Publications related to Wavelets on the 2-sphere and related manifolds

Complex data processing: fast wavelet analysis on the sphere

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 non-Euclidean manifolds

Iva Bogdanova Vandergheynst

This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...

EPFL2006

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

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

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Sai Siva Gorthi

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe ...

2005

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Direct observation of nondiffusive motion of a Brownian particle

László Forró, Andrzej Kulik, Sylvia Jeney, Branimir Lukic

The thermal position fluctuations of a single micron-sized sphere immersed in a fluid were recorded by optical trapping interferometry with nanometer spatial and microsecond temporal resolution. We find, in accord with the theory of Brownian motion includi ...

2005

Wavelets on the 2-sphere and related manifolds

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Complex data processing: fast wavelet analysis on the sphere

Wavelets on non-Euclidean manifolds

Omnidirectional views selection for scene representation

Stereographic Wavelet Frames on the Sphere

Correspondence principle between spherical and Euclidean wavelets

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Exponential-Spline Wavelet Bases

Generalized L-Spline Wavelet Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Direct observation of nondiffusive motion of a Brownian particle

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Exponential-Spline Wavelet Bases

Correspondence principle between spherical and Euclidean wavelets

Wavelets on non-Euclidean manifolds

Generalized L-Spline Wavelet Bases

Omnidirectional views selection for scene representation

Direct observation of nondiffusive motion of a Brownian particle

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Complex data processing: fast wavelet analysis on the sphere

Stereographic Wavelet Frames on the Sphere