# Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

arXiv: https://arxiv.org/abs/2207.11318 · HTML: https://mlsanity.com/paper/2207.11318/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2022.

## Built on by (most cited first, 4 of 4)

- [PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data](https://mlsanity.com/paper/2308.04605/) (2023)
- [Uncertainty-Informed Volume Visualization using Implicit Neural Representation](https://mlsanity.com/paper/2408.06018/) (2024)
- [Visual Analysis of Prediction Uncertainty in Neural Networks for Deep Image Synthesis](https://mlsanity.com/paper/2406.18545/) (2024)
- [An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations](https://mlsanity.com/paper/2409.08445/) (2024)

## Abstract (arXiv)

Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of level-set visualization for univariate data to multivariate data. In this paper, we present a statistical framework to quantify positional probabilities of fibers extracted from uncertain bivariate fields. Specifically, we extend the state-of-the-art Gaussian models of uncertainty for bivariate data to other parametric distributions (e.g., uniform and Epanechnikov) and more general nonparametric probability distributions (e.g., histograms and kernel density estimation) and derive corresponding spatial probabilities of fibers. In our proposed framework, we leverage Green's theorem for closed-form computation of fiber probabilities when bivariate data are assumed to have independent parametric and nonparametric noise. Additionally, we present a nonparametric approach combined with numerical integration to study the positional probability of fibers when bivariate data are assumed to have correlated noise. For uncertainty analysis, we visualize the derived probability volumes for fibers via volume rendering and extracting level sets based on probability thresholds. We present the utility of our proposed techniques via experiments on synthetic and simulation datasets.