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Title: Wavelet Representation of Contour Sets

Abstract

We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
15006196
Report Number(s):
UCRL-JC-144651
TRN: US200405%%332
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: 2001 Institute of Electrical and Electronic Engineers Visualization, San Diego, CA (US), 10/21/2001--10/26/2001; Other Information: PBD: 19 Jul 2001
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPRESSION; ENGINEERS; QUANTIZATION; RESOLUTION; SCALAR FIELDS; SIMULATION; TOPOLOGY; VECTOR FIELDS

Citation Formats

Bertram, M, Laney, D E, Duchaineau, M A, Hansen, C D, Hamann, B, and Joy, K I. Wavelet Representation of Contour Sets. United States: N. p., 2001. Web. doi:10.1109/VISUAL.2001.964525.
Bertram, M, Laney, D E, Duchaineau, M A, Hansen, C D, Hamann, B, & Joy, K I. Wavelet Representation of Contour Sets. United States. https://doi.org/10.1109/VISUAL.2001.964525
Bertram, M, Laney, D E, Duchaineau, M A, Hansen, C D, Hamann, B, and Joy, K I. Thu . "Wavelet Representation of Contour Sets". United States. https://doi.org/10.1109/VISUAL.2001.964525. https://www.osti.gov/servlets/purl/15006196.
@article{osti_15006196,
title = {Wavelet Representation of Contour Sets},
author = {Bertram, M and Laney, D E and Duchaineau, M A and Hansen, C D and Hamann, B and Joy, K I},
abstractNote = {We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.},
doi = {10.1109/VISUAL.2001.964525},
url = {https://www.osti.gov/biblio/15006196}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2001},
month = {7}
}

Conference:
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