Physics in a fantasy world vs robust statistical estimation

  • Terrance E. Boult
  • Samuel D. Fenster
  • Thomas O'Donnell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 994)


Deformable models in the “physically-based” paradigm are almost always formulated in an ad-hoc fashion, not related to physical reality — they apply the equations on physics in a fantasy world. This paper discusses some of the drawbacks of this approach. Still these techniques have shown themselves to be useful, so there must be something here. This paper reinterprets these “physics-based” techniques by putting them into a framework of robust statistics. We use this framework to analyze the problems and ad-hoc solutions found in common physically-based formulations. These include incorrect prior shape models; bad relative weights of various energies; and the two-stage approach to minimization (adjusting global, then local shape parameters). We examine the statistical implications of common deformable object formulations. In our reformulation, the units are meaningful, training data plays a fundamental role, different kinds of information may be fused, and certainties can be reported for the segmentation results. The robust aspects of the reformulation are necessary to combat interference from the necessarily large amount of unmodeled image information.


Mahalanobis Distance IEEE Conf Data Force Deformable Model Image Force 
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.


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  1. [Aka73]
    H. Akaike. Information theory and an extension of the maximum likelihood principle. In Proc. Second International Symposium on Information Theory, pages 267–281, 1973.Google Scholar
  2. [Bal94]
    Bernard Baldwin. personal conversations on thesis work, 1994. Mr. Baldwin is at the Courant Institute of New York University. Research in cooperation with the Memorial Sloan-Kettering Cancer Center.Google Scholar
  3. [Bat82]
    K.J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1982.Google Scholar
  4. [Boz87]
    H. Bozdogan. Model selection and akaike's information criterion (aic): General theory and its analytical extensions. Pyschometrika, 52(3):345–370, 1987.Google Scholar
  5. [CC90]
    L.D. Cohen and I Cohen. A finite element method applied to new active contour models and 3d reconstruction from cross-sections. In Proc. of the IEEE Int. Conf. on Computer Vision, pages 587–591, Osaka, Japan, 1990. IEEE.Google Scholar
  6. [CHTH93]
    T.F. Cootes, A. Hill, C.J. Taylor, and J. Haslam. The use of active shape models for locating structures in medical images. In Proceedings of the 13th International Conference on Information Processing in Medical Imaging, Flagstaff AZ, June 1993. Springer-Verlag.Google Scholar
  7. [Coh91]
    L.D. Cohen. On active contour models and balloons. Computer visoin graphics and image processing: Image Understanding (CVGIP:IU), pages 211–218, March 1991.Google Scholar
  8. [CSD94]
    A. Chakraborty, L.H. Staib, and J.S. Duncan. Deformable boundary finding influenced by region homogeneity. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 624–627, June 1994.Google Scholar
  9. [GG91]
    D. Geiger and F. Girosi. Parallel and deterministic algorithms from mrf's: Surface reconstruction. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-13(5):674–693, May 1991.Google Scholar
  10. [HG93]
    W.C. Huang and D. Goldgof. Nonridged motion analysis using non-linear fineite element modeling. In Geometric Methods in Computer Vision, volume 2031, pages 404–415. SPIE, 1993.Google Scholar
  11. [Hub81]
    P. Huber. Robust Statistics. Wiley, New York, 1981.Google Scholar
  12. [KH94]
    C. Kervrann and F. Heitz. A heirarchical stastical framework for the segmentation of deformable objects in image sequences. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 724–727, June 1994.Google Scholar
  13. [KW70]
    G.S. Kimeldorf and G. Wahba. A correspondence between bayesian estimation on stocastic processes and smoothing by splines. Annals of Math. Stat., 41(2):495–502, 1970.Google Scholar
  14. [KWT87]
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. In Proc. of the IEEE Int. Conf. on Computer Vision, pages 259–268, London UK, 1987. IEEE.Google Scholar
  15. [LC94]
    K.F. Lai and R.T. Chin. Deformable contours: Modeling and extraction. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 601–608, June 1994.Google Scholar
  16. [LL93]
    F. Leymarie and M.D. Levine. Tracking deformable objects in the plane using an active contour model. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15(6):617–633, June 1993.Google Scholar
  17. [MB88]
    M.L. Moerdler and T.E. Boult. The integration of information from stereo and multiple shape-from texture algorithms. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 514–529. IEEE, 1988.Google Scholar
  18. [MB93]
    M.J. Mirza and K.L. Boyer. Performance evaluation of a class of m-estimators for surface parameter estimation in noisy range data. IEEE Trans. on Robotics and Automation, 9:75–85, 1993.Google Scholar
  19. [MMRK91]
    P. Meer, D. Mintz, A. Rosenfeld, and D.Y. Kim. Robust regression methods for computer vision: A review. Inter. J. Computer Vision, 6(1):59–70, 1991.Google Scholar
  20. [NFSK94]
    W. Neuenschwander, P. Fua, G. Székely, and O. Kübler. Initializing snakes. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 658–663, June 1994.Google Scholar
  21. [OFBG94]
    T. O'Donnell, X.S. Fang, T.E. Boult, and A. Gupta. The extruded generalized cylinder: A deformable model for object recovery. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, June 1994.Google Scholar
  22. [OGB94]
    T. O'Donnell, A. Gupta, and T.E. Boult. A periodic generalized cylinder model with local deformations for tracking closed contours exhibiting repeating motion. In The International Conference on Pattern Recognition, Nov. 1994.Google Scholar
  23. [PMY94]
    J. Park, D. Metaxas, and A. Young. Deformable modles with parameter functions: Application to heart-wall modeling. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 437–442, June 1994.Google Scholar
  24. [PS91]
    A. Pentland and S. Sclaroff. Closed-form solutions for physically based shape modeling and recognition. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-13(7):715–729, July 1991.Google Scholar
  25. [RL87]
    P.J Rousseeuw and A.M. Leroy. Robust Regression and Outlier Detection. J. Wiley, New York, New York, 1987.Google Scholar
  26. [ST89]
    R. Szeliski and D. Terzopoulos. Constrained fractals. Computer Graphics, 23(3):51–60, 1989. (SIGGRAPH).Google Scholar
  27. [Sze89]
    R. Szeliski. Baysian Modeling of Uncertanity in Low-level Vision. Kluwer Academic Publishers, Boston, MA, 1989.Google Scholar
  28. [TM91]
    D. Terzopoulos and D. Metaxas. Dynamic 3d models with local and global deformations: Deformable superquadrics. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-13(7):703–714, July 1991.Google Scholar
  29. [TW93]
    D. Terzopoulos and K. Waters. Analysis and synthesis of facial images sequences using physical and anotomical models. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15:569–579, 1993.Google Scholar
  30. [VR93]
    B.C. Vemuri and A. Radisavljevic. From global to local, a continuum of shape models with fractal priors. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pages 307–313, NYC NY, June 1993.Google Scholar
  31. [VR94]
    B.C. Vemuri and A. Radisavljevic. Multiresolution stochastic hybrid spahe models with fractal priors. ACM TOGS, 1994. Special issue on Interactive Sculpting.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Terrance E. Boult
    • 1
  • Samuel D. Fenster
    • 2
  • Thomas O'Donnell
    • 2
  1. 1.EECS Dept., 304 Packard LaboratoryLehigh UniversityBethlehemUSA
  2. 2.Dept. of Computer ScienceColumbia Univ.NYCUSA

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