Publications related to Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

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

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

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

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

Locally Adaptive Wavelet-Based Image Interpolation

Martin Vetterli

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local s ...

2006

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

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Feature point extraction using scale-space representation

Touradj Ebrahimi, Yousri Abdeljaoued

An algorithm for feature point extraction is presented. It is based on a scale-space representation of the image as well as a system for tracking across scales. Using synthetic and real images, it is shown that the proposed algorithm produces stable and we ...

2004

Guest Editorial: Wavelets in Medical Imaging

Michaël Unser

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...

2003

Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

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

Continuous Wavelet Transform on the Hyperboloid

Fast directional correlation on the sphere with steerable filters

Locally Adaptive Wavelet-Based Image Interpolation

Wavelets on non-Euclidean manifolds

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelets on the 2-Hyperboloid

Feature point extraction using scale-space representation

Guest Editorial: Wavelets in Medical Imaging

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

Continuous Wavelet Transform on the Hyperboloid

Locally Adaptive Wavelet-Based Image Interpolation

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Guest Editorial: Wavelets in Medical Imaging

Fast directional correlation on the sphere with steerable filters

Wavelets on the 2-Hyperboloid

Wavelets on non-Euclidean manifolds

Feature point extraction using scale-space representation