DocumentCode :
54191
Title :
Uncertainty Quantification in Linear Interpolation for Isosurface Extraction
Author :
Athawale, Tushar ; Entezari, Alireza
Author_Institution :
Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL, USA
Volume :
19
Issue :
12
fYear :
2013
fDate :
Dec. 2013
Firstpage :
2723
Lastpage :
2732
Abstract :
We present a study of linear interpolation when applied to uncertain data. Linear interpolation is a key step for isosurface extraction algorithms, and the uncertainties in the data lead to non-linear variations in the geometry of the extracted isosurface. We present an approach for deriving the probability density function of a random variable modeling the positional uncertainty in the isosurface extraction. When the uncertainty is quantified by a uniform distribution, our approach provides a closed-form characterization of the mentioned random variable. This allows us to derive, in closed form, the expected value as well as the variance of the level-crossing position. While the former quantity is used for constructing a stable isosurface for uncertain data, the latter is used for visualizing the positional uncertainties in the expected isosurface level crossings on the underlying grid.
Keywords :
data visualisation; interpolation; statistical distributions; closed-form characterization; data uncertainty; isosurface extraction algorithm; isosurface extraction positional uncertainty; isosurface geometry; isosurface level crossings; level-crossing position; linear interpolation; positional uncertainty visualization; probability density function; random variable modeling; uniform distribution; Data models; Interpolation; Isosurfaces; Probability density function; Random variables; Uncertainty; Data models; Interpolation; Isosurfaces; Marching Cubes; Probability density function; Random variables; Uncertainty; Uncertainty quantification; isosurface extraction; linear interpolation; Algorithms; Computer Graphics; Computer Simulation; Data Interpretation, Statistical; Linear Models; Models, Statistical; Numerical Analysis, Computer-Assisted; User-Computer Interface;
fLanguage :
English
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
Publisher :
ieee
ISSN :
1077-2626
Type :
jour
DOI :
10.1109/TVCG.2013.208
Filename :
6634171
Link To Document :
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