Image Processing Reference
In-Depth Information
Fig. 14.4
Visualization of the derived field
κ
between electrostatic potentials defined by barnase
and barstar in the complex 1BRS.
Left
an overview of the regions with high values of
κ
in the
complex. The proteins are shown as alpha-carbon traces, with barnase in magenta and barstar in
yellow.
Right
a closeup of a hydrogen bond cluster.
Asp 39
of barstar hydrogen bonds with
Arg
87, Arg 83,
and
His 102
of barnase. All four residues are highly important in the interaction
between barnase and barstar. Image courtesy of Edelsbrunner et al. [
3
]
14.3 Alignment and Dependency Measures
We now discuss derived fields that capture the variation or dependency between
multiple (greater than two) fields.
14.3.1 Local Gradient-Based Comparison Measures
The gradient comparison measures discussed in the previous section also extends
to multiple scalar fields. We now describe these extensions, their properties and
applications.
14.3.1.1 Definitions and Properties
The gradient similarity measure GSIM is extended to
k
gradient fields by computing
the minimum gradient pair similarity
C
k
=
min
{
s
(
∇
f
i
,
∇
f
j
)
|
1
≤
i
<
j
≤
k
}
.
The measure assumes low values if the gradient directions are equally distrib-
uted in the domain. Given
k
fields, GSIM can be computed for all possible sub-
sets of fields. The size of this set grows exponentially with the number of fields
and hence it is impractical to compute and analyze GSIM for all subsets of fields.
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