Image Processing Reference
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(b)
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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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