Bucketing Techniques in Robust Regression for Computer Vision

  • Ariel Choukroun
  • Vincent Charvillat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2749)

Abstract

Robust parameter estimation methods have become very popular in the computer vision community. Nevertheless, both optimization models and resolution algorithms coming from robust statistics must be adapted to correctly tackle the specificities of visual data. Among these adapted techniques, computer-vision researchers frequently use bucket-based partitions of the data (bucketing techniques). This work points out the key ideas and features of bucketing techniques. A new stochastic sampling scheme is proposed and defended. We also try to answer several questions, which are generally -and perhaps voluntarily-bypassed : “does the bucketing strategy influence the regression process?”; “how should the data be split into buckets to get the best fits both numerically and physically?” . . .

Keywords

Computer Vision Ordinary Little Square Robust Estimator Robust Regression Minimal Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    P.T. Boggs, R.H. Byrd, and R.B Schnabel. A stable and efficient algorithm for non linear orthogonal distance regression. SIAM Journal on Scientific and Statistical Computing, pages 1052–1078, 1987.Google Scholar
  2. 2.
    V. Braivlovsky. An approach to outlier detection based on a probalistic model. ICPR’96, Vienna, 2:70–75, 1996.Google Scholar
  3. 3.
    M.A. Fischler and R.C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications for the Association for Computing Machinery, pages 381–895, 1981.Google Scholar
  4. 4.
    M.D. Levine G. Roth. Geometric primitives extraction using a genetic algorithm. IEEE transactions on Pattern Analysis and Machine Intelligence, pages 901–905, 1994.Google Scholar
  5. 5.
    S. Van Huffel. Recent advances in total least squares techniques and error-invariables modeling. SIAM, 1997.Google Scholar
  6. 6.
    S. Van Huffel and J. Vandewalle. The total least squares problem, computational aspects and analysis. SIAM, 1991.Google Scholar
  7. 7.
    B. Thiesse M. Douze, V. Charvillat. More precise and robust mosaics. In proceedings of RFIA, volume 1, Angers, France, 2002.Google Scholar
  8. 8.
    P. Meer, D. Mintz, A. Rosenfeld, and D.Y. Kim. Robust regression in computer vision: a review. International Journal in Computer Vision, pages 59–71, 1991.Google Scholar
  9. 9.
    A. Zisserman R. Hartley. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000.Google Scholar
  10. 10.
    P.J. Rousseeuw and K. Van Driessen. Computing lts for large data sets. Tech. Report. Univ. of Antwerp, 1999.Google Scholar
  11. 11.
    P.J. Rousseeuw and M. Hubert. Recent developments in progress. L1-Statistical procedures and related topics, 1997.Google Scholar
  12. 12.
    P.J. Rousseuw and A.M. Leroy. Robust regression and outlier detection. John Wiley and Sons, 1987.Google Scholar
  13. 13.
    C.V. Stewart. A new robust operator for computer vision: theorical analysis. Technical report, Departement of Computer Science, Rensselaer, NY, 1993.Google Scholar
  14. 14.
    C.V. Stewart. Minpran: a new robust operator for computer vision. IEEE transactions on Pattern Analysis and Machine Intelligence, 1995.Google Scholar
  15. 15.
    P.H.S Torr and D.W. Murray. The developpement and comparison of robust methods for estimating the fnudamental matrix. Int. Journal of Computer Vision, 24(2):271, 1997.CrossRefGoogle Scholar
  16. 16.
    P. Veelaert. Constructive fitting and extraction of geometric primitives. Graphical Models and Image Processing, pages 233–251, 1997.Google Scholar
  17. 17.
    Z. Zhang. Tutorial on parameter estimation techniques. http://wwwsop.inria.fr/robotvis/personnel/zzhang/Publis/Tutorial-Estim/node25.html, 1996.Google Scholar
  18. 18.
    Z. Zhang. Parameter estimation techniques: a tutorial with application to conic fitting. Image and Vision computing, pages 59–76, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ariel Choukroun
    • 1
  • Vincent Charvillat
    • 1
  1. 1.IRIT-ENSEEIHT UMR CNRS 5505Toulouse Cedex 7

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