Publications related to Riemann sphere

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

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

On the moduli space of singular Euclidean surfaces

Marc Troyanov

The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces. ...

Eur. Math. Soc., Zürich2007

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

Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

Klaus-Dieter Semmler, Thomas Gauglhofer

Summary: We explicitly give

calT

, the Teichmüller space of four-holed spheres (which we call

X

pieces) in trace coordinates, as well as its modular group and a fundamental domain for the action of this group on

calT

which is its moduli space. As a co ...

2005

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Riemann sphere

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The continous wavelet transform on conic sections

Unsaturated water flow across soil aggregate contacts

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

Complex data processing: fast wavelet analysis on the sphere

On the moduli space of singular Euclidean surfaces

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

Omnidirectional views selection for scene representation

Stereographic Wavelet Frames on the Sphere

Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

Correspondence principle between spherical and Euclidean wavelets

The continous wavelet transform on conic sections

Unsaturated water flow across soil aggregate contacts

Complex data processing: fast wavelet analysis on the sphere

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

Stereographic Wavelet Frames on the Sphere

Correspondence principle between spherical and Euclidean wavelets

On the moduli space of singular Euclidean surfaces

Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

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

Omnidirectional views selection for scene representation