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

arXiv: https://arxiv.org/abs/2409.08445 · HTML: https://mlsanity.com/paper/2409.08445/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Persistence Atlas for Critical Point Variability in Ensembles](https://mlsanity.com/paper/1807.11212/) (2018)
- [Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps](https://mlsanity.com/paper/1912.06341/) (2019)
- [Direct Volume Rendering with Nonparametric Models of Uncertainty](https://mlsanity.com/paper/2008.13576/) (2020)
- [A Structural Average of Labeled Merge Trees for Uncertainty Visualization](https://mlsanity.com/paper/1908.00113/) (2019)
- [Uncertainty Visualization of the Marching Squares and Marching Cubes Topology Cases](https://mlsanity.com/paper/2108.03066/) (2021)
- [Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models](https://mlsanity.com/paper/2207.11318/) (2022)

## Abstract (arXiv)

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.