Direct Volume Rendering with Nonparametric Models of Uncertainty

TL;DR

This paper introduces a nonparametric statistical framework for quantifying and visualizing uncertainty in direct volume rendering, improving upon parametric models by using quantile interpolation for more accurate uncertainty representation.

Contribution

It extends existing DVR frameworks to nonparametric models, enabling more precise uncertainty quantification and incorporating 2D transfer functions for enhanced visualization.

Findings

Nonparametric models outperform parametric ones in uncertainty accuracy.

Quantile interpolation enables closed-form probability distribution derivation.

Framework applicable to ensemble and multivariate datasets.

Abstract

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.