127 citations · 595 across the 29 of their papers we have counts for
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Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves
Martins Bruveris, Peter W. Michor, David Mumford
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2…
-transforms for Sobolev -metrics on spaces of plane curves
Martin Bauer, Martins Bruveris, Peter W. Michor
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second deriv…
Geometry of Image Registration: The Diffeomorphism Group and Momentum Maps
Martins Bruveris, Darryl D. Holm
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric m…
Overview of the Geometries of Shape Spaces and Diffeomorphism Groups
Martin Bauer, Martins Bruveris, Peter W. Michor
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism gro…