Image Processing Reference
In-Depth Information
Fig. 27.7
Computational pipeline for interactive feature exploration. Starting from a clan of feature
families represented by a sequence of merge trees (
a
) setting the feature parameter results in a
sequence of sets of features each represented by a subtree of elements (
b
). Aggregating statistical
attributes for each feature produces a set of features with attributes for each time step (
c
). A
subselection on an arbitrary attribute narrows this collection to features of interest (
d
). Subsequently,
either clan wide plots such as CDFs are created (
e
,
bottom
) or a reduction operator is applied to each
family to create a time series of aggregated attributes (
e
,
top
). Finally, the time series is plotted (
f
,
bottom
) or an additional reduction is used to create a clan wide aggregated scalar property (
f
,
top
),
which produces a single sample of a parameter study. A full study is created by repeatedly executing
the pipeline. ©IEEE. Republishedwith permission of IEEE, fromFeature-Based Statistical Analysis
of Combustion Simulation Data, Bennett, Krishnamoorthy, Liu, Grout, Hawkes, Chen, Shepherd,
Pascucci, Bremer, IEEE TVCG 17(12) 2011; permission conveyed through Copyright Clearance
Center, Inc.
Definition 27.6
(
Aggregation
)An
aggregation A
is an
operator that, given a set of features and an attribute index, returns the combined
attribute for the set of features.
:
P(
F
)
×{
0
, ...,
k
}→R
2
Definition 27.7
(
Subselection
)A
subselection U
:
P(
F
)
×{
0
, ...,
k
}×R
→
P(
F
)
is an operator that, given a set of features, an attribute index, and a corre-
sponding attribute interval range, returns the subset of features whose attribute value
is contained in the interval.
The subselection operator facilitates the creation of conditional plots, which are
often an important part of the analysis pipeline.
Definition 27.8
(
Reduction
)A
reduction R
is an operator that given
a set of scalar values returns a single scalar value, for example by computing the
mean.
:
P(
R
)
→ R
Using the operators described above we create three different types of plots as
summarized by Fig.
27.7
: species distributions, parameter studies, and time-series.
To simplify the discussion below, we assume that the input to each of the operators
is all feature families in a clan, even though in practice we support the restriction to
subsets of the data. All plots take as input a feature clan
C
, a parameter
p
, subselections
Q
att
i
min
,
att
i
max
)
}
,
att
i
min
,
att
i
max
), . . . , (
={
(
and an attribute index
i
. First, the parameter
Search WWH ::
Custom Search