Image Processing Reference
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(a)
(b)
(c)
(d)
Fig. 27.1 a
Merge trees represent the merging of contours as a function is lowered through its
range. Each branch represents a portion of the domain as indicated by the colors.
b
To increase
the resolution in parameter space we refine the merge tree by splitting long branches and refining
the segmentation accordingly.
c
A threshold based segmentation of a merge tree at a threshold
slightly above 80% of the global maximum.
d
A relevance based segmentation at relevance around
slightly above 0.2 (slightly below 80% of the local maximum per branch). All local maxima are
included and regions of higher function value (
red
) span a larger range. © IEEE. Republished
with permission of IEEE, from Feature-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.
Fig. 27.2
Examples of different merge tree hierarchies:
a
Burning cells in a premixed hydrogen
flame;
b
Extinction regions in turbulent non-premixed combustion simulation; and
c
Eddies in the
north atlantic extracted using the Okubo-Weiss threshold
such hierarchical segmentations have proven useful is, for example, the analysis of
Raleigh-Taylor instabilities [
11
]. As shown in Fig.
27.4
, stable manifolds naturally
segment the mixing interface into
bubbles
and the persistence simplification enables
a multi-scale analysis.
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