Image Processing Reference
In-Depth Information
Fig. 27.5
A cancellation operation on the 1-skeleton of the Morse-Smale complex removes two
critical points (
u
and
l
), and reconnects their neighborhood. In this example, each arc connected to
u
is
re-routed to reach the newmaximum. In practice, the new geometry is constructed by concatenating
three paths [
7
]. © 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. 27.6
The 1-skeleton of the Morse-Smale complex is computed for the simulated porous solid
(
left
). Applying simplification and filtering allows representation of the filament structure at multiple
scales (
middle
,
left
)
We apply the 1-skeleton of the Morse-Smale complex to finding the filament
structure of a porousmaterial [
8
],asshowninFig.
27.6
. Thematerial is represented by
a signed distance field from an interface surfaces demarking “inside” from “outside”
the solid portion of the domain. The 2-saddle-maximum arcs of the complex form
the space of possible reconstructions of the filaments. By combining filtering of the
arcs based on the 2-saddle and maximum function values with exploration of the
topological hierarchy, it is possible to study the filament structure at multiple scales
and for multiple thresholds.
27.4 Feature Attributes
In addition to the information necessary to encode a feature family we augment each
feature with an arbitrary number,
k
, of additional attributes
att
0
att
k
. Our sys-
tem currently supports various descriptive statistics such as minima, maxima, first
through fourth order statistical moments and sums, as well as as shape descriptors
such as volumes and various length-scales. Descriptive statistics are computed incre-
(
,...,
)
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