Uncertainty quantification in linear interpolation for isosurface extraction

IEEE Trans Vis Comput Graph. 2013 Dec;19(12):2723-32. doi: 10.1109/TVCG.2013.208.


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.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms*
  • Computer Graphics*
  • Computer Simulation
  • Data Interpretation, Statistical*
  • Linear Models*
  • Models, Statistical*
  • Numerical Analysis, Computer-Assisted*
  • User-Computer Interface*