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Visualizing the Variability of Gradients in Uncertain 2D Scalar Fields

Tobias Pfaffelmoser, Mihaela Mihai, Rudiger Westermann
2013 IEEE Transactions on Visualization and Computer Graphics  
While this framework generalizes to 3D uncertain scalar fields, we concentrate on the visualization of the resulting intervals in 2D fields.  ...  In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data.  ...  We then develop visualization techniques to qualitatively assess the gradient variability in uncertain 2D scalar fields.  ... 
doi:10.1109/tvcg.2013.92 pmid:24029913 fatcat:md7lfwoefnf4ppjvzplk2hmrdi

Direct Volume Rendering with Nonparametric Models of Uncertainty [article]

Tushar Athawale, Bo Ma, Elham Sakhaee, Chris R. Johnson, Alireza Entezari
2020 arXiv   pre-print
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  ...  We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.  ...  ACKNOWLEDGMENTS This work was supported in part by the NSF grant IIS-1617101; the NIH grants P41 GM103545-18 and R24 GM136986; the DOE grant DE-FE0031880; and the Intel Graphics and Visualization Institutes  ... 
arXiv:2008.13576v1 fatcat:77o2bsd2jngj3p4lo4ed4vxkei

Visualizing Contour Distributions in 2D Ensemble Data [article]

Tobias Pfaffelmoser, Rüdiger Westermann
2013 Eurographics Conference on Visualization  
Overlaid plots of iso-contours in individual members of a scalar ensemble field are a popular concept to visualize the data uncertainty.  ...  From this information, the uncertainty and topology of iso-contours can be determined, as well as the variations in gradient magnitude around these contours.  ...  Spatial Probability Distribution We first develop stochastic distribution functions for characterizing the spatial variability of iso-contours in uncertain scalar fields, i.e., the spatial cumulative distribution  ... 
doi:10.2312/pe.eurovisshort.eurovisshort2013.055-059 dblp:conf/vissym/PfaffelmoserW13 fatcat:dl2qk6ekyza3lanitfldysigvq

Positional Uncertainty of Isocontours: Condition Analysis and Probabilistic Measures

Kai Pothkow, Hans-Christian Hege
2011 IEEE Transactions on Visualization and Computer Graphics  
As input data we consider discretized uncertain scalar fields and model these as random fields.  ...  While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider uncertainty.  ...  We are also grateful for the provision of datasets by Bert G ünther (airfoil), Stefan Zachow (middle ear), the ECMWF [50] (temperature field) and -in memoriam -Dirk Bartz (fuel dataset).  ... 
doi:10.1109/tvcg.2010.247 pmid:21041883 fatcat:ahan6bgqzfghhev2jnjqkdihyu

Visualizing the Positional and Geometrical Variability of Isosurfaces in Uncertain Scalar Fields

Tobias Pfaffelmoser, Matthias Reitinger, Rüdiger Westermann
2011 Computer graphics forum (Print)  
We present a novel approach for visualizing the positional and geometrical variability of isosurfaces in uncertain 3D scalar fields.  ...  Experimental results confirm the effectiveness of our approach for the visualization of uncertainty related to position and shape of convex and concave isosurface structures.  ...  The work was funded by the Munich Centre for Advanced Computing and the International Graduate School of Science and Engineering (IGSSE) at the Technische Universität München.  ... 
doi:10.1111/j.1467-8659.2011.01944.x fatcat:cji6wyxjnzatxglmcd4w6coe7m

Multivariate spatial data visualization: a survey

Xiangyang He, Yubo Tao, Qirui Wang, Hai Lin
2019 Journal of Visualization  
In this paper, we present a comprehensive survey of the state-of-the-art techniques for multivariate spatial data visualization.  ...  We first introduce the basic concept and characteristics of multivariate spatial data, and describe three main tasks in multivariate data visualization: feature classification, fusion visualization, and  ...  Acknowledgement The authors would like to thank the anonymous reviewers for their valuable comments.  ... 
doi:10.1007/s12650-019-00584-3 fatcat:2evmvj76wjhvxe4gfrusvvggpm

Visualizing the stability of critical points in uncertain scalar fields

Mihaela Mihai, Rüdiger Westermann
2014 Computers & graphics  
21 of uncertainty on the variability of gradients in scalar fields.  ...  of features in scalar fields is based on 13 level-sets or iso-contours, i.e., the set of all points in the domain 14 where the scalar field takes on a prescribed value, also called 15 an iso-value.  ...  In the fol- The paper assesses the variability of gradients in 2D uncertain 213 scalar fields and derives confidence intervals for the gradient 214 magnitude and orientation.  ... 
doi:10.1016/j.cag.2014.01.007 fatcat:h4fxbl7sh5gzfg6r43ihokrkxe

Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation

Christoph Petz, Kai Pöthkow, Hans-Christian Hege
2012 Computer graphics forum (Print)  
The variability of the random fields in a spatial neighborhood is characterized by marginal distributions.  ...  In this paper methods for extraction of local features in crisp vector fields are extended to uncertain fields.  ...  Acknowledgements We are grateful to Leonid Goubergrits and Jens Schaller for helpful discussions and the provision of aneurysm datasets. We also thank the ECMWF [Pal04] for the climate dataset.  ... 
doi:10.1111/j.1467-8659.2012.03097.x fatcat:hvmpaj6hvvhyljteq4qalcyfv4

Interactive GPU-based Visualization of Scalar Data with Gaussian Distributed Uncertainty [article]

Steven Schlegel, Mathias Goldau, Gerik Scheuermann
2015 International Symposium on Vision, Modeling, and Visualization  
We present a GPU-based approach to visualize samples of normally distributed uncertain, three-dimensional scalar data.  ...  The potential of our method is demonstrated by an interactive volume rendering of three-dimensional data, where the gradient estimation is directly computed by the field function without the need of additional  ...  Additional work to compute the gradient of the probability density function of uncertain 3D scalar fields was done in [PMW12]. Kniss et al.  ... 
doi:10.2312/vmv.20151257 dblp:conf/vmv/SchlegelGS15 fatcat:buqgulnlfrbtfnmn5vedpwppdq

Linked exploratory visualizations for uncertain MR spectroscopy data

David Feng, Lester Kwock, Yueh Lee, Russell M. Taylor II, Chaomei Chen, Jinah Park, Ming C. Hao, Pak C. Wong
2010 Visualization and Data Analysis 2010  
Using MRS, radiologists generate multiple 3D scalar fields of metabolite concentrations within the brain and compare them to anatomical magnetic resonance imaging.  ...  Our system consists of three linked visualizations: a spatial glyph-based technique we call Scaled Data-Driven Spheres, a parallel coordinates visualization augmented to incorporate uncertainty in the  ...  CISMM is supported by the NIH National Institute of Biomedical Imaging and Bioengineering (NIH P41-EB002025).  ... 
doi:10.1117/12.839818 pmid:21152337 pmcid:PMC2997734 dblp:conf/vda/FengKLT10 fatcat:2drqp2i6irbstol7zf7pjr7xk4

An Information-Aware Framework for Exploring Multivariate Data Sets

Ayan Biswas, Soumya Dutta, Han-Wei Shen, Jonathan Woodring
2013 IEEE Transactions on Visualization and Computer Graphics  
In our framework, we compute the total entropy of the multivariate data set and identify the contribution of individual variables to the total entropy.  ...  Experiments with different data sets reveal the effectiveness of our proposed framework in depicting the interesting regions of the data sets taking into account the interaction among the variables.  ...  This work was supported in part by NSF grant IIS-1017635, IIS-1065025, US Department of Energy DOESC0005036, Battelle Contract No. 137365, and Department of Energy SciDAC grant DE-FC02-06ER25779, program  ... 
doi:10.1109/tvcg.2013.133 pmid:24051835 fatcat:f7mcoanghrcq7ne76dtikavjfq

Uncertainty-Oriented Ensemble Data Visualization and Exploration using Variable Spatial Spreading

Mingdong Zhang, Li Chen, Quan Li, Xiaoru Yuan, Junhai Yong
2020 IEEE Transactions on Visualization and Computer Graphics  
To resolve this issue, we propose a new perspective of ensemble data analysis using the attribute variable dimension as the primary analysis dimension.  ...  As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines.  ...  Suppose a scalar field defined by function f : p(x, y) → v, p(x, y) is a point in the spatial region and v is the scalar value of the variable at this point; therefore, the gradient at this point is defined  ... 
doi:10.1109/tvcg.2020.3030377 pmid:33048703 fatcat:7xtesv4oy5bb3bm2mgmuwfvuoi

Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction [chapter]

Kai Pöthkow, Hans-Christian Hege
2012 Mathematics and Visualization  
Scalar anisotropy indices are important means for the analysis and visualization of diffusion tensor fields.  ...  Using level crossing probabilities we quantify and visualize the spatial distribution of uncertain isosurfaces.  ...  For sensitivity analysis of isosurface extraction not only the scalar field but also the gradient magnitude has to be taken into account.  ... 
doi:10.1007/978-3-642-27343-8_11 fatcat:kgbmsfcdbnhhledxjgwl6236om

Mandatory Critical Points of 2D Uncertain Scalar Fields

David Günther, Joseph Salmon, Julien Tierny
2014 Computer graphics forum (Print)  
This paper introduces a novel, non-local characterization of critical points and their global relation in 2D uncertain scalar fields.  ...  These trees enable a visual exploration of the common topological structure of all possible realizations of the uncertain data.  ...  The authors are grateful to Sophie Masse for the graphical design of our demo program's user interface.  ... 
doi:10.1111/cgf.12359 fatcat:prk3ut6gpjd45flygi5yl5fymy

Statistical Rendering for Visualization of Red Sea Eddy Simulation Data [article]

Tushar M. Athawale, Alireza Entezari, Bei Wang, Chris R. Johnson
2021 arXiv   pre-print
Specifically, we demonstrate the applications of statistical volume rendering and statistical Morse complex summary maps to a velocity magnitude field for studying the eddy positions in the flow dataset  ...  In the statistical Morse complex summary maps, we derive histograms charactering uncertainty of gradient flow destinations to understand Morse complex topological variations across the ensemble.  ...  Figure 3 . 3 Visualizations of the uncertain velocity magnitude field for a series of time steps.  ... 
arXiv:2106.12138v1 fatcat:p357ejrx55dzzjjbd5eg2ay2ra
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