Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

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 dat...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2023-01, Vol.29 (1), p.613-623
Main Authors: Athawale, Tushar M., Johnson, Chris R., Sane, Sudhanshu, Pugmire, David
Format: Article
Language:English
Subjects:
and probability
Bivariate analysis
Data models
Data visualization
fiber surfaces
Fibers
Histograms
Multivariate analysis
Nonparametric statistics
Numerical integration
Optical fiber sensors
Power capacitors
Probability
Probability distribution
Scientific visualization
Shape
Statistical analysis
Uncertainty
Uncertainty analysis
Uncertainty visualization
Visualization
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Summary: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.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2022.3209424