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   -> Volume 4, Issue 2


Preprint: Spherical wavelets
 
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Peter Schröder (ps@math.sc.edu)
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PostPosted: Mon Dec 02, 2002 5:42 pm    
Subject: Preprint: Spherical wavelets
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Preprint: Spherical wavelets

Title: Spherical wavelets: Efficiently representing functions on the sphere
Authors: Peter Schröder and Wim Sweldens

Abstract:
Wavelets have proven to be powerful bases for use in numerical analysis and
signal processing. Their power lies in the fact that they only require a
small number of coefficients to represent general functions and large data
sets accurately. This allows compression and efficient computations.
Traditional constructions have been limited to simple domains such as
intervals and rectangles. In this paper we present a wavelet
construction for scalar functions defined on surfaces and more
particularly the sphere. Treating these bases in the fully biorthogonal
case we show how bases with custom properties can be constructed with the
lifting scheme. The bases are extremely easy to implement and allow fully
adaptive subdivisions. We give examples of functions defined on the sphere,
such as topographic data, bi-directional reflection distribution functions,
and illumination, and show how they can be efficiently represented with
spherical wavelets.

Industrial Mathematics Initiative, University of South Carolina,
Research Report 1995:01, available through anonymous ftp at
ftp://ftp.math.sc.edu/pub/imi_95/imi95_1.ps or imi95_1.ps.gz
Color tif images available in imi_95/imi95_1.pix/*.tif.
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