Publications related to Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Theoretical Model of Polymer Plasma Laser Ablation

Polymer plasma laser ablation has been investigated theoretically. An elegant mathematical tool using the fractal structure of space-time was developed. The model was verified with good accuracy on the existing experimental results. ...

2009

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. ...

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

Innovation Modelling and Wavelet Analysis of Fractal Processes in Bio-Imaging

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. In this paper, ...

IEEE2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

Charles Baur, Benoît Dagon

A method for extracting in real-time the position and size of liver vessels from 2D ultrasound images is described. It proceeds in two steps. Starting with a rough localization of the vessels using the scale-space theory, seed points are defined. Then, ves ...

2008

Nonlinear dynamics of cardiovascular aging

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series are applied with particular interests in the identification of changes associated with aging. Scale invariant and scale dependent approach ...

Lancaster University2007

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

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Theoretical Model of Polymer Plasma Laser Ablation

Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Innovation Modelling and Wavelet Analysis of Fractal Processes in Bio-Imaging

Shift-Invariant Spaces from Rotation-Covariant Functions

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

Nonlinear dynamics of cardiovascular aging

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Low-Rate Reduced Complexity Image Compression using Directionlets

Fast directional correlation on the sphere with steerable filters

Directionlets: Anisotropic Multidirectional representation with separable filtering

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Theoretical Model of Polymer Plasma Laser Ablation

Innovation Modelling and Wavelet Analysis of Fractal Processes in Bio-Imaging

Fast Wavelet based Ultrasound Image Segmentation for Liver Vessels Extraction

Shift-Invariant Spaces from Rotation-Covariant Functions

Nonlinear dynamics of cardiovascular aging

Low-Rate Reduced Complexity Image Compression using Directionlets

Directionlets: Anisotropic Multidirectional representation with separable filtering

Fast directional correlation on the sphere with steerable filters

Innovation modelling and wavelet analysis of fractal processes in bio-imaging