Motivated by the problem of analyzing shapes of fiber tracts in
DT-MRI data, we present a geometric framework for studying shapes of
open curves in $\real^3$. We start with a space of unit-length
curves and define the shape space to be its quotient space modulo
rotation and re-parametrization groups. Thus, the resulting shape
analysis is invariant to parameterizations of curves. Furthermore, a
Riemannian structure on this quotient shape space allows us to
compute geodesic paths between given curves and helps develop
algorithms for: (i) computing statistical summaries of a collection
of curves using means and covariances, and (ii) clustering a given
set of curves into clusters of similar shapes. Examples using fiber
tracts, extracted as parameterized curves from DT-MRI images, are
presented to demonstrate this framework.