Feature-Based Visualization of Multifields - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 182

fields created by their method requires the use of a multifield graph for interactive
correlation field selection. Regions with interesting field correlations can be easily
selected manually.
A related problem that is not so much concerned with correlations between dif-
ferent fields, but with statistical and stochastic properties of different instances of
the same field is known as ensemble data analysis. Ensembles are frequently used
in meteorological data analysis, where a number of simulation outputs created by
perturbed simulation input parameters are compared to investigate the likelihood
of certain weather events. For small perturbations, the resulting ensemble data sets
have high correlation and describe the same sets of variables. In the work by Smith
et al. [ 31 ] outputs from multiple simulation runs are clustered before visualization
to avoid the loss of distinct features when global averaging over all simulation runs
is applied. Potter et al. [ 28 ] visualize standard deviation and mean of ensembles by
color mapping and contouring. The simultaneous visualization of contours frommul-
tiple scalar fields called spaghetti plots facilitates analysis of relative distributions of
scalar values.
Correlation and variation can not only be computed for sets of fields, but also
for different instances of the same variable as common in time-varying data sets.
In such a way Jänicke et al. [ 16 ] compute local statistical complexity for different
quantities of CFDsimulations. Local statistical complexity is ameasure that describes
the predictability of values of a local variable overt time. Extrema of this measure
often correspond to interesting regions in the flow domain or feature regions as, for
example, extracted by vortex core techniques. The mathematical framework allows
application of the same visualization and feature extraction to different fields of the
same simulation, while providing independent visualization output for each analyzed
variable. Thus, it is a multifield visualization technique only in the sense that it can
be applied to several fields in a multi field data set in a consistent way.

17.3.4 Interactive Feature Specification

Features infields ormultifields have in the ideal case a precisemathematical definition
which does not depend on any “tuning” parameters. An example in hydrodynamics
are cavitation zones, which occur where the local pressure falls below the vapor
pressure at the given temperature. As another example, Hunt et al. [ 15 ] defined an
eddy as the region with positive second invariant, Q ,of

u , with the additional con-
dition that the pressure be lower than the ambient value. While this is a precise and
parameter-free definition, there are competing definitions of eddies, which in a visu-
alization can be used as well, possibly even in combination. An example of a feature
definition involving a parameter is the vortex definition of Jeong and Hussain [ 17 ].
In the original definition, the derived quantity

∇

λ 2 has to be negative, but practically,
for better isolation of the vortices a negative number is used as a threshold for λ 2 .

Such feature definitions involving a parameter require a visualization system where
parameters can be controlled by the user. For multifields the visualization system