Biomedical Engineering Reference
In-Depth Information
TABlE 11. 1
Metrics.Used.to.Assess.Image.Optimization
Metric.Name
Analytical.Formulation
Intensity.squared.Equation.11.1.(Langlois.et.al..2002)
∑
∑
I x y
2
( , )
pixels
(
)
2
I x y
( , )
pixels
Image.variance.Equation.11.2.(Subbarao.et.al..1993)
1
∑
2
( ( , )
I x y
− < >
I
)
N
pixels
∑
I x y
( , )
pixels
Fourier.ilter.Equation.11.3.(Walker.and.Tyson.2009)
∑
∑
F
F
{ ( , )}
{ ( , )}
I x y
I x y
masked
pixels
pixels
unmasked
Sobel.ilter.Equation.11.4
(
)
2
∑
(
)
2
Sob
∗
I
( , )
x y
+
Sob
∗
I
( , )
x y
x
y
pixels
∑
I x y
( , )
pixels
Wavelet.ilter.Equation.11.5.(Kautsky.et.al..2004)
(
)
∑
∑
LH x y
( , )
2
+
HL x y
( , )
2
pixels
pixels
(
)
∑
∑
∑
I x y
( , )
−
LH x y
( , )
+
HL x y
( , )
2
2
2
pixels
pixels
pixels
Equation.11.4,.which.we.propose.here,.is.calculated.using.the.irst.derivative.of.the.image.whose.approx-
imation.is.obtained.by.the.convolution.of.the.image.with.two.3.by.3.kernels,.
S
x
.and.S
y
.given.by
−
1
−
2
−
1
−
1 0
+
1
S
=
0
0
0
and
S
−
2
0
+
2
=
x
y
+
1
+
2
+
1
−
1 0
+
1
.
he.metrics.based.on.two-dimensional.wavelet.transforms.have.been.suggested.in.Ferzli.and.Karam.
(2005).and.Sherman.et.al..(2002)..he.wavelet.functions.are.convenient.to.represent.the.local.frequency.
content.of.an.image..he.irst.level.of.decomposition.consists.of.applying.a.one-dimensional.low-.and.
high-pass.ilter—irst.vertically.to.each.row.of.the.image.and.second,.horizontally.to.each.column.of.the.
image..hus,.the.result.of.a.two-dimensional.level-one.wavelet.decomposition.is.an.array.of.four.subim-
ages:.LL,.LH,.HL,.and.HH,.where.LL.indicates.a.low-pass.vertical.ilter.followed.by.a.low-pass.horizontal.
ilter,.LH.a.low-pass.vertical.ilter.followed.by.a.high-pass.horizontal.ilter,.and.so.on..LL.is.the.approxi-
mation.coeicient..HL,.LH,.and.HH.are,.respectively,.the.horizontal.detail,.vertical.detail,.and.diagonal.
detail.of.the.original.image..A.second-level.wavelet.decomposition.then.consists.of.applying.the.same.
irst-level. decomposition. twice,. by. reapplying. the. decomposition. on. LL.. In. Ferzli. and. Karam. (2005),.
a third-level.decomposition.is.performed.and.the.edge.widths.are.measured.and.summed.up.together.on.
the.absolute.value.of.the.vertical.LH.and.horizontal.HL.coeicients.image..he.metric.value.is.then.the.
average.of.the.edge.widths.summed.on.LH.and.HL..he.readers.who.are.interested.in.using.this.metric.
are.strongly.advised.to.read.the.references.given.and.the.further.references.within.these.articles..he.full.
details.of.wavelet.decomposition.are.well.beyond.the.scope.of.this.chapter.on.AO.
he.other.aspect.of.the.optimization.process.to.consider.is.the.algorithm.used.to.ind.the.best.solu-
tion.. he. original. optimization-based. nonlinear. AO. microscopy. work. used. a. modiied. hill-climbing.
algorithm.(Marsh.et.al..2003).or.a.genetic.algorithm.(Sherman.et.al..2002),.although.subsequently.results.
have.been.demonstrated.using.broader-range-optimization.routines,.including.random.search,.adap-
tive.random.search,.and.simulated.annealing.(Poland.et.al..2008)..All.of.these.methods.work,.although.
