Concept

N-sphere

Related publications (71)

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

The continous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the ...

2008

On the mode stability of a self-similar wave map

Roland Donninger

We study linear perturbations of a self-similar wave map from Minkowski space to the three-sphere which is conjectured to be linearly stable. Considering analytic mode solutions of the evolution equation for the perturbations we prove that there are no rea ...

American Institute of Physics2008

Unsaturated water flow across soil aggregate contacts

Unsaturated water flow through soil aggregates is controlled by the contacts between aggregates. The contacts are highly conductive when wet and become bottle-necks for flow when drained. We postulate that the hydraulic conductivity of the contacts is in f ...

2008

Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year WMAP and the NVSS data for correlation induced by the integrated Sachs-Wolfe (ISW) effect. The steerable wavelet constructed from the s ...

2008

Complex data processing: fast wavelet analysis on the sphere

Yves Wiaux, Jason Douglas McEwen

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sph ...

2007

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

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

Omnidirectional views selection for scene representation

Pascal Frossard, Ivana Tosic

This paper proposes a new method for the selection of sets of omnidirectional views, which contribute together to the efficient representation of a 3d scene. When the 3d surface is modelled as a function on a unit sphere, the view selection problem is most ...

2006

Stereographic Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper we exploit the Continuous Wavelet Transform (CWT) on the two dimensional sphere, introduced previously by two of us, to build associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e., frames where the position remains ...

2005

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