Journal
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
Volume 19, Issue 12, Pages 2723-2732Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TVCG.2013.208
Keywords
Uncertainty quantification; linear interpolation; isosurface extraction; marching cubes
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Funding
- AFOSR [FA9550-12-1-0304]
- NSF [CCF-1018149]
- ONR [N000141210862]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1018149] Funding Source: National Science Foundation
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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.
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