Rotationally invariant clustering of diffusion MRI data using spherical harmonics

Matthew George Liptrot, François Lauze

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation.

After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.

The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP).

We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Original languageEnglish
Title of host publicationProceedings of SPIE Medical Imaging 2016: Image Processing
Number of pages7
PublisherSPIE - International Society for Optical Engineering
Publication date2016
Article number97843C
ISBN (Print)978-1510-60019-5
Publication statusPublished - 2016
Externally publishedYes
EventSPIE Medical Imaging 2016: Image Processing - San Diego, United States
Duration: 27 Feb 20163 Mar 2016
Conference number: 9784


ConferenceSPIE Medical Imaging 2016
CountryUnited States
CitySan Diego
SeriesProceedings of SPIE, the International Society for Optical Engineering


  • MRI
  • DWI
  • Diffusion
  • Pherical harmonics

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