Measuring Brain Connectivity via Shape Analysis of fMRI Time Courses and Spectra.

We present a shape matching approach for functional magnetic resonance imaging (fMRI) time course and spectral alignment. We use ideas from differential geometry and functional data analysis to define a functional representation for fMRI signals. The space of fMRI functions is then equipped with a reparameterization invariant Riemannian metric that enables elastic alignment of both amplitude and phase of the fMRI time courses as well as their power spectral densities. Experimental results show significant increases in pairwise node to node correlations and coherences following alignment. We apply this method for finding group differences in connectivity between patients with major depression and healthy controls.