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Seminar Details

Date 24-5-2010
Time 11:00
Room/Location DISI-Sala Conferenze 3 piano
Title Steerable wavelet transforms and multiresolution monogenic image analysis
Speaker Prof. Unser
Affiliation Director of the Biomedical Imaging Group Ecole Polytechnique Federale de Lausanne, Switzerland
Link http://bigwww.epfl.ch/
Abstract We introduce an Nth-order extension of the Riesz transform that has the remarkable property of mapping any primary wavelet frame (or basis) of L_2(R^d) into another "steerable" wavelet frame, while preserving the frame bounds. Concretely, this means we can design reversible multi-scale decompositions in which the analysis wavelets (feature detectors) can be spatially rotated in any direction via a suitable linear combination of wavelet coefficients. The concept provides a rigorous functional counterpart to Simoncelli's steerable pyramid whose construction was entirely based on digital filter design. It allows for the specification of wavelets with any order of steerability in any number of dimensions. We illustrate the method with the design of new steerabl polyharmonic-spline wavelets that replicate the behavior of the Nth-order partial derivatives of an isotropic Gaussian kernel. The case N=1 is of special interest because it provides a functional framework for performing wavelet-domain monogenic signal analyses. Specifically we introduce a monogenic wavelet representation of images where each wavelet index is associated with a local orientation, an amplitude and a phase. We present examples of applications to directional image analyses and coherent optical imaging.
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