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On the unification of line processes, outlier rejection, and robust statistics with applications in early vision

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Abstract

The modeling of spatial discontinuities for problems such as surface recovery, segmentation, image reconstruction, and optical flow has been intensely studied in computer vision. While “line-process” models of discontinuities have received a great deal of attention, there has been recent interest in the use of robust statistical techniques to account for discontinuities. This paper unifies the two approaches. To achieve this we generalize the notion of a “line process” to that of an analog “outlier process” and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics. We also characterize a class of robust statistical problems for which an equivalent outlier-process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier-process formulation. We show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier-process formulation. These results indicate that the outlier-process approach provides a general framework which subsumes the traditional line-process approaches as well as a wide class of robust estimation problems. Examples in surface reconstruction, image segmentation, and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited. An appendix provides a catalog of common robust error norms and their equivalent outlier-process formulations.

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References

  • Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., and Tukey, J.W. 1972.Robust Estimates of Location: Survey and Advances, Princeton University Press, Princeton, N.J.

    Google Scholar 

  • Beaton, A.E. and Tukey, J.W. 1974. The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data.Technometrics, 16:147–185.

    Google Scholar 

  • Bertero, M., Poggio, T.A., and Torre, V. 1988. Ill-posed problems in early vision. In Proceedings of the IEEE, 76(8):869–889.

  • Besl, P.J., Birch, J.B., and Watson, L.T. 1988. Robust window operators. In Proc. Int. Conf. on Comp. Vision, ICCV-88, pp. 591–600.

  • Black, M.J. and Anandan, P. 1991. Robust dynamic motion estimation over time. In Proc. Computer Vision and Pattern Recognition, CVPR-91, Maui, Hawaii, pp. 296–302.

  • Black, M.J. 1992.Robust Incremental Optical Flow, Ph.D. thesis, Yale University, New Haven, CT, Research Report YALEU/DCS/RR-923.

  • Black, M.J. and Anandan, P. 1993. A framework for the robust estimation of optical flow. In Proc. Int. Conf. on Computer Vision, ICCV-93, Berlin, Germany, pp. 231–236.

  • Black, M.J. and Anandan, P. 1996. The robust estimation of optical flow: Parametric and piecewise-smooth flow fields.Computer Vision and Image Understanding, 63(1):75–104.

    Google Scholar 

  • Blake, A. and Zisserman, A. 1987.Visual Reconstruction. The MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Campbell, N.E. 1980. Robust procedures in multivariate analysis I: Robust covariance estimation.Appl. Statist., 29(3):231–237.

    Google Scholar 

  • Canny, J. 1986. A computational approach to edge detection.IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):679–698.

    Google Scholar 

  • Chen, D.S. and Schunck, B.G. 1990. Robust statistical methods for building classification procedures. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 72–85.

  • Chou, P.B. and Brown, C.M. 1990. The theory and practice of Bayesian image labeling.Int. Journal of Computer Vision, 4(3):185–210.

    Google Scholar 

  • Derin, H. and Elliott, H. 1987. Modeling and segmentation of noisy and textured images using Gibbs random fields.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9(1):39–55.

    Google Scholar 

  • Förstner, W. 1987. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision.Computer Vision Graphics and Image Processing, 40:273–310.

    Google Scholar 

  • Förstner, W. 1989. Tutorial Proceedings: Robust statistical methods for computer vision.Computer Vision and Pattern Recognition, San Diego, CVPR-89.

  • Geiger, D. and Girosi, F. 1991. Parallel and deterministic algorithms from MRFs: Surface reconstruction.IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(5):401–412.

    Google Scholar 

  • Geiger, D. and Pereira, R.A.M. 1992. Learning how to teach or selecting minimal surface data. In Advances in Neural Information Processing Systems 4, J.E. Moody, S.J. Hanson, and R.P. Lippmann (Eds.), pp. 364–371.

  • Geiger, D. and Yuille, A. 1991. A common framework for image segmentation.International Journal of Computer Vision, 6(3):227–243.

    Google Scholar 

  • Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distributions and Bayesian restoration of images.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6):721–741.

    Google Scholar 

  • Geman, S. and McClure, D.E. 1987. Statistical methods for tomographic image reconstruction.Bulletin of the International Statistical Institute, LII-4:5–21.

    Google Scholar 

  • Geman, D. and Reynolds, G. 1992. Constrained restoration and the recovery of discontinuities.IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(3):376–383.

    Google Scholar 

  • Geman, D., Geman, S., Graffigne, C., and Dong, P. 1990. Boundary detection by constrained optimization.IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):609–628.

    Google Scholar 

  • Hadamard, J. 1923.Lectures on the Cauchy Problem in Linear Partial Differential Equations, Yale University Press, New Haven, CT.

    Google Scholar 

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. 1986.Robust Statistics: The Approach Based on Influence Functions. John Wiley and Sons, New York, NY.

    Google Scholar 

  • Harris, J.G., Koch, C., Staats, E., and Luo, J. 1990. Analog hardware for detecting discontinuities in early vision.Int. Journal of Comp. Vision, 4(3):211–223.

    Google Scholar 

  • Hebert, T. and Leahy, R. 1989. A generalized EM algorithm for 3-D Bayesian reconstruction for Poisson data using Gibbs priors.IEEE Transactions on Medical Imaging, MI-8(2):194–202.

    Google Scholar 

  • Hinton, G. 1978.Relaxation and its Role in Vision. Ph.D. thesis, University of Edinburgh.

  • Horn, B.K.P. and Schunck, B.G. 1981. Determining optical flow.Artificial Intelligence, 17(1–3):185–203.

    Google Scholar 

  • Huber, P.J. 1981.Robust Statistics. John Wiley and Sons, New York, NY.

    Google Scholar 

  • Konrad, J. and Duhois, E. 1988. Multigrid Bayesian estimation of image motion fields using stochastic relaxation. In Int. Conf. on Computer Vision, pp. 354–362.

  • Kumar, R. and Hanson, A.R. 1990. Analysis of different robust methods for pose refinement. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 167–182.

  • Leelere, Y.G. 1989. Constructing simple stable descriptions for image partitioning.International Journal of Computer Vision, 3(1):73–102.

    Google Scholar 

  • Lee, M., Rangarajan, A., Zubal, I.G., and Gindi, G. 1993. A continuation method for emission tomography.IEEE Trans. Nuclear Science, 40:2049–2058.

    Google Scholar 

  • Lui, L., Schunck, B.G., and Meyer, C.C. 1990. On robust edge detection. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 261–286.

  • Marroquin, J., Mitter, S., and Poggio, T. 1987. Probabilistic solution of ill-posed problems in computational vision.J. of the American Statistical Assoc., 82(397):76–89.

    Google Scholar 

  • Meer, P., Mintz, D., and Rosenfeld, A. 1990. Robust recovery of piecewise polynomial image structure. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 109–126.

  • Meer, P., Mintz, D., Rosenfeld, A., and Kim, D.Y. 1991. Robust regression methods for computer vision: A review.International Journal of Computer Vision, 6(1):59–70.

    Google Scholar 

  • Mumford, D. and Shah, J. 1985. Boundary detection by minimizing functionals. In Proc. Computer Vision and Pattern Recognition, San Francisco, CVPR-85:22–25.

  • Murray, D.W. and Buxton, B.F. 1987. Scene segmentation from visual motion using global optimization.IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-9(2):220–228.

    Google Scholar 

  • Nevatia, R. and Babu, K.R. 1987. Linear feature extraction and description.Computer Graphics and Image Processing, 13:257–269.

    Google Scholar 

  • Perona, P. and Malik, J. 1990. Scale-space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639.

    Google Scholar 

  • Rangarajan, A. and Chellappa, R. 1993. A continuation method for image estimation using the adiabatic approximation. In Markov Random Fields: Theory and Applications, R. Chellappa and A. Jain (Eds.), Academic Press, Inc., pp. 69–91.

  • Robust Workshop, 1990.Proc. Int. Workshop on Robust Computer Vision, Seattle, WA.

  • Rousseeuw, P.J. and Leroy, A.M. 1987.Robust Regression and Outlier Detection. John Wiley & Sons, New York.

    Google Scholar 

  • Schunck, B.G. 1989. Image flow segmentation and estimation by constraint line clustering.IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(10):1010–1027.

    Google Scholar 

  • Schunck, B.G. 1990. Robust computational vision. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 1–18.

  • Shah, J. 1991. Segmentation by nonlinear diffusion. In Proc. Computer Vision and Pattern Recognition, CVPR-91, Maui, Hawaii, pp. 202–207.

  • Shulman, D. and Hervé, J. 1989. Regularization of discontinuous flow fields. In Proc. Workshop on Visual Motion, Irvine, CA, IEEE Computer Society Press, pp. 81–85.

    Google Scholar 

  • Sinha, S.S. and Schunck, B.G. 1992. A two-stage algorithm for discontinuity-preserving surface reconstruction.IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(1):36–55.

    Google Scholar 

  • Terzopoulos, D. 1986. Regularization of inverse visual problems involving discontinuities.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(4):413–424.

    Google Scholar 

  • Tian, Y. and Shah, M. 1992. MRF-Based motion estimation and segmentation, Technical Report CS-TR-92–13, University of Central Florida, Orlando, FL.

    Google Scholar 

  • Tirumalai, A.P., Schunck, B.G., and Jain, R.C. 1990. Robust dynamic stereo for incremental disparity map refinement. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 412–434.

  • Weng, J. and Cohen, P. 1990. Robust motion and structure estimation using stereo vision. In Proc. Int. Workshop on Robust Computer Vision, Seattle, WA, pp. 367–388.

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Authors and Affiliations

  1. Xerox Palo Alto Research Center, 94304, Palo Alto, CA

    Michael J. Black

  2. Department of Diagnostic Radiology, Yale University, 06520-8042, New Haven, CT

    Anand Rangarajan

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  1. Michael J. Black
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  2. Anand Rangarajan
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Black, M.J., Rangarajan, A. On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Int J Comput Vision 19, 57–91 (1996). https://doi.org/10.1007/BF00131148

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  • DOI: https://doi.org/10.1007/BF00131148

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