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Proceedings Paper

The wavelet transform on the two-sphere and related manifolds: a review
Author(s): Jean-Pierre Antoine; Daniela Roşca
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Paper Abstract

In a first part, we discuss several properties that seem desirable for any type of wavelet, such as smoothness, orthogonality, local support, Riesz stability, or vanishing moments. Then we review the construction of the spherical continuous wavelet transform based on the stereographic projection. Next we turn to the discrete wavelet transform. We review the various existing constructions and compare them in the light of the requirements listed above. Finally, we briefly describe the continuous wavelet transform on a two-sheeted hyperboloid and give some hints concerning the case of a general conic section.

Paper Details

Date Published: 25 April 2008
PDF: 15 pages
Proc. SPIE 7000, Optical and Digital Image Processing, 70000B (25 April 2008); doi: 10.1117/12.781312
Show Author Affiliations
Jean-Pierre Antoine, Univ. Catholique de Louvain (Belgium)
Daniela Roşca, Technical Univ. of Cluj-Napoca (Romania)

Published in SPIE Proceedings Vol. 7000:
Optical and Digital Image Processing
Peter Schelkens; Touradj Ebrahimi; Gabriel Cristóbal; Frédéric Truchetet, Editor(s)

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