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Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Related publications (152)

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Short Basis Functions for Constant-Variance Interpolation

Michaël Unser, Philippe Thévenaz, Thierry Blu

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...

SPIE2008

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Madeleine Jotz

In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...

2008

The double description method for the approximation of explicit MPC control laws

Colin Neil Jones

A standard model predictive controller (MPC) can be written as a parametric optimization problem whose solution is a piecewise affine (PWA) map from the measured state to the optimal control input. The primary limitation of this optimal `explicit solutionÂ ...

IEEE2008

Consistent And Regularized Magnification Of Images

Michaël Unser, Philippe Thévenaz, Aurélien Bourquard, Katarina Balac

Because more output data must be created than is available from the input, magnification is an III-posed problem. Traditional magnification relies on resampling an interpolation model at the appropriate rate; unfortunately, this simple solution is blind to ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Numerical Mathematics

Alfio Quarteroni

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and ...

Springer2007

Image alignment with rotation manifolds built on sparse geometric expansions

Pascal Frossard, Effrosyni Kokiopoulou

In this paper we discuss the problem of alignment of patterns under arbitrary rotation. When a generic image pattern is geometrically transformed, it typically spans a (possibly nonlinear) manifold in a high dimensional space. When the pattern of interest ...

2007

Numerical methods for multiscale problems

Assyr Abdulle

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation: symplectic and multisymplectic integrators for Hamiltonian systems, symmetric integrators for reversible syst ...

EMS2006

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006

FST-based Reconstruction of 3D-models from Non-Uniformly Sampled Datasets on the Sphere

Pascal Frossard, Ivana Tosic

This paper proposes a new method for reconstruction of star-shaped 3D surfaces from scattered datasets, where such surfaces are considered as signals living in the space of square integrable functions on the unit sphere. We first propose a generalization o ...

2006

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006