Skip to main content
SpringerLink
Log in

Large Deformation Diffeomorphic Metric Mapping of Orientation Distribution Functions

  • Conference paper
Information Processing in Medical Imaging (IPMI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6801))

Abstract

We propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by Orientation Distribution Functions (ODF). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. We first extend ODFs traditionally defined in a unit sphere to a generalized ODF defined in \(\Re^3\). This makes it easy for an affine transformation as well as a diffeomorphic group action to be applied on the ODF. We then construct a Riemannian space of the generalized ODFs and incorporate its Riemannian metric for the similarity of ODFs into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the generalized ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.

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. Aganj, I., Lenglet, C., Sapiro, G., Yacoub, E., Ugurbil, K., Harel, N.: Reconstruction of the orientation distribution function in single-and multiple-shell q-ball imaging within constant solid angle. MRM 64, 554–566 (2010)

    Google Scholar 

  2. Amari, S.: Differential-Geometrical Methods in Statistics. Springer, Heidelberg (1985)

    Book  MATH  Google Scholar 

  3. Barmpoutis, A., Hwang, M.S., Howland, D., Forder, J.R., Vemuri, B.C.: Regularized positive-definite fourth order tensor field estimation from DW-MRI. NeuroImage 45(1, suppl. 1), S153–S162 (2009)

    Article  Google Scholar 

  4. Barmpoutis, A., Vemuri, B.C., Forder, J.R.: Registration of high angular resolution diffusion MRI images using 4th order tensors. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 908–915. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Basser, P.J., Mattiello, J., Lebihan, D.: Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 103, 247–254 (1994)

    Article  Google Scholar 

  6. Behrens, T.E.J., Berg, H.J., Jbabdi, S., Rushworth, M.F.S., Woolrich, M.W.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34(1), 144–155 (2007)

    Article  Google Scholar 

  7. Bloy, L., Verma, R.: Demons registration of high angular resolution diffusion images. In: ISBI (2010)

    Google Scholar 

  8. Cencov, N.N.: Statistical decision rules and optimal inference. In: Translations of Mathematical Monographs, vol. 53. AMS, Providence (1982)

    Google Scholar 

  9. Cheng, G., Vemuri, B.C., Carney, P.R., Mareci, T.H.: Non-rigid registration of high angular resolution diffusion images represented by gaussian mixture fields. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 190–197. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Cheng, J., Ghosh, A., Jiang, T., Deriche, R.: A riemannian framework for orientation distribution function computing. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 911–918. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical Q-ball imaging. MRM 58, 497–510 (2007)

    Article  Google Scholar 

  12. Dupuis, P., Grenander, U., Miller, M.I.: Variational problems on flows of diffeomorphisms for image matching. Quart. App. Math. 56, 587–600 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. MRM 47(6), 1083–1099 (2002)

    Article  Google Scholar 

  14. Geng, X., Ross, T.J., Gu, H., Shin, W., Zhan, W., Chao, Y.-P., Lin, C.-P., Schuff, N., Yang, Y.: Diffeomorphic image registration of diffusion MRI using spherical harmonics. IEEE TMI 30(3), 747 (2011)

    Google Scholar 

  15. Ghosh, A., Descoteaux, M., Deriche, R.: Riemannian framework for estimating symmetric positive definite 4th order diffusion tensors. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 858–865. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Glaunès, J., Qiu, A., Miller, M., Younes, L.: Large deformation diffeomorphic metric curve mapping. IJCV 80(3), 317–336 (2008)

    Article  Google Scholar 

  17. Goh, A., Lenglet, C., Thompson, P.M., Vidal, R.: A nonparametric Riemannian framework for processing High Angular Resolution Diffusion Images and its apps. to ODF-based morphometry. NeuroImage (2011)

    Google Scholar 

  18. Hess, C.P., Mukherjee, P., Han, E.T., Xu, D., Vigneron, D.B.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. MRM 56(1), 104–117 (2006)

    Article  Google Scholar 

  19. Hong, X., Arlinghaus, L.R., Anderson, A.W.: Spatial normalization of the fiber orientation distribution based on high angular resolution diffusion imaging data. MRM 61, 1520–1527 (2009)

    Article  Google Scholar 

  20. Leergaard, T.B., White, N.S., de Crespigny, A., Bolstad, I., D’Arceuil, H., Bjaalie, J.G., Dale, A.M.: Quantitative histological validation of diffusion MRI fiber orientation distributions in the rat brain. PLoS One 5, e8595 (2010)

    Article  Google Scholar 

  21. Miller, M.I., Beg, M.F., Ceritoglu, C., Stark, C.: Increasing the power of functional maps of the medial temporal lobe by using large deformation diffeomorphic metric mapping. PNAS 102, 9685–9690 (2005)

    Article  Google Scholar 

  22. Özarslan, E., Mareci, T.H.: Generalized DTI and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. MRM 50, 955–965 (2003)

    Article  Google Scholar 

  23. Rao, C.R.: Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81–89 (1945)

    MathSciNet  MATH  Google Scholar 

  24. Srivastava, A., Jermyn, I., Joshi, S.H.: Riemannian analysis of probability density functions with applications in vision. In: IEEE CVPR (2007)

    Google Scholar 

  25. Tuch, D.S.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. MRM 48, 577–582 (2002)

    Article  Google Scholar 

  26. Yap, P.-T., Chen, Y., An, H., Yang, Y., Gilmore, J.H., Lin, W., Shen, D.: SPHERE: SPherical Harmonic Elastic REgistration of HARDI data. NeuroImage 55(2), 545–556 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Bioengineering, National University of Singapore, Singapore

    Jia Du & Anqi Qiu

  2. Department of Mathematics, National University of Singapore, Singapore

    Alvina Goh

  3. Clinical Imaging Research Center, National University of Singapore, Singapore

    Anqi Qiu

Authors
  1. Jia Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alvina Goh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anqi Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Swiss Federal Institute of Technology, Computer Vision Laboratory, Medical Image Analysis and Visualization Group,, ETH-Zentrum, Sternwartstr. 7, 8092, Zurich, Switzerland

    Gábor Székely

  2. Fraunhofer MEVIS, Universitätsallee 29, 28359, Bremen, Germany

    Horst K. Hahn

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Du, J., Goh, A., Qiu, A. (2011). Large Deformation Diffeomorphic Metric Mapping of Orientation Distribution Functions. In: Székely, G., Hahn, H.K. (eds) Information Processing in Medical Imaging. IPMI 2011. Lecture Notes in Computer Science, vol 6801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22092-0_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22092-0_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22091-3

  • Online ISBN: 978-3-642-22092-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation