Advertisement

Diffusion of Fiber Orientation Distribution Functions with a Rotation-Induced Riemannian Metric

  • Junning Li
  • Yonggang Shi
  • Arthur W. Toga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)

Abstract

Advanced diffusion weighted MR imaging allows non-invasive study on the structural connectivity of human brains. Fiber orientation distributions (FODs) reconstructed from diffusion data are a popular model to represent crossing fibers. For this sophisticated image representation of connectivity, classical image operations such as smoothing must be redefined. In this paper, we propose a novel rotation-induced Riemannian metric for FODs, and introduce a weighted diffusion process for FODs regarding this Riemannian manifold. We show how this Riemannian manifold can be used for smoothing, interpolation and building image-pyramids, yielding more accurate or intuitively more reasonable results than the linear or the unit hyper-sphere manifold.

Keywords

Riemannian Manifold Spherical Function Linear Manifold Image Pyramid Fiber Orientation Distribution 
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.

References

  1. 1.
    Human Connectome Project, http://www.humanconnectomeproject.org/
  2. 2.
    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, Part I. LNCS, vol. 5761, pp. 911–918. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Du, J., Goh, A., Qiu, A.: Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions. IEEE Transactions on Medical Imaging 31(5), 1021–1033 (2012)CrossRefGoogle Scholar
  4. 4.
    Srivastava, A., Jermyn, I., Joshi, S.: Riemannian analysis of probability density functions with applications in vision. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2007, pp. 1–8. IEEE (2007)Google Scholar
  5. 5.
    Ncube, S., Srivastava, A.: A novel Riemannian metric for analyzing HARDI data. In: SPIE Medical Imaging, p. 79620Q. International Society for Optics and Photonics (2011)Google Scholar
  6. 6.
    Cetingul, H.E., Afsari, B., Wright, M.J., Thompson, P.M., Vidal, R.: Group action induced averaging for HARDI processing. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp. 1389–1392. IEEE (2012)Google Scholar
  7. 7.
    Hill, D.A.: Electromagnetic Fields in Cavities: Deterministic and Statistical Theories. Wiley-IEEE Press (2009)Google Scholar
  8. 8.
    Tran, G., Shi, Y.: Adaptively constrained convex optimization for accurate fiber orientation estimation with high order spherical harmonics. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part III. LNCS, vol. 8151, pp. 485–492. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Junning Li
    • 1
  • Yonggang Shi
    • 1
  • Arthur W. Toga
    • 1
  1. 1.Laboratory of Neuro Imaging (LONI), Institute for Neuroimaging and Informatics (INI)Keck School of Medicine of USCUSA

Personalised recommendations