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In this paper we study the shape space of curves with values in a homogeneousspace $M = G/K$, where $G$ is a Lie group and $K$ is a compact Lie subgroup. Wegeneralize the square root velocity framework to obtain a reparametrizationinvariant metric on the space of curves in $M$. By identifying curves in $M$with their horizontal lifts in $G$, geodesics then can be computed. We can alsomod out by reparametrizations and by rigid motions of $M$. In each of thesequotient spaces, we can compute Karcher means, geodesics, and perform principalcomponent analysis. We present numerical examples including the analysis of aset of hurricane paths.

The Square Root Velocity Framework for Curves in a Homogeneous Space