# Direct Volume Rendering with Nonparametric Models of Uncertainty

arXiv: https://arxiv.org/abs/2008.13576 · HTML: https://mlsanity.com/paper/2008.13576/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2020.

## Built on by (most cited first, 10 of 10)

- [PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data](https://mlsanity.com/paper/2308.04605/) (2023)
- [Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network](https://mlsanity.com/paper/2407.19082/) (2024)
- [Uncertainty-Aware Deep Neural Representations for Visual Analysis of Vector Field Data](https://mlsanity.com/paper/2407.16119/) (2024)
- [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 Image-based Typology for Visualization](https://mlsanity.com/paper/2403.05594/) (2024)
- [REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization](https://mlsanity.com/paper/2601.17689/) (2026)
- [An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations](https://mlsanity.com/paper/2409.08445/) (2024)
- [Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty](https://mlsanity.com/paper/2510.01190/) (2025)
- [Efficient Level-Crossing Probability Calculation for Gaussian Process Modeled Data](https://mlsanity.com/paper/2512.12442/) (2025)

## Abstract (arXiv)

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.