  We consider the results of combining two approaches developed for the design
of Riemannian metrics on curves and surfaces, namely parametrization-invariant
metrics of the Sobolev type on spaces of immersions, and metrics derived
through Riemannian submersions from right-invariant Sobolev metrics on groups
of diffeomorphisms (the latter leading to the "large deformation diffeomorphic
metric mapping" framework). We show that this quite simple approach inherits
the advantages of both methods, both on the theoretical and experimental
levels, and provide additional flexibility and modeling power, especially when
dealing with complex configurations of shapes. Experimental results
illustrating the method are provided for curve and surface registration.
