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.

翻译：多变量数据及其不确定性的可视化和分析是数据可视化的最大研究挑战。构建纤维表面是一种常用的多变量数据可视化技术,它概括了将单轨数据定级可视化概念应用于多变量数据。在本文中,我们提出了一个统计框架,以量化从不确定的双变量字段中提取的纤维的定位概率。具体地说,我们将双轨数据最先进的高斯不确定性模型扩展至其他参数分布(例如,统一和Epanechnikov)和更普遍的非参数概率分布(例如,直方图和内核密度估计)和更普遍的非参数概率分布,并得出相应的纤维空间概率。在我们提议的框架中,我们利用Green的理论来计算从不确定的双变量字段中提取的纤维概率。此外,我们提出了一种非参数性的方法,结合了在通过可视性模型分析我们目前预测的概率数据时,我们研究双轨数据的位置概率的可能性,我们假设了通过测算的概率水平。