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We derive a new fiber tracking algorithm for DT-MRI that parts with the locally ldquogreedyrdquo paradigm intrinsic to conventional tracking algorithms. We demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer-generated DT-MRI data, for which well-known conventional tracking algorithms are shown to fail. Our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph. Voxels serve as vertices, and edges are included between neighboring voxels. We assign probabilities (weights) to edges using a Bayesian framework. Higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity. We compute optimal paths of maximum probability using computationally scalable shortest path algorithms. The salient features of our approach are: global optimality-unlike conventional tracking algorithms, local errors do not accumulate and one ldquowrong-turnrdquo does not spell disaster; a target point is specified a priori; precise reconstruction is demonstrated for extremely low signal-to-noise ratio; impartiality to which of two endpoints is used as a seed; and, faster computation times than conventional all-paths tracking. We can use our new tracking algorithm in either a single-path tracking mode (deterministic tracking) or an all-paths tracking mode (probabilistic tracking).