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In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal(More)
Progressive supranuclear palsy (PSP) is a debilitating progressive neurodegenerative disorder for which there is no proven pharmacological treatment. Zolpidem immediate release formulation has been reported to show short-term improvements in motor function and voluntary saccadic eye movements, but the benefits were not sustained. A 61-year-old man with a(More)
  • M Bauer, M Bruveris, C Cotter, S Marsland, P W Michor, Martin Bauer +4 others
  • 2012
—Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curves, that includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family(More)
We introduce a new mixed finite element for solving the 2-and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1 D-P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new(More)
The Clebsch method provides a unifying approach for deriving vari-ational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group via a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be(More)
We present a numerical algorithm for a new matching approach for parameterisation independent diffeomorphic registration of curves in the plane, targeted at robust registration between curves that require large deformations. This condition is particularly useful for the geodesic constrained approach in which the matching functional is minimised subject to(More)
We develop a particle-mesh method for two-layer shallow-water equations subject to the rigid-lid approximation. The method is based on the recently proposed Hamiltonian particle-mesh (HPM) method and the interpretation of the rigid-lid approximation as a set of holonomic constraints. The suggested spatial discretization leads to a constrained Hamiltonian(More)
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra is implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to(More)
Accurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that(More)