Visual Analysis of Spatial Variability and Global Correlations in Ensembles of Iso-Contours

For an ensemble of iso‐contours in multi‐dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We firs...

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Vydáno v:Computer graphics forum Ročník 35; číslo 3; s. 221 - 230
Hlavní autoři: Ferstl, F., Kanzler, M., Rautenhaus, M., Westermann, R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.06.2016
Témata:
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Color coding
Computation
Computer graphics
Correlation
Datasets
I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation
Mathematical analysis
Mathematical models
Reduced order
Shape
Studies
Three dimensional
Visualization
ISSN:0167-7055, 1467-8659
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Shrnutí:For an ensemble of iso‐contours in multi‐dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We first show how to derive a statistical model describing the contour variability, by representing the contours implicitly via signed distance functions and clustering similar functions in a reduced order space. We show that the spatial patterns of the ensemble can then be derived by analytically transforming the boundaries of a confidence interval computed from each cluster into the spatial domain. Furthermore, we introduce a mathematical basis for computing correlations between the occurrences of iso‐contours at different locations. We show that the computation of these correlations can be posed in the reduced order space as an integration problem over a region bounded by four hyper‐planes. To visualize the derived statistical properties we employ a variant of variability plots for streamlines, now including the color coding of probabilities of joint contour occurrences. We demonstrate the use of the proposed techniques for ensemble exploration in a number of 2D and 3D examples, using artificial and meteorological data sets.
Bibliografie:ark:/67375/WNG-RHG13TPG-W
Supporting InformationSupporting Information
ArticleID:CGF12898
istex:E25783FBF2FA352E1A0BFA24AD243D0427C16A5A
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12898