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

Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

Physical systems encompassing a variety of strongly coupled scales pose major computational challenges in terms of analysis modeling and simulation. In this report we first discuss a multiscale modeling approach for the transport of particles such as DNA i ...

EMS2005

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005

Green-Ampt approximations

David Andrew Barry

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of a ...

2005

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Dimitri Nestor Alice Van De Ville, Thierry Blu

We provide a new comparison between hexagonal and orthogonal lattices, based on approximation theory. For each of the lattices, we select the “natural” spline basis function as generator for a shift-invariant function space; i.e., the tensor-product B-spli ...

IEEE2005

Optimal control of geodesics in Riemannian manifolds

Klaus-Dieter Semmler, Roland Rozsnyo

Summary: We present a method based on an optimal control technique for numerical computations of geodesic paths between two fixed points of a Riemannian manifold under the assumption of existence. In this method, the control variable is the tangent vector ...

2004

Ideal bicombings for hyperbolic groups and applications

Nicolas Monod

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that s ...

2004

Stereographic Frames of Wavelets on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the con ...

2004

Multiwavelet-Like Bases for High Quality Image Interpolation

Michaël Unser, Thierry Blu

We present a simple but generalized interpolation method for digital images that uses multiwavelet-like basis functions. Most of interpolation methods uses only one symmetric basis function; for example, standard and shifted piecewise-linear interpolations ...

SPIE2003

Interpolation method and apparatus

Michaël Unser, Philippe Thévenaz, Thierry Blu

Method of interpolating digital samples (fN, fn) using interpolation functions ( psi , psi (x-x0)) that are shifted by an arbitrary shift value (x0) relative to said samples (fN, fn). It will be shown that there is a non-zero and non-trivial optimal value ...

2003

Global regularity of wave maps from $R^{3+1}$ to surfaces

Joachim Krieger

We consider Wave Maps with smooth compactly supported initial data of small (H) over dot (3/2)-norm from R3+1 to certain 2-dimensional Riemannian manifolds and show that they stay smooth globally in time. Our methods are based on the introduction of a glob ...

Springer Verlag2003

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

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Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Green-Ampt approximations

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Optimal control of geodesics in Riemannian manifolds

Ideal bicombings for hyperbolic groups and applications

Stereographic Frames of Wavelets on the Sphere

Multiwavelet-Like Bases for High Quality Image Interpolation

Interpolation method and apparatus

Global regularity of wave maps from $R^{3+1}$ to surfaces

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Ideal bicombings for hyperbolic groups and applications

Interpolation method and apparatus

Global regularity of wave maps from $R^{3+1}$ to surfaces

Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Optimal control of geodesics in Riemannian manifolds

Green-Ampt approximations

Stereographic Frames of Wavelets on the Sphere

Multiwavelet-Like Bases for High Quality Image Interpolation