메뉴 건너뛰기




Volumn 50, Issue 1, 2002, Pages 35-61

Bayesian model estimation and selection for epipolar geometry and generic manifold fitting

Author keywords

Bayesian methods; Epipolar geometry; Model selection; Robust methods

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CURVE FITTING; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DENSITY FUNCTION; STATISTICAL TESTS;

EID: 0036804760     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020224303087     Document Type: Article
Times cited : (235)

References (92)
  • 1
    • 0016355478 scopus 로고
    • A new look at the statistical model identification
    • Akaike, H. 1974 A new look at the statistical model identification. IEEE Trans. on Automatic Control, AC-19(6):716-723.
    • (1974) IEEE Trans. on Automatic Control , vol.AC-19 , Issue.6 , pp. 716-723
    • Akaike, H.1
  • 2
    • 0002468753 scopus 로고
    • Prediction and entropy
    • A.C. Atkinson and S.E. Feinberg (Eds.). Springer: New York
    • Akaike, H. 1985 Prediction and entropy. In A Celebration of Statistics. The ISI Centenary Volume, A.C. Atkinson and S.E. Feinberg (Eds.). Springer: New York, pp. 1-24.
    • (1985) A Celebration of Statistics. The ISI Centenary Volume , pp. 1-24
    • Akaike, H.1
  • 3
    • 0011244619 scopus 로고    scopus 로고
    • Bayes rules in finite models
    • Arnborg, S. and Sjödin, G. 2000. Bayes rules in finite models. In European Conference on Artificial Intelligence pp. 571-575. Also available at ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/fobcl.pdf.
    • (2000) European Conference on Artificial Intelligence , pp. 571-575
    • Arnborg, S.1    Sjödin, G.2
  • 4
    • 84957879151 scopus 로고    scopus 로고
    • 3D model acquisition from extended image sequences
    • B. Buxton and Cipolla R. (Eds.). LNCS 1065, Springer-Verlag: Berlin
    • Beardsley, P., Torr, P.H.S., and Zisserman, A. 1996 3D model acquisition from extended image sequences. In Proc. 4th European Conference on Computer Vision, Cambridge, B. Buxton and Cipolla R. (Eds.). LNCS 1065, Springer-Verlag: Berlin, pp. 683-695.
    • (1996) Proc. 4th European Conference on Computer Vision, Cambridge , pp. 683-695
    • Beardsley, P.1    Torr, P.H.S.2    Zisserman, A.3
  • 7
    • 0000913755 scopus 로고
    • Spatial interaction and statistical analysis of lattice systems
    • Besag, J. 1974 Spatial interaction and statistical analysis of lattice systems. J. Roy. Stat. Soc. Lond. B., 36:192-225.
    • (1974) J. Roy. Stat. Soc. Lond. B. , vol.36 , pp. 192-225
    • Besag, J.1
  • 10
    • 34250108028 scopus 로고
    • Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions
    • Bozdogan, H. 1987 Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3):245-370.
    • (1987) Psychometrika , vol.52 , Issue.3 , pp. 345-370
    • Bozdogan, H.1
  • 11
    • 0003886761 scopus 로고    scopus 로고
    • Efficient approximation for the marginal likelihood of bayesian networks with hidden variables
    • Microsoft, Technical Report msr-tr-96-08
    • Chickering, D. and Heckerman, D. 1996 Efficient approximation for the marginal likelihood of bayesian networks with hidden variables. Microsoft, Technical Report msr-tr-96-08.
    • (1996)
    • Chickering, D.1    Heckerman, D.2
  • 12
    • 0002282678 scopus 로고
    • Probability, frequency, and reasonable expectation
    • Cox, R.T. 1946. Probability, frequency, and reasonable expectation. Am. Jour. Phys., 14:1-13.
    • (1946) Am. Jour. Phys. , vol.14 , pp. 1-13
    • Cox, R.T.1
  • 14
    • 0031258448 scopus 로고    scopus 로고
    • Characterizing the uncertainty of the fundamental matrix
    • Csurka, G., Zeller, C., Zhang, Z., and Faugeras, O. 1996 Characterizing the uncertainty of the fundamental matrix. CVIU, 68(1):18-36.
    • (1996) CVIU , vol.68 , Issue.1 , pp. 18-36
    • Csurka, G.1    Zeller, C.2    Zhang, Z.3    Faugeras, O.4
  • 15
    • 0000042224 scopus 로고
    • Prequential analysis, stochastic complexity and bayesian inference
    • Dawid, A.P. 1992. Prequential analysis, stochastic complexity and bayesian inference. In Bayesian Statistics 4, pp. 109-125.
    • (1992) Bayesian Statistics , vol.4 , pp. 109-125
    • Dawid, A.P.1
  • 17
    • 33747353205 scopus 로고
    • What can be seen in three dimensions with an uncalibrated stereo rig?
    • G. Sandini (Ed.). LNCS 588, Springer-Verlag
    • Faugeras, O.D. 1992. What can be seen in three dimensions with an uncalibrated stereo rig? In Proc. 2nd European Conference on Computer Vision, Santa Margherita Ligure, G. Sandini (Ed.). LNCS 588, Springer-Verlag, pp. 563-578.
    • (1992) Proc. 2nd European Conference on Computer Vision, Santa Margherita Ligure , pp. 563-578
    • Faugeras, O.D.1
  • 19
    • 0027579189 scopus 로고
    • A theory of the motion fields of curves
    • Faugeras, O. and Papadopoulo, T. 1993. A theory of the motion fields of curves. Int. J. Computer Vision, 10(2):125-156.
    • (1993) Int. J. Computer Vision , vol.10 , Issue.2 , pp. 125-156
    • Faugeras, O.1    Papadopoulo, T.2
  • 20
    • 0019574599 scopus 로고
    • Random sample consensus: A paradigm for model fitting with application to image analysis and automated cartography
    • 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.
    • (1981) Commun. Assoc. Comp. Mach. , vol.24 , pp. 381-395
    • Fischler, M.A.1    Bolles, R.C.2
  • 24
    • 0021518209 scopus 로고
    • Stochastic relaxation, gibbs distributions, and the bayesian restoration of images
    • Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(6):721-741.
    • (1984) IEEE Trans. on Pattern Analysis and Machine Intelligence , vol.6 , Issue.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 27
    • 0004798493 scopus 로고
    • Bayesian data analysis: Straight line fitting
    • Kluwer: Dordrecht
    • Gull, S.F. 1989. Bayesian data analysis: Straight line fitting. In Maximum Entropy and Bayesian Methods. Kluwer: Dordrecht.
    • (1989) Maximum Entropy and Bayesian Methods
    • Gull, S.F.1
  • 28
    • 85032868426 scopus 로고
    • Structure from motion under orthographic projection
    • O. Faugeras, (Eds.). Springer-Verlag: Berlin
    • Harris, C. 1990. Structure from motion under orthographic projection. In Proc. 1st European Conf. Computer Vision, O. Faugeras, (Eds.). Springer-Verlag: Berlin. pp. 118-123.
    • (1990) Proc. 1st European Conf. Computer Vision , pp. 118-123
    • Harris, C.1
  • 30
    • 84947592350 scopus 로고
    • Estimation of relative camera positions for uncalibrated cameras
    • G. Sandini (Eds.). LNCS 588, Springer-Verlag: Berlin
    • Hartley, R.I. 1992. Estimation of relative camera positions for uncalibrated cameras. In Proc. 2nd European Conference on Computer Vision, Santa Margherita Ligure, G. Sandini (Eds.). LNCS 588, Springer-Verlag: Berlin, pp. 579-587.
    • (1992) Proc. 2nd European Conference on Computer Vision, Santa Margherita Ligure , pp. 579-587
    • Hartley, R.I.1
  • 32
    • 38249005872 scopus 로고
    • On model selection in the computer age
    • Hjorth, U. 1989. On model selection in the computer age. J. Statist. Planng. Inf., 23:101-115.
    • (1989) J. Statist. Planng. Inf. , vol.23 , pp. 101-115
    • Hjorth, U.1
  • 33
    • 84957796660 scopus 로고    scopus 로고
    • From reference frames to reference planes: Multi-view parallax geometry and its applications
    • H. Burkhardt and B. Neumann (Eds.). LNCS 1406, Springer-Verlag: Berlin
    • Irani, M., Anandan, P., and Weinshall, D. 1998. From reference frames to reference planes: Multi-view parallax geometry and its applications. In Proc. 5th European Conference on Computer Vision, Freiburg, H. Burkhardt and B. Neumann (Eds.). LNCS 1406, Springer-Verlag: Berlin. pp. 829-846.
    • (1998) Proc. 5th European Conference on Computer Vision, Freiburg , pp. 829-846
    • Irani, M.1    Anandan, P.2    Weinshall, D.3
  • 35
    • 0011256315 scopus 로고
    • Straight line fitting-A bayesian solution
    • Jaynes, E.T. 1991. Straight line fitting-A bayesian solution. Available at http://bayes.wustl.edu/etj/node2.html.
    • (1991)
    • Jaynes, E.T.1
  • 36
    • 25544449401 scopus 로고    scopus 로고
    • Probability theory as extended logic
    • Not yet published
    • Jaynes E.T. 1999. Probability Theory as Extended Logic. Not yet published, a postcript version of this excellent book is available at http://bayes.wustl.edu/etj/node2.html.
    • (1999)
    • Jaynes, E.T.1
  • 37
    • 0002624774 scopus 로고
    • An alternative to the rejection of observations
    • Jeffreys, H. 1932. An alternative to the rejection of observations. Proc. Roy. Soc. London A, 137:78-87.
    • (1932) Proc. Roy. Soc. London A , vol.137 , pp. 78-87
    • Jeffreys, H.1
  • 39
    • 0011230513 scopus 로고
    • What is the geometric AIC? Reply to my reviewers
    • unpublished report
    • Kanatani, K. 1987. What is the geometric AIC? Reply to my reviewers. unpublished report.
    • (1987)
    • Kanatani, K.1
  • 46
    • 0023104537 scopus 로고
    • Model selection and validation methods for non-linear systems
    • Leontaritis, I.J. and Billings, S.A. 1987. Model selection and validation methods for non-linear systems. Int. J. Control, 45(1):311-341.
    • (1987) Int. J. Control , vol.45 , Issue.1 , pp. 311-341
    • Leontaritis, I.J.1    Billings, S.A.2
  • 48
    • 51849176383 scopus 로고
    • Approximate Bayesian methods
    • J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith (Eds.). Valencia University Press: Valencia
    • Lindley, D.V. 1980. Approximate Bayesian methods. In Bayesian Statistics, J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith (Eds.). Valencia University Press: Valencia, pp. 223-237.
    • (1980) Bayesian Statistics , pp. 223-237
    • Lindley, D.V.1
  • 49
    • 0001025418 scopus 로고
    • Bayesian interpolation
    • MacKay, D.I.C. 1992. Bayesian Interpolation. Neural Computation, 4:415-447.
    • (1992) Neural Computation , vol.4 , pp. 415-447
    • MacKay, D.I.C.1
  • 51
    • 4644290127 scopus 로고    scopus 로고
    • MDL, collineations and the fundamental matrix
    • Maybank, S.J. and Sturm, P.F. 1999. MDL, collineations and the fundamental matrix. In BMVC, pp. 53-62.
    • (1999) BMVC , pp. 53-62
    • Maybank, S.J.1    Sturm, P.F.2
  • 56
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson, K. 1901. On lines and planes of closest fit to systems of points in space. Philos. Mag. Ser., 6(2):559.
    • (1901) Philos. Mag. Ser. , vol.6 , Issue.2 , pp. 559
    • Pearson, K.1
  • 58
    • 0018151395 scopus 로고
    • Fitting straight lines when both variables are subject to errors
    • Riggs, D., Guarnieri, J., and Addelman, S. 1978. Fitting straight lines when both variables are subject to errors. Life Sciences, 22:1305-1360.
    • (1978) Life Sciences , vol.22 , pp. 1305-1360
    • Riggs, D.1    Guarnieri, J.2    Addelman, S.3
  • 60
    • 0018015137 scopus 로고
    • Modeling by shortest data description
    • Rissanen, J. 1978. Modeling by shortest data description. Automatica, 14:465-471.
    • (1978) Automatica , vol.14 , pp. 465-471
    • Rissanen, J.1
  • 63
    • 0000120766 scopus 로고
    • Estimating dimension of a model
    • Schwarz, G. 1978. Estimating dimension of a model. Ann. Stat., 6:461-464.
    • (1978) Ann. Stat. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 64
    • 0003766008 scopus 로고
    • Affine analysis of image sequences
    • Ph.D. Thesis, Oxford University
    • Shapiro, L.S. 1993. Affine analysis of image sequences. Ph.D. Thesis, Oxford University.
    • (1993)
    • Shapiro, L.S.1
  • 65
    • 0031212528 scopus 로고    scopus 로고
    • Bias in robust estimation caused by discontinuities and multiple structures
    • Stewart, C.V. 1997. Bias in robust estimation caused by discontinuities and multiple structures. IEEE Trans. on Pattern Analysis and Machine Intelligence, 19(8):818-833.
    • (1997) IEEE Trans. on Pattern Analysis and Machine Intelligence , vol.19 , Issue.8 , pp. 818-833
    • Stewart, C.V.1
  • 66
    • 0000859675 scopus 로고
    • An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion
    • Stone, M. 1977. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. Roy. Statist. Soc. B, 39:44-47.
    • (1977) J. Roy. Statist. Soc. B , vol.39 , pp. 44-47
    • Stone, M.1
  • 67
    • 0000169287 scopus 로고
    • Bayesian modelling of uncertainty in low-level vision
    • Szeliski, R. 1990. Bayesian modelling of uncertainty in low-level vision. Int. J. Computer Vision, 5(3):271-301.
    • (1990) Int. J. Computer Vision , vol.5 , Issue.3 , pp. 271-301
    • Szeliski, R.1
  • 68
    • 0011216873 scopus 로고
    • Outlier detection and motion segmentation
    • Ph.D. Thesis, Department of Engineering Science, University of Oxford
    • Torr, P.H.S. 1995. Outlier detection and motion segmentation. Ph.D. Thesis, Department of Engineering Science, University of Oxford.
    • (1995)
    • Torr, P.H.S.1
  • 69
    • 3242741982 scopus 로고    scopus 로고
    • Geometric motion segmentation and model selection
    • J. Lasenby, A. Zisserman, r. Cipolla, and H. Longuet-Higgins (Eds.). Roy Soc,: London
    • Torr, P.H.S. 1998a. Geometric motion segmentation and model selection. In Philosopical Transactions of the Royal Society A, J. Lasenby, A. Zisserman, r. Cipolla, and H. Longuet-Higgins (Eds.). Roy Soc,: London, pp. 1321-1340.
    • (1998) Philosopical Transactions of the Royal Society A , pp. 1321-1340
    • Torr, P.H.S.1
  • 70
    • 0011187379 scopus 로고    scopus 로고
    • Selecting model selection paradigms
    • In D. Fosyth and R. Cipolla (Eds.)
    • Torr, P.H.S. 1998b. Selecting model selection paradigms. In D. Fosyth and R. Cipolla (Eds.) Workshop on Shape, Contour and Grouping, pp. 69-113, 1998.
    • (1998) Workshop on Shape, Contour and Grouping , pp. 69-113
    • Torr, P.H.S.1
  • 71
    • 0002573182 scopus 로고    scopus 로고
    • Model selection for structure and motion recovery from multiple images
    • Springer-Verlag: Berlin
    • Torr, P.H.S. 2000. In Data Segmentation and Model Selection for Computer Vision. Model selection for structure and motion recovery from multiple images. Springer-Verlag: Berlin, pp. 143-182.
    • (2000) Data Segmentation and Model Selection for Computer Vision , pp. 143-182
    • Torr, P.H.S.1
  • 73
    • 0032316034 scopus 로고    scopus 로고
    • Maintaining multiple motion model hypotheses through many views to recover matching and structure
    • U Desai (Eds.). Narosa Publishing House
    • Torr, P.H.S., Fitzgibbon, A., and Zisserman, A. 1998a. Maintaining multiple motion model hypotheses through many views to recover matching and structure. In ICCV6, U Desai (Eds.). Narosa Publishing House, pp. 485-492.
    • (1998) ICCV6 , pp. 485-492
    • Torr, P.H.S.1    Fitzgibbon, A.2    Zisserman, A.3
  • 74
    • 0032597866 scopus 로고    scopus 로고
    • The problem of degeneracy in structure and motion recovery from uncalibrated image sequences
    • Marr Prize Paper ICCV 1999
    • Torr, P.H.S., Fitzgibbon, A., and Zisserman, A. 1999. The problem of degeneracy in structure and motion recovery from uncalibrated image sequences. IJCV, 32(1):27-45. Marr Prize Paper ICCV 1999.
    • (1999) IJCV , vol.32 , Issue.1 , pp. 27-45
    • Torr, P.H.S.1    Fitzgibbon, A.2    Zisserman, A.3
  • 75
    • 0031233843 scopus 로고    scopus 로고
    • The development and comparison of robust methods for estimating the fundamental matrix
    • Torr, P.H.S. and Murray, D.W. 1997. The development and comparison of robust methods for estimating the fundamental matrix. Int. Journal of Computer Vision, 24(3):271-300.
    • (1997) Int. Journal of Computer Vision , vol.24 , Issue.3 , pp. 271-300
    • Torr, P.H.S.1    Murray, D.W.2
  • 76
    • 0031207058 scopus 로고    scopus 로고
    • Robust parameterization and computation of the trifocal tensor
    • Torr, P.H.S. and Zisserman, A. 1997. Robust parameterization and computation of the trifocal tensor. Image and Vision Computing, 15:591-607.
    • (1997) Image and Vision Computing , vol.15 , pp. 591-607
    • Torr, P.H.S.1    Zisserman, A.2
  • 77
    • 0000195504 scopus 로고    scopus 로고
    • Concerning Bayesian motion segmentation, model averaging, matching and the trifocal tensor
    • H. Burkharddt and B. Neumann (Eds.). Springer: Berlin
    • Torr, P.H.S. and Zisserman, A. 1998a. Concerning Bayesian motion segmentation, model averaging, matching and the trifocal tensor. In ECCV98, Vol. 1, H. Burkharddt and B. Neumann (Eds.). Springer: Berlin, pp. 511-528.
    • (1998) ECCV98 , vol.1 , pp. 511-528
    • Torr, P.H.S.1    Zisserman, A.2
  • 78
    • 0032319452 scopus 로고    scopus 로고
    • Robust computation and parametrization of multiple view relations
    • U Desai (Ed.). Narosa Publishing House
    • Torr, P.H.S. and Zisserman, A. 1998b. Robust computation and parametrization of multiple view relations. In ICCV6, U Desai (Ed.). Narosa Publishing House, pp. 727-732.
    • (1998) ICCV6 , pp. 727-732
    • Torr, P.H.S.1    Zisserman, A.2
  • 79
    • 0033894631 scopus 로고    scopus 로고
    • MLESAC: A new robust estimator with application to estimating image geometry
    • Torr, P.H.S. and Zisserman, A. 2000. MLESAC: A new robust estimator with application to estimating image geometry. CVIU, 78(1):138-156.
    • (2000) CVIU , vol.78 , Issue.1 , pp. 138-156
    • Torr, P.H.S.1    Zisserman, A.2
  • 80
    • 0032166743 scopus 로고    scopus 로고
    • Robust detection of degenerate configurations for the fundamental matrix
    • Torr, P.H.S., Zisserman, A., and Maybank, S. 1998b. Robust detection of degenerate configurations for the fundamental matrix. CVIU, 71(3):312-333.
    • (1998) CVIU , vol.71 , Issue.3 , pp. 312-333
    • Torr, P.H.S.1    Zisserman, A.2    Maybank, S.3
  • 81
    • 0002929783 scopus 로고    scopus 로고
    • The geometry and matching of curves in multiple views
    • H. Burkharddt and B. Neumann (Eds.). Springer: Berlin
    • Triggs, B. 1998. The geometry and matching of curves in multiple views. In ECCV98, vol. 1, H. Burkharddt and B. Neumann (Eds.). Springer: Berlin pp. 89-105.
    • (1998) ECCV98 , vol.1 , pp. 89-105
    • Triggs, B.1
  • 82
    • 0029226180 scopus 로고
    • The geometry of projective reconstruction I: Matching constraints and the joint image
    • Triggs, W. 1995. The geometry of projective reconstruction I: Matching constraints and the joint image. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pp. 338-343.
    • (1995) Proc. 5th Int'l Conf. on Computer Vision, Boston , pp. 338-343
    • Triggs, W.1
  • 84
    • 0000107517 scopus 로고
    • An information measure for classification
    • Wallace, C.S. and Boulton, D.M. 1968. An information measure for classification. Computer Journal, 11(2):195-209.
    • (1968) Computer Journal , vol.11 , Issue.2 , pp. 195-209
    • Wallace, C.S.1    Boulton, D.M.2
  • 85
    • 0030683247 scopus 로고    scopus 로고
    • Smoothness in layers: Motion segmentation using nonparametric mixture estimation
    • Weiss, Y. 1997. Smoothness in layers: Motion segmentation using nonparametric mixture estimation. In CVPR. IEEE, pp. 520-526.
    • (1997) CVPR. IEEE , pp. 520-526
    • Weiss, Y.1
  • 87
    • 0035332903 scopus 로고    scopus 로고
    • A Bayesian method for fitting parametric and nonparametric model to noisy data
    • Werman, M. and Keren, D. 2001. A Bayesian method for fitting parametric and nonparametric model to noisy data. IEEE PAMI, 23(5):528-534.
    • (2001) IEEE PAMI , vol.23 , Issue.5 , pp. 528-534
    • Werman, M.1    Keren, D.2
  • 90
    • 0011230514 scopus 로고
    • Jeffreys-Bayes posterior odds ratio and the akaike information criterion for discriminating between models
    • Zellner, A. 1978. Jeffreys-Bayes posterior odds ratio and the akaike information criterion for discriminating between models. Economics Letters, 1:337-442.
    • (1978) Economics Letters , vol.1 , pp. 337-442
    • Zellner, A.1
  • 91
    • 0032024706 scopus 로고    scopus 로고
    • Determining the epipolar geometry and its uncertainty: A review
    • Zhang, Z. 1997a. Determining the epipolar geometry and its uncertainty: A review. IJCV, 27(2):161-195.
    • (1997) IJCV , vol.27 , Issue.2 , pp. 161-195
    • Zhang, Z.1
  • 92
    • 0030815476 scopus 로고    scopus 로고
    • Parameter estimation techniques: A tutorial with application to conic fitting
    • Zhang, Z. 1997b. Parameter estimation techniques: A tutorial with application to conic fitting. IVC, 15(1):59-76.
    • (1997) IVC , vol.15 , Issue.1 , pp. 59-76
    • Zhang, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.