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Visual Analysis of Spatial Variability and Global Correlations in Ensembles of Iso-Contours
- Source :
- Computer Graphics Forum. 35:221-230
- Publication Year :
- 2016
- Publisher :
- Wiley, 2016.
-
Abstract
- 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.
- Subjects :
- Scalar (mathematics)
Conditional probability
020207 software engineering
Statistical model
Signed distance function
02 engineering and technology
01 natural sciences
Computer Graphics and Computer-Aided Design
010104 statistics & probability
Bounded function
0202 electrical engineering, electronic engineering, information engineering
Spatial ecology
Spatial variability
0101 mathematics
Cluster analysis
Algorithm
Mathematics
Subjects
Details
- ISSN :
- 01677055
- Volume :
- 35
- Database :
- OpenAIRE
- Journal :
- Computer Graphics Forum
- Accession number :
- edsair.doi...........3abc95b52a94913fc4134aa2dc120eb2