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An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations

Robert Sisneros, Tushar M. Athawale, David Pugmire, Kenneth Moreland

TL;DR

This work uses an entropy calculation directly on ensemble data to establish an expected result and then compares the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models, to verify that models matching the distribution of the ensemble indeed match the entropy.

Abstract

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.

An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations

TL;DR

This work uses an entropy calculation directly on ensemble data to establish an expected result and then compares the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models, to verify that models matching the distribution of the ensemble indeed match the entropy.

Abstract

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.
Paper Structure (7 sections, 7 figures, 3 tables)

This paper contains 7 sections, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background and Related Works
  3. Evaluation Framework
  4. Results and Discussion
  5. Wind Dataset Results
  6. Red Sea Results
  7. Conclusion and Future Directions

Figures (7)

  • Figure 1: Renderings of the negative of the velocity magnitude of the first ensemble (of 15) of the wind dataset without and with noise.
  • Figure 2: Total summed entropy from contouring the wind dataset using the histogram and quantile models containing between 1 and 1000 bins. The baseline of each chart is set at the target entropy of the full distribution (see \ref{['tab:windNoise']}). Quantile models generally converge to the baseline entropy with an increase in the number of quantiles.
  • Figure 3: Entropy of uncertain contours from the full distribution of the wind dataset.
  • Figure 4: Total summed entropy from contouring the wind dataset using the histogram and quantile models containing between 1 and 1000 bins. The baseline of each chart is set at the target entropy of the full distribution (see \ref{['tab:wind']}).
  • Figure 5: Velocity magnitude of the Red Sea dataset.
  • ...and 2 more figures