In this paper we study the shape space of curves with values in a homogeneous
space M=G/K, where G is a Lie group and K is a compact Lie subgroup. We
generalize the square root velocity framework to obtain a reparametrization
invariant 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 also
mod out by reparametrizations and by rigid motions of M. In each of these
quotient spaces, we can compute Karcher means, geodesics, and perform principal
component analysis. We present numerical examples including the analysis of a
set of hurricane paths.Comment: To appear in 3rd International Workshop on Diff-CVML Workshop, CVPR
201