  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.
