Hyperspherical von Mises-Fisher mixture (HvMF) modelling of high angular resolution diffusion MRI

Authors:
Abhir Bhalerao;Carl-Fredrik Westin
Affiliations:
Department of Computer Science, University of Warwick, Coventry;Laboratory of Mathematics in Imaging, Harvard Medical School, Brigham and Womens Hospital, Boston, MA
Venue:
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Year:
2007

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Abstract

A mapping of unit vectors onto a 5D hypersphere is used to model and partition ODFs from HARDI data. This mapping has a number of useful and interesting properties and we make a link to interpretation of the second order spherical harmonic decompositions of HARDI data. The paper presents the working theory and experiments of using a von Mises-Fisher mixture model for directional samples. The MLE of the second moment of the HvMF pdf can also be related to fractional anisotropy. We perform error analysis of the estimation scheme in single and multi-fibre regions and then show how a penalised-likelihood model selection method can be employed to differentiate single and multiple fibre regions.