This paper presents a novel approach for improved diffusion tensor fibre tractography, aiming to tackle a number of the limitations of current fibre tracking algorithms, and describes a quantitative analysis tool for probabilistic tracking algorithms. We consider the sampled random paths generated by a probabilistic tractography algorithm from a seed point as a set of curves, and develop a statistical framework for analysing the curve-set geometrically that finds the average curve and dispersion measures of the curve-set statistically. This study is motivated firstly by the goal of developing a robust fibre tracking algorithm, combining the power of both deterministic and probabilistic tracking methods using average curves. These typical curves produce strong connections to every anatomically distinct fibre tract from a seed point and also convey important information about the underlying probability distribution. These single well-defined trajectories overcome a number of the limitations of deterministic and probabilistic approaches. A new clustering algorithm for branching curves is employed to separate fibres into branches before applying the averaging methods. Secondly, a quantitative analysis tool for probabilistic tracking methods is introduced using statistical measures of curve-sets. Results on phantom and in vivo data confirm the efficiency and effectiveness of the proposed approach for the tracking algorithm and the quantitative analysis of the probabilistic methods
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