Publication de 6 numéros par an
ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099
Indexed in
APPROXIMATE LEVEL-CROSSING PROBABILITIES FOR INTERACTIVE VISUALIZATION OF UNCERTAIN ISOCONTOURS
RÉSUMÉ
A major method for quantitative visualization of a scalar field is depiction of its isocontours. If the scalar field is afflicted with uncertainties, uncertain counterparts to isocontours have to be extracted and depicted. We consider the case where the input data is modeled as a discretized Gaussian field with spatial correlations. For this situation we want to compute level-crossing probabilities that are associated to grid cells. To avoid the high computational cost of Monte Carlo integrations and direction dependencies of raycasting methods, we formulate two approximations for these probabilities that can be utilized during rendering by looking up precomputed univariate and bivariate distribution functions. The first method, called maximum edge crossing probability, considers only pairwise correlations at a time. The second method, called linked-pairs method, considers joint and conditional probabilities between vertices along paths of a spanning tree over the n vertices of the grid cell; with each possible tree an n-dimensional approximate distribution is associated; the choice of the distribution is guided by minimizing its Bhattacharyya distance to the original distribution. We perform a quantitative and qualitative evaluation of the approximation errors on synthetic data and show the utility of both approximations on the example of climate simulation data.
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Mirzargar Mahsa, He Yanyan, Kirby Robert M., Application of Uncertainty Modeling Frameworks to Uncertain Isosurface Extraction, in Integrated Uncertainty in Knowledge Modelling and Decision Making, 9376, 2015. Crossref
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Hazarika Subhashis, Biswas Ayan, Dutta Soumya, Shen Han-Wei, Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets, Entropy, 20, 7, 2018. Crossref
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Raidou Renata Georgia, Visual Analytics for the Representation, Exploration, and Analysis of High-Dimensional, Multi-faceted Medical Data, in Biomedical Visualisation, 1138, 2019. Crossref
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Vidal Jules, Budin Joseph, Tierny Julien, Progressive Wasserstein Barycenters of Persistence Diagrams, IEEE Transactions on Visualization and Computer Graphics, 2019. Crossref
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He Wenbin, Guo Hanqi, Shen Han-Wei, Peterka Tom, eFESTA: Ensemble Feature Exploration with Surface Density Estimates, IEEE Transactions on Visualization and Computer Graphics, 2019. Crossref
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Hazarika Subhashis, Dutta Soumya, Shen Han-Wei, Chen Jen-Ping, CoDDA: A Flexible Copula-based Distribution Driven Analysis Framework for Large-Scale Multivariate Data, IEEE Transactions on Visualization and Computer Graphics, 25, 1, 2019. Crossref
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Pont Mathieu, Vidal Jules, Delon Julie, Tierny Julien, Wasserstein Distances, Geodesics and Barycenters of Merge Trees, IEEE Transactions on Visualization and Computer Graphics, 28, 1, 2022. Crossref
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Favelier Guillaume, Faraj Noura, Summa Brian, Tierny Julien, Persistence Atlas for Critical Point Variability in Ensembles, IEEE Transactions on Visualization and Computer Graphics, 25, 1, 2019. Crossref