Jean-Pierre Antoine

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The two-dimensional continuous wavelet transform (CWT), derived from a square in-tegrable representation of the similitude group of IR 2 , is characterized by a rotation parameter, in addition to the usual translations and dilations. This enables it to detect edges and directions in images, provided a directional wavelet is used. First we review the general(More)
Given a two-dimensional smooth manifold M and a bijective projection p from M on a fixed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection p−1. Examples where the projection maps the whole manifold onto a plane include the two-sphere, the upper sheet of(More)
The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters(More)
Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention for instance works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, . . . In(More)