.
33. Maronna, R.A. 1976. Robust M-estimators of multivariate location and scatter. Ann. Stat., 4:51-67.
34. McLauchlan, P.F. 1990. Describing Textured Surfaces Using Stereo Vision. Ph.D. Thesis, AI Vision Research Unit, University of Sheffield.
35. Meer, M., Mintz, D., and Rosenfeld, A. (1991). Robust regression methods for computer vision: A review. International Journal of Computer Vision, 6:59-70.
36. Mosteller, F. and Tukey, J.W. 1977. Data and Analysis and Regression. Addison-Wesley: Reading, MA.
37. Numerical Algorithms Group, 1988. NAG Fortran Library, vol 7.
38. Olsen, S.I. 1992. Epipolar line estimation. In Proc. 2nd European Conference on Computer Vision, G. Sandini (Ed.), Santa Margherita Ligure, Italy, Springer-Verlag, vol. LNCS 588, pp. 307-311.
39. Pearson, K. 1901. On lines and planes of closest fit to systems of points in space. Philos. Mag. Ser. 6, 2:559.
40. Pratt, V. 1987. Direct least squares fitting of algebraic surfaces. Computer Graphics, 21(4):145-152.
41. Roth, G. and Levine, M.D. 1993. Extracting geometric primitives. Computer Vision, Graphics, and Image Processing, 58(1):1-22.
42. Rousseeuw, P.J. 1987. Robust Regression and Outlier Detection. Wiley: New York.
43. Sampson, P.D. 1982. Fitting conic sections to 'very scattered' data: An iterative refinement of the Bookstein algorithm. Computer Graphics and Image Processing, 18:97-108.
44. Shapiro, L.S. and Brady, J.M. 1995. Rejecting outliers and estimating errors in an orthogonal regression framework. Phil. Trans. R. Soc. Lond. A, 350:407-439.
45. Spetsakis, M. and Aloimonos, Y. 1991. A multi-frame approach to visual motion perception. International Journal of Computer Vision, 6:245-255.
46. Sprent, P. 1989. Applied Nonparametric Statistical Methods. Chapman and Hall: London.
47. Stewart, C.V. 1995. MINPRAN, a new robust estimator for computer vision. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(10):925-938.
48. Taubin, G. 1991. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 13(11):1115-1138.
49. Thisted, R.A. 1988. Elements of Statistical Computing. Chapman and Hall: New York.
50. Torr, P.H.S. 1995. Outlier Detection and Motion Segmentation. D.Phil. Thesis, University of Oxford.
51. Torr, P.H.S. and Murray, D.W. 1992. Statistical detection of non-rigid motion. In Proc. 3rd British Machine Vision Conference, Leeds, D. Hogg (Ed.), Springer-Verlag, pp. 79-88.
52. Torr, P.H.S. and Murray, D.W. 1993a. Statistical detection of independent movement from a moving camera. Image and Vision Computing, 1(4):180-187.
53. Torr, P.H.S. and Murray, D.W. 1993b. Outlier detection and motion segmentation. In Proc. Sensor Fusion VI, Boston, MA, P.S. Schenker (Ed.), vol. SPIE 2059, pp. 432-443.
54. Torr, P.H.S. and Murray, D.W. 1994. Stochastic motion segmentation. In Proc. 3rd European Conference on Computer Vision,
55. Stockholm, J.-O. Ecklundh (Ed.), Springer-Verlag, pp. 328-338.
56. Torr, RH.S., Zisserman, A., and Maybank, S. 1995a. Robust detection of degeneracy. Proc. 5th Int. Conf. on Computer Vision, Boston, MA, IEEE Computer Society Press: Los Alamitos CA, pp. 1037-1044.
57. Torr, P.H.S, Zisserman, A., and Murray, D.W. 1995b. Motion clustering using the trilinear constraint over three views. In Europe-China Workshop on Geometrical Modelling and Invariants for Computer Vision, R. Mohr and C. Wu (Eds.), Springer-Verlag, pp. 118-125.
58. Torr, P.H.S, Maybank, S., and Zisserman, A. 1996. Robust detection of degenerate configurations for the fundamental matrix. OUEL Report 2090/96, Department of Engineering Science, University of Oxford.
59. Teukolsky, S.A., Press, W.H., Flannery, B.P., and Vetterling, W.T. 1988. Numerical Recipes in C, the Art of Scientific Computing. Cambridge University Press: Cambridge.
60. Tsai, R.Y. and Huang, T.S. 1984. Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:13-27.
61. Weng, J., Huang, T.S., and Ahuja, N. 1989. Motion and structure from two perspective views: Algorithms, error analysis, and error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:451-476.
62. Weng, J., Ahuja, N., and Huang, T.S. 1993. Optimal motion and structure estimation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15(9):864-884.
63. Zhang, Z., Deriche, R., Faugeras, O.D., and Luong, Q.T. 1994. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. AI Journal, 78:87-119.