Publications by Martins Bruveris

Constructing reparameterization invariant metrics on spaces of plane curves

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES

Martins Bruveris

Cambridge, Cambridge University Press2014

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martin Bauer, Martins Bruveris

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 of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martin Bauer, Martins Bruveris

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martin Bauer, Martins Bruveris

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

Martin Bauer, Martins Bruveris

We study Sobolev-type metrics of fractional order s a parts per thousand yen 0 on the group Diff (c) (M) of compactly supported diffeomorphisms of a manifold M. We show that for the important special case M = S (1), the geodesic distance on Diff (c) (S (1) ...

Springer Verlag2013

Mixture Of Kernels And Iterated Semidirect Product Of Diffeomorphisms Groups

Martins Bruveris

In the framework of large deformation diffeomorphic metric mapping (LDDMM), a multiscale theory for the diffeomorphism group is developed based on previous works of the authors. The purpose of this paper is (1) to develop in detail a variational approach f ...

Siam Publications2012

The Momentum Map Representation of Images

Tudor Ratiu, François Gay-Balmaz, Martins Bruveris

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a ...

Springer Verlag2011