Unrolling Shape Curves

The relationship between the connections on two Riemannian manifolds that are related by a Riemannian submersion are used to characterise parallel translation on shape space in terms of its behaviour on the pre‐shape sphere and so to derive a concrete procedure for the unrolling, or development, of curves in shape space onto tangent spaces. This will enable one to adapt to shape spaces the standard statistical procedures for fitting curves to Euclidean data.