On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Maintaining Multi-Modality through Mixture Tracking
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Clustering on the Unit Hypersphere using von Mises-Fisher Distributions
The Journal of Machine Learning Research
Hyperspherical von Mises-Fisher mixture (HvMF) modelling of high angular resolution diffusion MRI
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Probabilistic tractography using Q-ball modeling and particle filtering
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
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Particle filtering has recently been introduced to perform probabilistic tractography in conjunction with DTI and Q-Ball models to estimate the diffusion information. Particle filters are particularly well adapted to the tractography problem as they offer a way to approximate a probability distribution over all paths originated from a specified voxel, given the diffusion information. In practice however, they often fail at consistently capturing the multi-modality of the target distribution. For brain white matter tractography, this means that multiple fiber pathways are unlikely to be tracked over extended volumes. We propose to remedy this issue by formulating the filtering distribution as an adaptive M-component non-parametric mixture model. Such a formulation preserves all the properties of a classical particle filter while improving multi-modality capture. We apply this multi-modal particle filter to both DTI and Q-Ball models and propose to estimate dynamically the number of modes of the filtering distribution. We show on synthetic and real data how this algorithm outperforms the previous versions proposed in the literature.