Skip to main content
SpringerLink
Log in
Book cover

Biennial International Conference on Information Processing in Medical Imaging

IPMI 1993: Information Processing in Medical Imaging pp 17–32Cite as

Non-rigid motion analysis in medical images: a physically based approach

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 687))

Abstract

We present a physically-based deformable model which can be used to track and to analyze non-rigid motion of dynamic structures in time sequences of 2D or 3D medical images. The model considers an object undergoing an elastic deformation as a set of masses linked by springs, where the classical natural lengths of the springs is set equal to zero, and is replaced by a set of constant equilibrium forces, which characterize the shape of the elastic structure in the absence of external forces. This model has the extremely nice property of yielding dynamic equations which are linear and decoupled for each coordinate, whatever the amplitude of the deformation. Compared to the former work of Terzopoulos and his colleagues [12, 27, 26, 15] and Pentland and his colleagues [22, 21, 23, 10], our model can be viewed as a continuation and unification; it provides a reduced algorithmic complexity, and a sound framework for modal analysis, which allows a compact representation of a general deformation by a reduced number of parameters. The power of the approach to segment, track and analyze 2-D and 3-D images is demonstrated by a set of experimental results on various complex medical images (ultrasound and magnetic resonance images).

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, R. Owen, L. Staib, P. Anandan, and J. Duncan. Non-rigid motion models for tracking the left ventricular wall. Lecture notes in computer science: Information processing in medical images. Springer-Verlag, 1991.

    Google Scholar 

  2. Klaus-Jurgen Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.

    Google Scholar 

  3. Fred L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-11(6):567–585, June 1989.

    Article  Google Scholar 

  4. Isaac Cohen, Nicholas Ayache, and Patrick Sulger. Tracking points on deformable objects. In Proceedings of the Second European Conference on Computer Vision (ECCV) 1992, Santa Margherita Ligure, Italy, May 1992.

    Google Scholar 

  5. Isaac Cohen, Laurent D. Cohen, and Nicholas Ayache. Using deformable surfaces to segment-D images and infer differential structures. Computer Vision, Graphics, and Image Processing, 1992.

    Google Scholar 

  6. P. E. Danielsson. Euclidean distance mapping. Computer Vision, Graphics, and Image Processing, 14:227–248, 1980.

    Google Scholar 

  7. J.S. Duncan, R.L. Owen, L.H. Staib, and P. Anandan. Measurement of non-rigid motion using contour shape descriptors. In Proc. Computer Vision and Pattern Recognition, pages 318–324. IEEE Computer Society Conference, June 1991. Lahaina, Maui, Hawaii.

    Google Scholar 

  8. Andre Gueziec. Large deformable splines: Crest lines and matching. In Proceedings of the Fourth International Conference on Computer Vision, Berlin, May 1993.

    Google Scholar 

  9. I.L. Herlin and N. Ayache. Features extraction and analysis methods for sequences of ultrasound images. In Proceedings of the Second European Conference on Computer Vision (ECCV) 1992, Santa Margherita Ligure, Italy, May 1992.

    Google Scholar 

  10. Bradley Horowitz and Alex Pentland. Recovery of non-rigid motion and structure. In Proc. Computer Vision and Pattern Recognition, pages 325–330. IEEE Computer Society Conference, June 1991. Lahaina, Maui, Hawaii.

    Google Scholar 

  11. Wen-Chen Huang and Dmitry B. Goldgof. Adaptive-size physically based models for nonrigid motion analysis. In Proc. Computer Vision and Pattern Recognition, pages 833–835. IEEE Computer Society Conference, June 1992. Champaign, Illinois.

    Google Scholar 

  12. Michael Kass, Andrew Witkin, and Demetri Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision, 1:321–331, 1987.

    Article  Google Scholar 

  13. F. Leitner, I. Marque, S. Lavallée, and P. Cinquin. Dynamic segmentation: finding the edge with snake-splines. In Proceedings of International Conference on Curves and Surfaces, pages 1–4, Chamonix, France, June 1990. Academic Press.

    Google Scholar 

  14. F. Leymarie and M.D. Levine, Simulating the grassfire transform using an active contour model. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-14, January 1992.

    Google Scholar 

  15. Dimitri Metaxas and Demetri Terzopoulos. Constrained deformable superquadrics and nonrigid motion tracking. In Proc. Computer Vision and Pattern Recognition, pages 337–343. IEEE Computer Society Conference, June 1991. Lahaina, Maui, Hawaii.

    Google Scholar 

  16. Sanjoy K. Mishra, Dmitry B. Goldgof, and Thomas S. Huang. Motion analysis and epicardial deformation estimation from angiography data. In Proc. Computer Vision and Pattern Recognition, pages 331–336. IEEE Computer Society Conference, June 1991. Lahaina, Maui, Hawaii.

    Google Scholar 

  17. Olivier Monga, Serge Benayoun, and Olivier D. Faugeras. From partial derivatives of 3d density images to ridge lines. In Proc. Computer Vision and Pattern Recognition, pages 354–359. IEEE Computer Society Conference, June 1992. Champaign, Illinois.

    Google Scholar 

  18. Chahab Nastar and Nicholas Ayache. Fast segmentation, tracking, and analysis of deformable objects. In Proceedings of the Fourth International Conference on Computer Vision (ICCV '93), Berlin, May 1993.

    Google Scholar 

  19. Chahab Nastar and Nicholas Ayache. A New Physically Based Model for Efficient Tracking and Analysis of Deformations. Lecture notes in computer science: Geometric Reasoning — from Perception to Action. Springer-Verlag, 1993.

    Google Scholar 

  20. G.N Pande, G. Beer, and J.R. Williams. Numerical Methods in Rock Mechanics. John Wiley and Sons, 1990.

    Google Scholar 

  21. A. Pentland and Williams J. Good vibrations: Modal dynamics for graphics and animation. In Computer Graphics, 1989.

    Google Scholar 

  22. A. Pentland and Williams J. The perception of non-rigid motion: Inference of material properties and force. In Proceedings of the International Joint Conference on Artificial Intelligence, August 1989.

    Google Scholar 

  23. Alex Pentland and Stan Sclaroff. Closed-form solutions for physically based shape modelling and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(7):715–729, July 1991.

    Article  Google Scholar 

  24. Lawrence H. Staib and James S. Duncan. Deformable fourier models for surface finding in 3d images. In Proceedings of Visualization in Biomedical Computing, Chapell Hill,USA, October 1992.

    Google Scholar 

  25. Demetri Terzopoulos and Manuela Vasilescu. Sampling and reconstruction with adaptive meshes. In Proc. Computer Vision and Pattern Recognition, pages 829–832. IEEE Computer Society Conference, June 1991. Lahaina, Maui, Hawaii.

    Google Scholar 

  26. Demetri Terzopoulos and Keith Waters. Physically-based facial modelling, analysis, and animation. The Journal of Visualization and Computer Animation, 1:73–80, 1990.

    Google Scholar 

  27. Demetri Terzopoulos, Andrew Witkin, and Michael Kass. Constraints on deformable models: recovering 3-D shape and nonrigid motion. AI Journal, 36:91–123, 1988.

    Google Scholar 

  28. J-P. Thirion, O. Monga, Benayoun S., Gueziec A., and Ayache N. Automatic registration of 3d images using surface curvature. In IEEE Int. Symp. on Optical Applied Science and Engineering, San-Diego, July 1992.

    Google Scholar 

  29. Manuela Vasilescu and Demetri Terzopoulos. Adaptive meshes and shells. In Proc. Computer Vision and Pattern Recognition, pages 829–832. IEEE Computer Society Conference, June 1992. Champaign, Illinois.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Domaine de Voluceau, Rocquencourt, INRIA, B.P. 105, 78153, Le Chesnay Cedex, France

    Chahab Nastar

  2. INRIA, B.P. 93, F-06902, Sophia-Antipolis, France

    Nicholas Ayache

Authors
  1. Chahab Nastar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicholas Ayache
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Harrison H. Barrett A. F. Gmitro

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nastar, C., Ayache, N. (1993). Non-rigid motion analysis in medical images: a physically based approach. In: Barrett, H.H., Gmitro, A.F. (eds) Information Processing in Medical Imaging. IPMI 1993. Lecture Notes in Computer Science, vol 687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013778

Download citation

  • DOI: https://doi.org/10.1007/BFb0013778

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56800-1

  • Online ISBN: 978-3-540-47742-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation