Snakes and splines for tracking non-rigid heart motion

  • Amir A. Amini
  • Rupert W. Curwen
  • John C. Gore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1065)


MRI is unique in its ability to non-invasively and selectively alter tissue magnetization, and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns (radial or SPAMM patterns) define a time-varying curvilinear coordinate system on the tissue, which we track with B-snakes and coupled B-snake grids. The B-snakes are optimized by a dynamic programming algorithm operating on B-spline control points in discrete pixel space. Coupled B-snake optimization based on an extension of dynamic programming to two dimensions, and gradient descent are proposed. Novel spline warps are also proposed which can warp an area in the plane such that two embedded snake grids obtained from two SPAMM frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a second order continuous vector field is interpolated.


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  1. 1.
    A. A. Amini. A scalar function formulation for optical flow. In European Conference on Computer Vision, Stockholm, Sweden, May 1994.Google Scholar
  2. 2.
    A. A. Amini and et al. Energy-minimizing deformable grids for tracking tagged MR cardiac images. In Computers in Cardiology, pages 651–654, 1992.Google Scholar
  3. 3.
    L. Axel, R. Goncalves, and D. Bloomgarden. Regional heart wall motion: Two-dimensional analysis and functional imaging with MR imaging. Radiology, 183:745–750, 1992.Google Scholar
  4. 4.
    B. Bascle and R. Deriche. Stereo matching, reconstruction, and refinement of 3d curves using deformable contours. In International Conference on Computer Vision, 1993.Google Scholar
  5. 5.
    A. Blake, R. Curwen, and A. Zisserman. A framework for spatio-temporal control in the tracking of visual contours. International Journal of Computer Vision, 11(2):127–145, 1993.Google Scholar
  6. 6.
    F. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on PAMI, 1989.Google Scholar
  7. 7.
    A. Gueziec. Surface representation with deformable splines: Using decoupled variables. IEEE Computational Science and Engineering, pages 69–80, Spring 1995.Google Scholar
  8. 8.
    S. Gupta and J. Prince. On variable brightness optical flow for tagged MRI. In Information Processing in Medical Imaging (IPMI), pages 323–334, 1995.Google Scholar
  9. 9.
    M. Guttman, J. Prince, and E. McVeigh. Tag and contour detection in tagged MR images of the left ventricle. IEEE-TMI, 13(1):74–88, 1994.Google Scholar
  10. 10.
    T. Huang. Modeling, analysis, and visualization of nonrigid object motion. In International Conference on Pattern Recognition, 1990.Google Scholar
  11. 11.
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision, 1(4):321–331, 1988.Google Scholar
  12. 12.
    S. Menet, P. Saint-Marc, and G. Medioni. B-snakes: Implementation and application to stereo. In International Conference on Computer Vision, pages 720–726, 1990.Google Scholar
  13. 13.
    F. Meyer, T. Constable, A. Sinusas, and J. Duncan. Tracking myocardial deformations using spatially constrained velocities. In IPMI, pages 177–188, 1995.Google Scholar
  14. 14.
    C. Nastar and N. Ayache. Non-rigid motion analysis in medical images: A physically based approach. In IPMI, pages 17–32, 1993.Google Scholar
  15. 15.
    J. Park, D. Metaxas, and L. Axel. Volumetric deformable models with parameter functions: A new approach to the 3d motion analysis of the LV from MRI-SPAMM. In International Conference on Computer Vision, pages 700–705, 1995.Google Scholar
  16. 16.
    N. Pelc, R. Herfkens, A. Shimakawa, and D. Enzmann. Phase contrast cine magnetic resonance imaging. Magnetic Resonance Quarterly, 7(4):229–254, 1991.Google Scholar
  17. 17.
    D. Reynard, A. Blake, A. Azzawi, P. Styles, and G. Radda. Computer tracking of tagged 1H MR images for motion analysis. In Proc. of CVRMed, 1995.Google Scholar
  18. 18.
    A. Young, D. Kraitchman, and L. Axel. Deformable models for tagged MR images: Reconstruction of two-and three-dimensional heart wall motion. In IEEE Workshop on Biomedical Image Analysis, pages 317–323, Seattle, WA, June 1994.Google Scholar
  19. 19.
    E. Zerhouni, D. Parish, W. Rogers, A. Yang, and E. Shapiro. Human heart: Tagging with MR imaging — a method for noninvasive assessment of myocardial motion. Radiology, 169:59–63, 1988.PubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Amir A. Amini
    • 1
  • Rupert W. Curwen
    • 1
  • John C. Gore
    • 1
  1. 1.Yale UniversityNew Haven

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