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We consider the results of combining two approaches developed for the designof Riemannian metrics on curves and surfaces, namely parametrization-invariantmetrics of the Sobolev type on spaces of immersions, and metrics derivedthrough Riemannian submersions from right-invariant Sobolev metrics on groupsof diffeomorphisms (the latter leading to the "large deformation diffeomorphicmetric mapping" framework). We show that this quite simple approach inheritsthe advantages of both methods, both on the theoretical and experimentallevels, and provide additional flexibility and modeling power, especially whendealing with complex configurations of shapes. Experimental resultsillustrating the method are provided for curve and surface registration.

Hybrid Riemannian Metrics for Diffeomorphic Shape Registration