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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 1X, NO. X, XXX XXXX 1 Positional Uncertainty of Isocontours
 

Summary: IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 1X, NO. X, XXX XXXX 1
Positional Uncertainty of Isocontours:
Condition Analysis and Probabilistic Measures
Kai P¨othkow and Hans-Christian Hege
Abstract--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.
Index Terms--Uncertainty, probability, isolines, isosurfaces, numerical condition, error analysis, volume visualization.
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1 INTRODUCTION
NUMERICAL quantities with continuous range, like
scalar variables y R, can be measured only with

  

Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin

 

Collections: Computer Technologies and Information Sciences