Publications related to The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

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

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

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

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

Automatic Tracking of Individual Fluorescence Particles: Application to the Study of Chromosome Dynamics

Michaël Unser, Daniel Sage

We present a new, robust, computational procedure for tracking fluorescent markers in time-lapse microscopy. The algorithm is optimized for finding the time-trajectory of single particles in very noisy dynamic (two- or three-dimensional) image sequences. I ...

IEEE2005

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Shift-Invariant Spaces from Rotation-Covariant Functions

The Marr Wavelet Pyramid

Generalized Daubechies Wavelet Families

Wavelets on non-Euclidean manifolds

From Differential Equations to the Construction of New Wavelet-Like Bases

Automatic Tracking of Individual Fluorescence Particles: Application to the Study of Chromosome Dynamics

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Shift-Invariant Spaces from Rotation-Covariant Functions

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Marr Wavelet Pyramid

From Differential Equations to the Construction of New Wavelet-Like Bases

Automatic Tracking of Individual Fluorescence Particles: Application to the Study of Chromosome Dynamics

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelets on non-Euclidean manifolds

Generalized Daubechies Wavelet Families