Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition

EMMCVPR 1997: Energy Minimization Methods in Computer Vision and Pattern Recognition pp 35–50Cite as

Adaptive parametrically deformable contours

  • Contours and Deformable Models
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1223))

Abstract

In this paper, we introduce an unsupervised contour estimation strategy based on parametrically deformable models. The problem is formulated in a (statistical) parameter estimation framework with the parameters of both the contour the and observation model (the likelihood function) being considered unknown. Although other choices could fit in our formulation, we focus on Fourier and B-spline contour descriptors. To estimate the optimal parametrization order (e.g., the number of Fourier coefficients) we adopt the minimum description length (MDL) principle. The result is a parametrically deformable contour with an adaptive degree of smoothness and which also autonomously estimates the observation model parameters.

The work described in this paper was partially supported by the NATO Collaborative Research Grant #CRG 960010.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Amini, T. Weymouth, and R. Jain. “Using dynamic programming for solving variational problems in vision”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 12, pp. 855–867, 1990.

    Google Scholar 

  2. Y. Amit, U. Grenander, and M. Piccioni. “Structural image restoration through deformable templates”. Jour. of the American Statistical Association, vol. 86, pp. 376–387, 1991.

    Google Scholar 

  3. S. Campbell and Jr. C. Meyer. Generalized Inverses of Linear Transformations. Pitman, London, 1979.

    Google Scholar 

  4. V. Caselles, R. Kimmel, and G. Sapiro. “Geodesic active contours”, in Intern. Conference on Computer Vision — ICCV'95, pp. 694—699, Cambridge (MA), 1995.

    Google Scholar 

  5. A. Chakraborty, L. Staib, and J. Duncan. “Deformable boundary finding influenced by region homogeneity”, in IEEE Conference on Computer Vision and Pattern Recognition — CVPR'94, pp. 624–627, Seattle, 1994.

    Google Scholar 

  6. L. Cohen. “On active contour models and baloons”. Computer Vision, Graphics, and Image Processing (CVGIP): Image Understanding, vol. 53, pp. 211–218, 1991.

    Google Scholar 

  7. L. Cohen. “Auxiliary variables and two-step iterative algorithms in computer vision problems”. Jour. of Mathematical Imaging and Vision, vol. 6, pp. 59–83, 1996.

    Google Scholar 

  8. L. Cohen and I. Cohen. “Finite-element methods for active contour models and baloons for 2D and 3D images”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 15, pp. 1131–1147, 1993.

    Google Scholar 

  9. T. Cover and J. Thomas. Elements of Information Theory. John Wiley & Sons, New York, 1991.

    Google Scholar 

  10. C. deBoor. A Practical Guide to Splines. Springer Verlag, N. York, 1978.

    Google Scholar 

  11. A. Dempster, N. Laird, and D. Rubin. “Maximum likelihood estimation from incomplete data via the EM algorithm”. Jour. of the Royal Statistical Society B, vol. 39, pp. 1–38, 1977.

    Google Scholar 

  12. J. Dias and J. LeitÃo. “Wall position and thickness estimation from sequences of echocardiographic images”. IEEE Trans. on Medical Imaging, vol. 15, pp. 25–38, 1996.

    Google Scholar 

  13. B. Dom. MDL Estimation for Small Sample Sizes and Its Application to Linear Regression. IBM Research Report RJ 10030, Almaden Research Center, San Jose (CA), 1996.

    Google Scholar 

  14. G. Farin. Curves and Surfaces for Computer Aided Geometrical Design. Academic Press, Boston, 1990.

    Google Scholar 

  15. M. Figueiredo and J. LeitÃo. “Bayesian estimation of ventricular contours in angiographic images”. IEEE Trans. on Medical Imaging, vol. 11, pp. 416–429, 1992.

    Google Scholar 

  16. U. Grenander. General Pattern Theory: A Mathematical Study of Regular Structures. Oxford University Press, Oxford, 1993.

    Google Scholar 

  17. U. Grenander and M. Miller. “Representation of knowledge in complex systems”. Jour. of the Royal Statistical Society B, vol. 56, pp. 1–33, 1994.

    Google Scholar 

  18. J. Ivins and J. Porrill. “Active region models for segmenting medical images”, in IEEE Intern. Conference on Image Processing — ICIP'94, pp. 227–231, Austin, 1995.

    Google Scholar 

  19. A. Jain. Fundamentals of Digital Image Processing. Prentice Hall, Englewood Cliffs, 1989.

    Google Scholar 

  20. A. Jain, Y. Zhong, and S. Lakshmanan. “Object matching using deformable templates”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 18, pp. 267–277, 1996.

    Google Scholar 

  21. M. Dubuisson Jolly, S. Lakshmanan, and A. Jain. “Vehicle segmentation and classification using deformable templates”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 18, pp. 293–308, 1996.

    Google Scholar 

  22. M. Kass, A. Witkin, and D. Terzopoulos. “Snakes: Active contour models”. Intern. Journal of Computer Vision, vol. 1, pp. 259–268, 1987.

    Google Scholar 

  23. E. Kreyszig. Introductory Functional Analysis with Applications. John Wiley & Sons, New York, 1978.

    Google Scholar 

  24. D. Luenberger. Linear and Nonlinear Programming. Addison Wesley Publishing Company, Reading, Massachusetts, 1984. 2nd Edition.

    Google Scholar 

  25. R. Malladi, J. Sethian, and B. Vemuri. “Shape modeling with front propagation”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 17, pp. 158–175, 1995.

    Article  Google Scholar 

  26. T. McInerney and D. Terzopoulos. “Topologically adaptable snakes”, in Intern. Conference on Computer Vision — ICCV'95, pp. 840–845, Cambridge, 1995.

    Google Scholar 

  27. B. Porat. Digital Processing of Random Signals. Prentice Hall, New Jersey, 1994.

    Google Scholar 

  28. P. Radeva, J. Serrat, and E. Martí. “A snake for model-based segmentation”, in Intern. Conference on Computer Vision — ICCV'95, pp. 816–821, Cambridge, 1995.

    Google Scholar 

  29. J. Rissanen. “A universal prior for integers and estimation by minimum description length”. Annals of Statistics, vol. 11, pp. 416–431, 1983.

    Google Scholar 

  30. J. Rissanen. Stochastic Complexity in Stastistical Inquiry. World Scientific, Singapore, 1989.

    Google Scholar 

  31. R. Ronfard. “Region-based strategies for active contour models”. Intern. Journal of Computer Vision, vol. 13, pp. 229–251, 1994.

    Article  Google Scholar 

  32. J. Rosen. “The gradient projection method of nonlinear programming. Part I, linear constraints”. SIAM Journal, vol. 8, pp. 181–217, 1960.

    Google Scholar 

  33. L. Staib and J. Duncan. “Boundary finding with parametrically deformable models”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 14, pp. 1061–1075, 1992.

    Article  Google Scholar 

  34. G. Storvik. “A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 16, pp. 976–986, 1994.

    Article  Google Scholar 

  35. D. Youla. “Generalized image restoration by the method of alternating projections”. IEEE Trans. on Circuits and Systems, vol. 25, pp. 694–702, 1978.

    Article  Google Scholar 

  36. A. Yuille. “Generalized deformable models, statistical physics, and the matching problem”. Neural Computation, vol. 2, pp. 1–24, 1990.

    Google Scholar 

  37. A. Yuille and P. Hallinan. “Deformable templates”, in A. Blake and A. Yuille, editors, Active Vision, pp. 21–38. MIT Press, 1992.

    Google Scholar 

  38. S. Zhu, and A. Yuille. “Region competition: unifying snakes, region growing, and Bayes/MDL for multi-band image segmentation”. IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 18, pp. 884–900, 1996.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Telecomunicações, 1096, Lisboa Codex, Portugal

    Mário A. T. Figueiredo & José M. N. Leitão

  2. Departamento de Engenharia Electrotécnica e de Computadores, Instituto Superior Técnico, 1096, Lisboa Codex, Portugal

    Mário A. T. Figueiredo & José M. N. Leitão

  3. Department of Computer Science, Michigan State University, 48824, East Lansing, MI, USA

    Anil K. Jain

Authors
  1. Mário A. T. Figueiredo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José M. N. Leitão
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anil K. Jain
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marcello Pelillo Edwin R. Hancock

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Figueiredo, M.A.T., Leitão, J.M.N., Jain, A.K. (1997). Adaptive parametrically deformable contours. In: Pelillo, M., Hancock, E.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1997. Lecture Notes in Computer Science, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62909-2_71

Download citation

  • DOI: https://doi.org/10.1007/3-540-62909-2_71

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62909-2

  • Online ISBN: 978-3-540-69042-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation