We develop a fully non-parametric method for the estimation ofcurve trajectories using HARDI data. For a set of locations Xi ∈ G, Grepresenting a region of the brain, we consider the diffusion process byapplying multivariate kernel smoothing techniques for the estimationof a general function f describing the signal process obtained fromthe MRI image. At each location x ∈ G we search for the directionof maximum diffusion on the unit sphere to obtain estimates of curvetrajectories. We establish the convergence of the deviation betweenestimated and true curves to a Gaussian process to develop tests forthe connectivity likelihood of regions. This method is computationallyefficient as with each step of the curve tracing we construct a pointwiseconfidence ellipsoid region rather than exhaustive iterative samplingmethods.
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