Uncertainty quantification in linear interpolation for isosurface extraction.
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.
University of Florida.
Tushar
T
Athawale
Alireza
A
Entezari
D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016014:Linear Models; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D014584:User-Computer Interface