Closed stream lines in uncertain vector fields

137

This paper presents the state of the art in the area of topology-based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

Section: Uncertainty In Vector Fieldssupporting

confidence: 57%

A Survey of Topology‐based Methods in Visualization

Heine

Leitte

Hlawitschka³

et al. 2016

137

“…Our method for critical point detection is closely related to the method proposed by Otto et al [OGHT10,OGT11b,OGT11a]. Both methods compute scalar fields to indicate relative critical point strengths.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast to previous global methods [OGHT10,OGT11a,OGT11b], we take a different perspective on the topic. Our local method is able to extract features also in divergence-free fields and to detect saddle points in a straightforward way.…”

Section: Discussionmentioning

confidence: 99%

Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation

Petz

Pöthkow

Hege

2012

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.

“…A global approach to feature extraction is uncertain vector field topology which was presented by Otto et al [OGHT10]. Subsequent work extended these methods to detect closed streamlines [OGT11a] and topological structures of 3D vector fields [OGT11b]. Friman et al presented methods to compute spatial distributions of pathlines in blood flow measurements [FHH*11].…”

Section: Related Workmentioning

confidence: 99%

Nonparametric Models for Uncertainty Visualization

Pöthkow

Hege

2013

An uncertain (scalar, vector, tensor) field is usually perceived as a discrete random field with a priori unknown probability distributions. To compute derived probabilities, e.g. for the occurrence of certain features, an appropriate probabilistic model has to be selected. The majority of previous approaches in uncertainty visualization were restricted to Gaussian fields. In this paper we extend these approaches to nonparametric models, which are much more flexible, as they can represent various types of distributions, including multimodal and skewed ones. We present three examples of nonparametric representations: (a) empirical distributions, (b) histograms and (c) kernel density estimates (KDE). While the first is a direct representation of the ensemble data, the latter two use reconstructed probability density functions of continuous random variables. For KDE we propose an approach to compute valid consistent marginal distributions and to efficiently capture correlations using a principal component transformation. Furthermore, we use automatic bandwidth selection, obtaining a model for probabilistic local feature extraction. The methods are demonstrated by computing probabilities of level crossings, critical points and vortex cores in simulated biofluid dynamics and climate data.