Spatial domain wavelet design for feature preservation in computational data sets

High-fidelity wavelet transforms can facilitate visualization and analysis of large scientific data sets. However, it is important that salient characteristics of the original features be preserved under the transformation. We present a set of filter design axioms in the spatial domain which ensure...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics Vol. 11; no. 2; pp. 149 - 159
Main Authors: Craciun, G., Ming Jiang, Thompson, D., Machiraju, R.
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2005
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Axioms
Computational fluid dynamics
Computational modeling
Computer Graphics
Computer Simulation
Computer vision
Data analysis
Data visualization
Databases, Factual
Design engineering
Discrete wavelet transforms
feature preservation
Filters (fluid)
flow fields
Frequency domain analysis
Index Terms- Filter bank
Information Storage and Retrieval - methods
lifting scheme
Low pass filters
Models, Theoretical
Numerical Analysis, Computer-Assisted
Rheology - methods
Signal Processing, Computer-Assisted
TVD schemes
User-Computer Interface
Visualization
wavelet design
Wavelet domain
Wavelet transforms
ISSN:1077-2626, 1941-0506
Online Access:Get full text
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Summary:High-fidelity wavelet transforms can facilitate visualization and analysis of large scientific data sets. However, it is important that salient characteristics of the original features be preserved under the transformation. We present a set of filter design axioms in the spatial domain which ensure that certain feature characteristics are preserved from scale to scale and that the resulting filters correspond to wavelet transforms admitting in-place implementation. We demonstrate how the axioms can be used to design linear feature-preserving filters that are optimal in the sense that they are closest in L 2 to the ideal low pass filter. We are particularly interested in linear wavelet transforms for large data sets generated by computational fluid dynamics simulations. Our effort is different from classical filter design approaches which focus solely on performance in the frequency domain. Results are included that demonstrate the feature-preservation characteristics of our filters
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ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2005.35