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Algebraic Methods for Direct and Feature Based Registration of Diffusion Tensor Images

  • Alvina Goh
  • René Vidal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3953)

Abstract

We present an algebraic solution to both direct and feature-based registration of diffusion tensor images under various local deformation models. In the direct case, we show how to linearly recover a local deformation from the partial derivatives of the tensor using the so-called Diffusion Tensor Constancy Constraint, a generalization of the brightness constancy constraint to diffusion tensor data. In the feature-based case, we show that the tensor reorientation map can be found in closed form by exploiting the spectral properties of the rotation group. Given this map, solving for an affine deformation becomes a linear problem. We test our approach on synthetic, brain and heart diffusion tensor images.

Keywords

Singular Value Decomposition Deformation Model Point Correspondence Single Voxel Registration Problem 
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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References

  1. 1.
    Mori, S., van Zijl, P.: Fiber tracking: principles and strategies - a technical review. NMR in Biomedicine 15, 468–480 (2002)CrossRefGoogle Scholar
  2. 2.
    Lazar, M., et al.: White matter tractography using diffusion tensor deflection. Human Brain Mapping 18, 306–321 (2003)CrossRefGoogle Scholar
  3. 3.
    Vemuri, B., et al.: Fiber tract mapping from diffusion tensor MRI. In: IEEE workshop on Variational and Level Set Methods in Computer Vision (2001)Google Scholar
  4. 4.
    Lori, N.F., et al.: Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results. NMR in Biomedicine 15, 494–515 (2002)CrossRefGoogle Scholar
  5. 5.
    Lal, R.: Probabilistic cortical and myocardinal fiber tracking in diffusion tensor imaging. Master’s thesis, The Johns Hopkins University (2001)Google Scholar
  6. 6.
    Wang, Z., Vemuri, B.: An affine invariant tensor dissimilarity measure and its applications to tensor-valued image segmentation. In: IEEE Conference on Computer Vision and Pattern Recognition (2004)Google Scholar
  7. 7.
    Zhang, H., Yushkevich, P., Gee, J.: Registration of diffusion tensor images. IEEE Conference on Computer Vision and Pattern Recognition (2004)Google Scholar
  8. 8.
    Ding, Z., et al.: Classification and quantification of neuronal fiber pathways using diffusion tensor MRI. Magnetic Resonance in Medicine 49, 716–721 (2003)CrossRefGoogle Scholar
  9. 9.
    Brun, A., Knutsson, H., Park, H.J., Shenton, M.E., Westin, C.F.: Clustering fiber tracts using normalized cuts. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 368–375. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence 22 (2000)Google Scholar
  11. 11.
    Zhukov, L., Museth, K., Breen, D., Whitaker, R., Barr, A.: Level set segmentation and modeling of DT-MRI human brain data. Journal of Electronic Imaging (2003)Google Scholar
  12. 12.
    Alexander, D., et al.: Spatial transformation of diffusion tensor magnetic resonance images. IEEE Transactions on Medical Imaging 20, 1131–1139 (2001)CrossRefGoogle Scholar
  13. 13.
    Ruiz-Alzola, J., et al.: Nonrigid registration of 3D tensor medical data. Medical Image Analysis 6, 143–161 (2002)CrossRefGoogle Scholar
  14. 14.
    Guimond, A., et al.: Deformable registration of DT-MRI data based on transformation invariant tensor characteristics. In: IEEE International Symposium on Biomedical Imaging (2002)Google Scholar
  15. 15.
    Park, H.J., et al.: Spatial normalization of diffusion tensor MRI using multiple channels. Neuroimage 20, 1995–2009 (2003)CrossRefGoogle Scholar
  16. 16.
    Gallier, J.: Geometric Methods and Applications for Computer Science and Engineering. Springer, New York (2001)MATHGoogle Scholar
  17. 17.
    Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)MATHGoogle Scholar
  18. 18.
    Battiti, R., Amaldi, E., Koch, C.: Computing optical flow across multiple scales: An adaptive coarse-to-fine strategy. International Journal of Computer Vision 6, 133–145 (1991)CrossRefGoogle Scholar
  19. 19.
    Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1985)MATHGoogle Scholar
  20. 20.
    Fletcher, P.T., et al.: Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Transactions on Medical Imaging 23, 995–1005 (2004)CrossRefGoogle Scholar
  21. 21.
    Kindlmann, G., Alexander, A.: Brain dataset. University of Utah, and University of Wisconsin-Madison, http://www.sci.utah.edu/~gk/DTI-data/Google Scholar
  22. 22.
    Helm, P.A., Winslow, R.L., McVeigh, E.: Cardiovascular DTMRI data sets, http://www.ccbm.jhu.edu
  23. 23.
    Goh, A., Vidal, R.: An algebraic solution to rigid registration of diffusion tensor images. In: IEEE International Symposium on Biomedical Imaging (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alvina Goh
    • 1
  • René Vidal
    • 1
  1. 1.Center for Imaging Science, Department of BMEJohns Hopkins UniversityBaltimoreUSA

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