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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003958
pages 101-117

APPROXIMATE LEVEL-CROSSING PROBABILITIES FOR INTERACTIVE VISUALIZATION OF UNCERTAIN ISOCONTOURS

Kai Poethkow
Zuse Institute Berlin, Takustrasse 7,14195 Berlin, Germany
Christoph Petz
Zuse Institute Berlin, Takustrasse 7,14195 Berlin, Germany
Hans-Christian Hege
Zuse Institute Berlin, Takustrasse 7,14195 Berlin, Germany

ABSTRACT

A major method for quantitative visualization of a scalar field is depiction of its isocontours. If the scalar field is afflicted with uncertainties, uncertain counterparts to isocontours have to be extracted and depicted. We consider the case where the input data is modeled as a discretized Gaussian field with spatial correlations. For this situation we want to compute level-crossing probabilities that are associated to grid cells. To avoid the high computational cost of Monte Carlo integrations and direction dependencies of raycasting methods, we formulate two approximations for these probabilities that can be utilized during rendering by looking up precomputed univariate and bivariate distribution functions. The first method, called maximum edge crossing probability, considers only pairwise correlations at a time. The second method, called linked-pairs method, considers joint and conditional probabilities between vertices along paths of a spanning tree over the n vertices of the grid cell; with each possible tree an n-dimensional approximate distribution is associated; the choice of the distribution is guided by minimizing its Bhattacharyya distance to the original distribution. We perform a quantitative and qualitative evaluation of the approximation errors on synthetic data and show the utility of both approximations on the example of climate simulation data.