A method is developed for fitting smooth curves through a series of shapes of landmarks in two dimensions using unrolling and unwrapping procedures in Riemannian manifolds. An explicit method of calculation is given which is analogous to that of Jupp & Kent (1987) for spherical data. The...

We propose an alternative to Kendall's shape space for reflection shapes of configurations in <inline-formula><inline-graphic xlink:href="asn050ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach...