  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.
