Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation

In this paper methods for extraction of local features in crisp vector fields are extended to uncertain fields. While in a crisp field local features are either present or absent at some location, in an uncertain field they are present with some probability. We model sampled uncertain vector fields...

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Bibliographic Details
Published in:Computer graphics forum Vol. 31; no. 3pt2; pp. 1045 - 1054
Main Authors: Petz, Christoph, Pöthkow, Kai, Hege, Hans-Christian
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.06.2012
Subjects:
Analysis
Computer graphics
Computer simulation
Correlation
Crisps
Critical point
I.3.3 [Computer Graphics]: Picture/Image Generation-Viewing algorithms
I.6.8 [Simulation and Modeling]: Types of Simulation-Monte Carlo
Image processing systems
Mathematical analysis
Monte Carlo methods
Monte Carlo simulation
Probability theory
Studies
Vectors (mathematics)
Visual G.3 [Mathematics of Computing]: Probability and Statistics-Probabilistic algorithms
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:In this paper methods for extraction of local features in crisp vector fields are extended to uncertain fields. While in a crisp field local features are either present or absent at some location, in an uncertain field they are present with some probability. We model sampled uncertain vector fields by discrete Gaussian random fields with empirically estimated spatial correlations. The variability of the random fields in a spatial neighborhood is characterized by marginal distributions. Probabilities for the presence of local features are formulated in terms of low‐dimensional integrals over such marginal distributions. Specifically, we define probabilistic equivalents for critical points and vortex cores. The probabilities are computed by Monte Carlo integration. For identification of critical points and cores of swirling motion we employ the Poincaré index and the criterion by Sujudi and Haimes. In contrast to previous global methods we take a local perspective and directly extract features in divergence‐free fields as well. The method is able to detect saddle points in a straight forward way and works on various grid types. It is demonstrated by applying it to simulated unsteady flows of biofluid and climate dynamics.
Bibliography:istex:F69C52E63B1846D6146FB111198577395C830CFE
ArticleID:CGF3097
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03097.x