Positional Uncertainty of Isocontours: Condition Analysis and Probabilistic Measures

Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2011-10, Vol.17 (10), p.1393-1406
Main Authors: Pothkow, K., Hege, H-C
Format: Article
Language:English
Subjects:
Aids
error analysis
Interactive
isolines
Isosurfaces
Level set
Mathematical models
Measurement uncertainty
numerical condition
probability
Probability theory
Random variables
Studies
Systematics
Three dimensional
Two dimensional
Uncertainty
Visualization
volume visualization
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Summary:Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider uncertainty. We present mathematical formulations for uncertain equivalents of isocontours based on standard probability theory and statistics and employ them in interactive visualization methods. As input data, we consider discretized uncertain scalar fields and model these as random fields. To create a continuous representation suitable for visualization we introduce interpolated probability density functions. Furthermore, we introduce numerical condition as a general means in feature-based visualization. The condition number-which potentially diverges in the isocontour problem-describes how errors in the input data are amplified in feature computation. We show how the average numerical condition of isocontours aids the selection of thresholds that correspond to robust isocontours. Additionally, we introduce the isocontour density and the level crossing probability field; these two measures for the spatial distribution of uncertain isocontours are directly based on the probabilistic model of the input data. Finally, we adapt interactive visualization methods to evaluate and display these measures and apply them to 2D and 3D data sets.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2010.247