Probabilistic Fiber Tracking Using Particle Filtering and Von Mises-Fisher Sampling

This paper presents a novel and fast probabilistic method for white matter fiber tracking from diffusion weighted magnetic resonance imaging (DWI). We formulate fiber tracking on a nonlinear state space model which is able to capture both smoothness regularity of fibers and uncertainties of the local fiber orientations due to noise and partial volume effects. The global tracking model is implemented using particle filtering. This sequential Monte Carlo technique allows us to recursively compute the posterior distribution of the potential fibers, while there is no limitation on the forms of the prior and observed information. Fast and efficient sampling is realised using the von Mises-Fisher distribution on unit spheres. The fiber orientation distribution is theoretically formulated by combining the axially symmetric tensor model and the formal noise model for DWI. Given a seed point, the method is able to rapidly locate the global optimal fiber and also provide a connectivity map. The proposed method is demonstrated both on synthetic and real-world brain MRI dataset.