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We study a family of Sobolev-type Riemannian metrics of order one on the space Imm(S1,R2) of parametrized plane curves and the quotient space Imm(S1,R2)/Diff(S1) of unparametrized curves. Thereâ€¦ (More)

- Martin Bauer, Martins Bruveris, Peter W. Michor
- Journal of Mathematical Imaging and Vision
- 2013

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 group and the space ofâ€¦ (More)

- Martins Bruveris, FranÃ§ois Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
- J. Nonlinear Science
- 2011

This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework ofâ€¦ (More)

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. Inâ€¦ (More)

- Martins Bruveris, Laurent Risser, FranÃ§ois-Xavier Vialard
- Multiscale Modeling & Simulation
- 2012

We develop a multi-scale theory for group of diffeomorphisms based on previous works [BGBHR11, RVW11, SNLP11, SLNP11]. The purpose of the paper is to develop in details a variational approach forâ€¦ (More)

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 and higher isâ€¦ (More)

- Martins Bruveris
- 2015

On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphismâ€¦ (More)

- Martins Bruveris
- SIAM J. Math. Analysis
- 2016

The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to theâ€¦ (More)

The geodesic distance vanishes on the group Diffc(M) of compactly supported diffeomorphisms of a Riemannian manifold M of bounded geometry, for the right invariant weak Riemannian metric which isâ€¦ (More)

The Virasoro-Bott group endowed with the right-invariant L2metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesicâ€¦ (More)