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.

中文翻译：

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使用不确定性非参数模型的直接体积渲染

我们提出了一个用于量化、分析和传播直接体积渲染 (DVR) 中数据不确定性的非参数统计框架。最先进的统计 DVR 框架允许在可视化不确定数据时保留地面实况函数的传递函数 (TF)；然而，现有框架仅限于不确定性的参数模型。在本文中，我们通过扩展非参数分布的 DVR 框架来解决现有 DVR 框架的局限性。我们利用分位数插值技术推导出表示封闭形式的观察射线样本强度不确定性的概率分布，这允许准确和有效的计算。我们通过与平均场和参数统计模型（例如均匀和高斯以及高斯混合）的定性和定量比较来评估我们提出的非参数统计模型。此外，我们将最先进的渲染参数框架扩展到 2D TF，以改进 DVR 分类。我们展示了我们的不确定性量化框架对标量场数据集的集成、下采样和双变量版本的适用性。