We present a new methodology based on directional data clustering to represent white matter fiber orientations in magnetic resonance analyses for high angular resolution diffusion imaging. A probabilistic methodology is proposed for estimating intravoxel principal fiber directions, based on clustering directional data arising from orientation distribution function (ODF) profiles. ODF reconstructions are used to estimate intravoxel fiber directions using mixtures of von Mises-Fisher distributions. The method focuses on clustering data on the unit sphere, where complexity arises from representing ODF profiles as directional data. The proposed method is validated on synthetic simulations, as well as on a real data experiment. Based on experiments, we show that by clustering profile data using mixtures of von Mises-Fisher distributions it is possible to estimate multiple fiber configurations in a more robust manner than currently used approaches, without recourse to regularization or sharpening procedures. The method holds promise to support robust tractographic methodologies and to build realistic models of white matter tracts in the human brain. 1. Introduction Diffusion magnetic resonance imaging (MRI) is an MRI method that is able to characterize the diffusion displacement of water molecules in structured tissues of the human brain [1]. The key idea behind diffusion MRI is that of anisotropic diffusion. In structured tissues water mobility is not always the same in all directions. Molecular motion is favored in directions aligned with bundles of parallel fibers, such as in the human brain’s white matter. The natural diffusion of water molecules can reveal in vivo microscopic details about the architecture of both normal and diseased tissues. White matter fiber tractography is commonly implemented using the principal diffusion direction of the diffusion tensor imaging (DTI) model [2]. Popular fiber tracking approaches, such as the streamline tracking algorithm [3], uses the DTI model to extract the orientation dependence of the diffusion probability density function (PDF) of water molecules. However, the standard single-tensor DTI model is based on a Gaussian diffusion assumption; thus unable to resolve crossing and splitting of fiber bundles. Extended tensor models for fiber tracking based on mixture of Gaussian densities [4] and multitensor models [5] have been proposed to enable detection of multiple orientation distribution function (ODF) maxima per voxel. On the other hand, several studies have shown that fiber tracking based on high angular
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