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Piecewise smooth affine registration of point-sets with application to DT-MRI brain fiber-data

In this paper we present a variational probabilistic approach to the registration of brain white matter tractographies extracted from DT-MRI scans. Initially, the fibers are projected into a D-dimensional feature space based on the sequence of their spatial coordinates. The alignment of two fiber-sets is considered a probability density estimation problem, where one point-set represents Gaussian Mixture Model (GMM) centroids, and the other represents the data points. The transformation parameters are represented as spatially-dependent coefficients of the same invertible affine transformation model. The alignment term of the energy-function is minimized by maximizing the likelihood of correspondence between the data-sets while the smoothness term penalizes spatial changes in the coefficient functions. The energy-function, composed of the alignment and smoothness terms, is minimized using gradient descent optimization. Results of preliminary experiments on inter-subject full-brain data show improvement over global linear (affine) registration schemes.