Visualizing the Positional and Geometrical Variability of Isosurfaces in Uncertain Scalar Fields

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Abstract

We present a novel approach for visualizing the positional and geometrical variability of isosurfaces in uncertain 3D scalar fields. Our approach extends recent work by Pöthkow and Hege [PH10] in that it accounts for correlations in the data to determine more reliable isosurface crossing probabilities. We introduce an incremental update-scheme that allows integrating the probability computation into front-to-back volume ray-casting efficiently. Our method accounts for homogeneous and anisotropic correlations, and it determines for each sampling interval along a ray the probability of crossing an isosurface for the first time. To visualize the positional and geometrical uncertainty even under viewing directions parallel to the surface normal, we propose a new color mapping scheme based on the approximate spatial deviation of possible surface points from the mean surface. The additional use of saturation enables to distinguish between areas of high and low statistical dependence. Experimental results confirm the effectiveness of our approach for the visualization of uncertainty related to position and shape of convex and concave isosurface structures.

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