Rotation Invariant Features for HARDI

  • Evan Schwab
  • H. Ertan Çetingül
  • Bijan Afsari
  • Michael A. Yassa
  • René Vidal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


Reducing the amount of information stored in diffusion MRI (dMRI) data to a set of meaningful and representative scalar values is a goal of much interest in medical imaging. Such features can have far reaching applications in segmentation, registration, and statistical characterization of regions of interest in the brain, as in comparing features between control and diseased patients. Currently, however, the number of biologically relevant features in dMRI is very limited. Moreover, existing features discard much of the information inherent in dMRI and embody several theoretical shortcomings. This paper proposes a new family of rotation invariant scalar features for dMRI based on the spherical harmonic (SH) representation of high angular resolution diffusion images (HARDI). These features describe the shape of the orientation distribution function extracted from HARDI data and are applicable to any reconstruction method that represents HARDI signals in terms of an SH basis. We further illustrate their significance in white matter characterization of synthetic, phantom and real HARDI brain datasets.


rotation invariance spherical functions feature extraction diffusion magnetic resonance imaging orientation distribution functions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jones, D.K.: Diffusion MRI: Theory, Methods, and Application. Oxford University Press (2010)Google Scholar
  2. 2.
    Smith, S.M., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T.E., Mackay, C.E., Watkins, K.E., Ciccarelli, O., Cader, M.Z., Matthews, P.M., Behrens, T.E.: Tract-based spatial statistics: Voxelwise analysis of multi-subject diffusion data. NeuroImage 31(4), 1487–1505 (2006)CrossRefGoogle Scholar
  3. 3.
    Basser, P.: Inferring microstructural features and the physiological state of tissues from diffusion weighted images. NMR in Biomedicine (1995)Google Scholar
  4. 4.
    Westin, C.F., Maier, S.E., Mamata, H., Nabavi, A., Jolesz, F.A., Kikinis, R.: Processing and visualization for diffusion tensor MRI. Medical Image Analysis 6(2), 93–108 (2002)CrossRefGoogle Scholar
  5. 5.
    Ghosh, A., Papadopoulo, T., Deriche, R.: Biomarkers for HARDI: 2nd & 4th order tensor invariants. In: IEEE International Symposium on Biomedical Imaging, pp. 26–29 (2012)Google Scholar
  6. 6.
    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), S153–S162 (2009)Google Scholar
  7. 7.
    Barmpoutis, A., Vemuri, B.C.: A unified framework for estimating diffusion tensors of any order with symmetric positive-definite constraints. In: IEEE International Symposium on Biomedical Imaging, pp. 1385–1388 (2010)Google Scholar
  8. 8.
    Tuch, D.: Q-ball imaging. Magnetic Resonance in Medicine 52(6), 1358–1372 (2004)CrossRefGoogle Scholar
  9. 9.
    Tristan-Vega, A., Westin, C.F., Aja-Fernandez, S.: Estimation of fiber orientation probability density functions in high angular resolution diffusion imaging. NeuroImage 47(2), 638–650 (2009)CrossRefGoogle Scholar
  10. 10.
    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. Magnetic Resonance in Medicine 64(2), 554–566 (2010)Google Scholar
  11. 11.
    Assemlal, H.E., Tschumperlé, D., Brun, L., Siddiqi, K.: Recent advances in diffusion mri modeling: Angular and radial reconstruction. Medical Image Analysis 15(4), 369–396 (2011)CrossRefGoogle Scholar
  12. 12.
    Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted mri. Magnetic Resonance in Medicine 47(6), 1083–1099 (2002)CrossRefGoogle Scholar
  13. 13.
    Ozarslan, E., Vemuri, B.C., Mareci, T.H.: Generalized scalar measures for diffusion mri using trace, variance, and entropy. Magnetic Resonance in Medicine 53(4), 866–876 (2005)CrossRefGoogle Scholar
  14. 14.
    Ghosh, A., Deriche, R.: Extracting geometrical features & peak fractional anisotropy from the odf for white matter characterization. In: IEEE International Symposium on Biomedical Imaging, pp. 266–271 (2011)Google Scholar
  15. 15.
    Fuster, A., van de Sande, J., Astola, L., Poupon, C., ter Haar Romeny, B.: Fourth-order tensor invariants in high angular resolution diffusion imaging. In: MICCAI 2011 Workshop on Computational Diffusion MRI (2011)Google Scholar
  16. 16.
    Basser, P.J., Pajevic, S.: Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI. Signal Processing 87(2), 220–236 (2007)zbMATHCrossRefGoogle Scholar
  17. 17.
    Grenander, U., Szego, G.: Toeplitz Forms and their Applications. University of California Press (1958)Google Scholar
  18. 18.
    Okikiolu, K.: The analogue of the strong Szego limit theorem on the 2 and 3-dimensional spheres. Journal of the American Mathematical Society 9, 345–372 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Shirdhonkar, S., Jacobs, D.: Non-negative lighting and specular object recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (2005)Google Scholar
  20. 20.
    Cetingul, H.E., Afsari, B., Vidal, R.: An algebraic solution to rotation recovery in hardi from correspondences of orientation distribution functions. In: IEEE International Symposium on Biomedical Imaging (2012)Google Scholar
  21. 21.
    Chirikjian, G., Kyatkin, A.: Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups. CRC Press (2000)Google Scholar
  22. 22.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical Q-ball imaging. Magnetic Resonance in Medicine 58(3), 497–510 (2007)CrossRefGoogle Scholar
  23. 23.
    Schwab, E., Afsari, B., Vidal, R.: Estimation of non-negative ODFs using the eigenvalue distribution of spherical functions. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part II. LNCS, vol. 7511, pp. 322–330. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Fillard, P., Descoteaux, M., Goh, A., Gouttard, S., Jeurissen, B., Malcolm, J., Ramirez-Manzanares, A., Reisert, M., Sakaie, K., Tensaouti, F., Yo, T., Mangin, J.F., Poupon, C.: Quantitative evaluation of 10 tractography algorithms on a realistic diffusion mr phantom. NeuroImage 56(1), 220–234 (2011)CrossRefGoogle Scholar
  25. 25.
    Poupon, C., Rieul, B., Kezele, I., Perrin, M., Poupon, F., Mangin, J.F.: New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models. Magnetic Resonance in Medicine 60(6), 1276–1283 (2008)CrossRefGoogle Scholar
  26. 26.
    Hofer, S., Karaus, A., Frahm, J.: Reconstruction and dissection of the entire human visual pathway using diffusion tensor MRI. Frontiers in Neuroanatomy 4(15) (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Evan Schwab
    • 1
  • H. Ertan Çetingül
    • 3
  • Bijan Afsari
    • 1
  • Michael A. Yassa
    • 2
  • René Vidal
    • 1
  1. 1.Center for Imaging ScienceJohns Hopkins UniversityUSA
  2. 2.Department of Psychological and Brain SciencesJohns Hopkins UniversityUSA
  3. 3.Imaging and Computer VisionSiemens Corporation, Corporate TechnologyUSA

Personalised recommendations