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10th IEEE Visualization 1999 (VIS '99)
Optimal Triangular Haar Bases for Spherical Data
San Francisco, CA
October 25-October 28
ISBN: 0-7803-5897-X
ASCII Text
x 
 
Georges-Pierre Bonneau, "Optimal Triangular Haar Bases for Spherical Data," Visualization Conference, IEEE, pp. 47, 10th IEEE Visualization 1999 (VIS '99), 1999.
 
 
BibTex
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@article{ 10.1109/VISUAL.1999.809898,
author = {Georges-Pierre Bonneau},
title = {Optimal Triangular Haar Bases for Spherical Data},
journal ={Visualization Conference, IEEE},
volume = {0},
year = {1999},
issn = {1070-2385},
pages = {47},
doi = {http://doi.ieeecomputersociety.org/10.1109/VISUAL.1999.809898},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - CONF
JO - Visualization Conference, IEEE
TI - Optimal Triangular Haar Bases for Spherical Data
SN - 1070-2385
SP
EP
A1 - Georges-Pierre Bonneau,
PY - 1999
KW - visualization
KW - multiresolution
KW - wavelets
KW - orthogonality
VL - 0
JA - Visualization Conference, IEEE
ER -
 
Multiresolution analysis based on FWT (Fast Wavelet Transform) is now widely used in Scientific Visualization. Spherical bi-orthogonal wavelets for spherical triangular grids where introduced in [5]. In order to improve on the orthogonality of the wavelets, the concept of nearly orthogonality, and two new piecewise-constant (Haar) bases were introduced in [4]. In our paper, we extend the results of [4]. First we give two one-parameter families of triangu-lar Haar wavelet bases that are nearly orthogonal in the sense of [4]. Then we introduce a measure of orthogonality. This measure vanishes for orthogonal bases. Eventually, we show that we can find an optimal parameter of our wavelet families, for which the measure of orthogonality is minimized. Several numerical and visual examples for a spherical topographic data set illustrates our results.
Index Terms:
visualization, multiresolution, wavelets, orthogonality
Citation:
Georges-Pierre Bonneau, "Optimal Triangular Haar Bases for Spherical Data," ieee_vis, pp.47, 10th IEEE Visualization 1999 (VIS '99), 1999
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