We study completeness properties of the Sobolev diffeomorphism groups $\mathcal D^s(M)$ endowed with strong right-invariant Riemannian metrics when $M$ is $\mathbb R^d$ or a compact manifold without boundary. We prove that for $s >$ dim $(M)/2+1$, the group $\mathcal D^s(M)$ is geodesically and metrically complete and any two diffeomorphisms in the same component can be joined by a minimal geodesic. We then present the connection between the Sobolev diffeomorphism group and the _large deformation matching_ framework in order to apply our results to diffeomorphic image matching.

关于微分同态群的完备性

马丁斯·布鲁弗斯

弗朗索瓦·沙维耶·维亚拉德

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