2010 Winter Project Week HARDI RSH

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Key Investigators

  • UPenn: Luke Bloy, Ragini Verma
  • BWH: Carl-Fredrik Westin


We would like to provide support for high angular resolution diffusion imaging (HARDI) data models which make use of the symmetric real spherical harmonic functions (RSH) as a basis for functions on the sphere.

Approach, Plan

First consensus must be reached on the exact form of the RSH basis to be used. This will provide a basis for future development.

The functionality we would like to provide is the following:

  1. MRML representations for images of RSH coefficients
  2. Visualization of images of RSH coefficients
  3. Routines for estimating the orientation distribution function (ODF) (Descoteaux2007)
  4. Routines for estimating the fiber orientation distribution (FOD) (Tournier2007) using both filtered and constrained spherical deconvolution.


We have implemented the RSH basis and RSH coefficients as ITK based C++ classes, and written ITK image filters to perform the model estimation. Slicer modules need to be written to perform the integrated these filters into the Slicer framework.

MRML nodes have been written for RSH volumes. These nodes were based (blindly) off of the DiffusionTensor MRML nodes. There is a mathematics class which computes scalar maps based off of the RSH coefficients, as well as glpyher which currently only supports sphere sources. Support for line glyph source, to show only the principle diffusion directions would be very beneficial since rendering all the points on the sphere source is very resource intensive.

Visualization is currently being achieved by an extension to the Volumes module in slicer. The display widget nodes to facilitate this were again based on the Diffusion Widget classes.


  • Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, and Rachid Deriche, “Regularized, fast, and robust analytical q-ball imaging,” Magnetic Resonance in Medicine, vol. 58, no. 3, pp. 497–510, 2007.
  • J-Donald Tournier, Fernando Calamante, and Alan Connelly, “Robust determination of the fibre orientation distribution in diffusion mri: Non-negativity constrained super-resolved spherical deconvolution,” NeuroImage, vol. 35, no. 4, pp. 1459–1472, May 2007.