Skip to main content
SpringerLink
Log in

DT-MRI Images : Estimation, Regularization, and Application

  • Conference paper
Computer Aided Systems Theory - EUROCAST 2003 (EUROCAST 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2809))

Included in the following conference series:

Abstract

Diffusion-Tensor MRI is a technique allowing the measurement of the water molecule motion in the tissues fibers, by the mean of rendering multiple MRI images under different oriented magnetic fields. This large set of raw data is then further estimated into a volume of diffusion tensors (i.e. 3× 3 symmetric and positive-definite matrices) that describe through their spectral elements, the diffusivities and the main directions of the tissues fibers. We address two crucial issues encountered for this process : diffusion tensor estimation and regularization. After a review on existing algorithms, we propose alternative variational formalisms that lead to new and improved results, thanks to the introduction of important tensor constraint priors (positivity, symmetry) in the considered schemes. We finally illustrate how our set of techniques can be applied to enhance fiber tracking in the white matter of the brain.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alvarez, L., Lions, P.L., Morel, J.M.: Image selective smoothing and edge detection by nonlinear diffusion (II). SIAM Journal of Numerical Analysis 29, 845–866 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  2. ter Haar Romeny, B.M.: Geometry-driven diffusion in computer vision. Computational imaging and vision. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  3. Basser, P.J., Mattiello, J., LeBihan, D.: Estimation of the effective self-diffusion tensor from the nmr spin echo. Journal of Magnetic Resonance B(103), 247–254 (1994)

    Google Scholar 

  4. Basser, P.J., Pajevic, S., Pierpaoli, C., Aldroubi, A.: Fiber-tract following in the human brain using dt-mri data. IEICE TRANS. INF & SYST. E(85), 15–21 (2002)

    Google Scholar 

  5. Brox, T., Weickert, J.: Nonlinear matrix diffusion for optic flow estimation. In: DAGM-Symposium, pp. 446–453 (2002)

    Google Scholar 

  6. Campbell, J.S.W., Siddiqi, K., Vemuri, B.C., Pike, G.B.: A geometric flow for white matter fibre tract reconstruction. In: IEEE International Symposium on Biomedical Imaging Conference Proceedings, July 2002, pp. 505–508 (2002)

    Google Scholar 

  7. Chan, T., Shen, J.: Variational restoration of non-flat image features: Models and algorithms. In: Research Report. Computational and applied mathematics department of mathematics Los Angeles (June 1999)

    Google Scholar 

  8. Charbonnier, P., Aubert, G., Blanc-Féraud, M., Barlaud, M.: Two deterministic half-quadratic regularization algorithms for computed imaging. In: Proceedings of the International Conference on Image Processing, vol. II, pp. 168–172 (1994)

    Google Scholar 

  9. Chefd’hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O.: Constrained flows on matrix-valued functions: application to diffusion tensor regularization. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 251–265. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Chu, M.T.: A list of matrix flows with applications. Technical report, Department of Mathematics, North Carolina State University (1990)

    Google Scholar 

  11. Coulon, O., Alexander, D.C., Arridge, S.R.: A geometrical approach to 3d diffusion tensor magnetic resonance image regularisation. Technical report, Department of Computer Science, University College London (2001)

    Google Scholar 

  12. Golub, G.H., Van Loan, C.F.: Matrix computations. The John Hopkins University Press, Baltimore (1983)

    MATH  Google Scholar 

  13. Kimmel, R., Malladi, R., Sochen, N.: Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images. International Journal of Computer Vision 39(2), 111–129 (2000)

    Article  MATH  Google Scholar 

  14. Le Bihan, D.: Methods and applications of diffusion mri. In: Young, I.R. (ed.) Magnetic Resonance Imaging and Spectroscopy in Medicine and Biology. John Wiley and Sons, Chichester (2000)

    Google Scholar 

  15. Mamata, H., Mamata, Y., Westin, C.F., Shenton, M.E., Jolesz, F.A., Maier, S.E.: High-resolution line-scan diffusion-tensor mri of white matter fiber tract anatomy. In: AJNR Am NeuroRadiology, vol. 23, pp. 67–75 (2002)

    Google Scholar 

  16. Mori, S., Crain, B.J., Chacko, V.P., Van Zijl, P.C.M.: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology 45(2), 265–269 (1999)

    Article  Google Scholar 

  17. Parker, G.J.M., Wheeler-Kingshott, C.A.M., Barker, G.J.: Distributed anatomical brain connectivity derived from diffusion tensor imaging. In: Insana, M.F., Leahy, R.M. (eds.) IPMI 2001. LNCS, vol. 2082, pp. 106–120. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  18. Poupon, C.: Détection des faisceaux de fibres de la substance blanche pour l’étude de la connectivité anatomique cérébrale. PhD thesis, Ecole Nationale Supérieure des Télécommunications (December 1999)

    Google Scholar 

  19. Poupon, C., Mangin, J.F., Frouin, V., Regis, J., Poupon, F., Pachot-Clouard, M., Le Bihan, D., Bloch, I.: Regularization of mr diffusion tensor maps for tracking brain white matter bundles. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 489–498. Springer, Heidelberg (1998)

    Google Scholar 

  20. Sapiro, G.: Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  21. Stejskal, E.O., Tanner, J.E.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics 42, 288–292 (1965)

    Article  Google Scholar 

  22. Tang, B., Sapiro, G., Caselles, V.: Diffusion of general data on non-flat manifolds via harmonic maps theory: The direction diffusion case. The International Journal of Computer Vision 36(2), 149–161 (2000)

    Article  Google Scholar 

  23. Tschumperlé, D.: PDE’s Based Regularization of Multivalued Images and Applications. PhD thesis, Université de Nice-Sophia Antipolis (December 2002)

    Google Scholar 

  24. Tschumperlé, D., Deriche, R.: Diffusion tensor regularization with constraints preservation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Kauai Marriott, Hawaii (December 2001)

    Google Scholar 

  25. Tschumperlé, D., Deriche, R.: Diffusion PDE’s on Vector-Valued images. IEEE Signal Processing Magazine 19(5), 16–25 (2002)

    Article  Google Scholar 

  26. Tschumperlé, D., Deriche, R.: Vector-valued image regularization with PDE’s: A common framework for different applications. In: IEEE Conference on Computer Vision and Pattern Recognition, Madison, Wisconsin (United States) (June 2003)

    Google Scholar 

  27. Vemuri, B., Chen, Y., Rao, M., McGraw, T., Mareci, T., Wang, Z.: Fiber tract mapping from diffusion tensor mri. In: 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM 2001) (July 2001)

    Google Scholar 

  28. Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart (1998)

    MATH  Google Scholar 

  29. Westin, C.F., Maier, S.E.: A dual tensor basis solution to the stejskal-tanner equations for dt-mri. In: Proceedings of International Society for Magnetic Resonance in Medicine (2002)

    Google Scholar 

  30. Westin, C.F., Maier, S.E., Mamata, H., Nabavi, A., Jolesz, F.A., Kikinis, R.: Processing and visualization for diffusion tensor mri. In: Proceedings of Medical Image Analysis, vol. 6, pp. 93–108 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Odyssée Lab, INRIA Sophia-Antipolis, France

    D. Tschumperlé & R. Deriche

Authors
  1. D. Tschumperlé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Deriche
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Cybernetics, Universidad de Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Systems Theory, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040, Linz, Austria

    Franz Pichler

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tschumperlé, D., Deriche, R. (2003). DT-MRI Images : Estimation, Regularization, and Application. In: Moreno-Díaz, R., Pichler, F. (eds) Computer Aided Systems Theory - EUROCAST 2003. EUROCAST 2003. Lecture Notes in Computer Science, vol 2809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45210-2_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45210-2_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20221-9

  • Online ISBN: 978-3-540-45210-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation