Advertisement

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Multiple Disconnected Brain Subcortical Structures

  • Ameer Pasha Hosseinbor
  • Moo K. Chung
  • Stacey M. Schaefer
  • Carien M. van Reekum
  • Lara Peschke-Schmitz
  • Matt Sutterer
  • Andrew L. Alexander
  • Richard J. Davidson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8149)

Abstract

We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can’t represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441.

Keywords

Mean Square Error Spherical Harmonic Reconstruction Error Stereographic Projection Degree Spherical Harmonic 
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.
    Angenent, S., Hacker, S., Tannenbaum, A., Kikinis, R.: On the laplace-beltrami operator and brain surface flattening. IEEE Transactions on Medical Imaging 18, 700–711 (1999)CrossRefGoogle Scholar
  2. 2.
    Avants, B., Epstein, C., Grossman, M., Gee, J.: Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain. Medical Image Analysis 12, 26–41 (2008)CrossRefGoogle Scholar
  3. 3.
    Bonvallet, B., Griffin, N., Li, J.: 3D shape descriptors: 4D hyperspherical harmonics “An exploration into the fourth dimension”. In: IASTED International Conference on Graphics and Visualization in Engineering, pp. 113–116 (2007)Google Scholar
  4. 4.
    Chung, M., Worsley, K., Brendon, M., Dalton, K., Davidson, R.: General multivariate linear modeling of surface shapes using SurfStat. NeuroImage 53, 491–505 (2010)CrossRefGoogle Scholar
  5. 5.
    Domokos, G.: Four-dimensional symmetry. Physical Review 159, 1387–1403 (1967)CrossRefGoogle Scholar
  6. 6.
    Fock, V.: Zur theorie des wasserstoffatoms. Z. Physik 98, 145–154 (1935)CrossRefGoogle Scholar
  7. 7.
    Gerig, G., Styner, M., Jones, D., Weinberger, D., Lieberman, J.: Shape analysis of brain ventricles using spharm. In: MMBIA, pp. 171–178 (2001)Google Scholar
  8. 8.
    Koay, C.G., Ozarslan, E., Basser, P.J.: A signal transformational framework for breaking the noise floor and its applications in MRI. J. Magn. Reson. 197, 108–119 (2009)CrossRefGoogle Scholar
  9. 9.
    Mason, J.K., Schuh, C.A.: Hyperspherical harmonics for the representation of crystallographic texture 56, 6141–6155 (2008)Google Scholar
  10. 10.
    Shen, L., Ford, J., Makedon, F., Saykin, A.: surface-based approach for classification of 3d neuroanatomical structures. Intelligent Data Analysis 8, 519–542 (2004)Google Scholar
  11. 11.
    Smith, S.: Fast robust automated brain extraction. Human Brain Mapping 17, 143–155 (2002)CrossRefGoogle Scholar
  12. 12.
    Van Reekum, C., Schaefer, S., Lapate, R., Norris, C., Greischar, L., Davidson, R.: Aging is associated with positive responding to neutral information but reduced recovery from negative information. Social Cognitive and Affective Neuroscience 6, 177–185 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ameer Pasha Hosseinbor
    • 1
  • Moo K. Chung
    • 1
  • Stacey M. Schaefer
    • 1
  • Carien M. van Reekum
    • 2
  • Lara Peschke-Schmitz
    • 1
  • Matt Sutterer
    • 1
  • Andrew L. Alexander
    • 1
  • Richard J. Davidson
    • 1
  1. 1.University of Wisconsin-MadisonUSA
  2. 2.University of ReadingUK

Personalised recommendations