Biomedical Engineering Reference
In-Depth Information
bilinear interpolation since, based on the formula, the new pixel value is a con-
vex combination of old ones. This property is used in the implementation and
steps are only calculated once and never changed thereafter.
The overlapping pixels are scanned and the joint histogram is then computed.
Let the joint histogram be
H
(
i
,
j
). The marginal histograms are then
H
r
(
i
)
=
H
(
i
,
j
)
,
j
H
f
(
j
)
=
H
(
i
,
j
)
.
i
Here the subscripts
r
and
f
stand for reference and floating, respectively. Let
N
be the total number of pixel pairs examined in the overlapping region then the
joint and marginal pdfs are estimated as
H
(
i
,
j
)
N
,
p
(
i
,
j
)
=
H
r
(
i
)
N
,
p
r
(
i
)
=
H
f
(
j
)
N
.
Substituting those estimated joint and marginal pdfs into the definition of mutual
information, its value can be readily computed. Since the iterative optimization
routine is for minimization problem, the negated mutual information is actually
computed.
p
f
(
j
)
=
4.2.5
Optimization
The sole goal of mutual information approach to image registration is to find a
transformation under which the mutual information between the reference im-
age and the transformed floating image is maximized. This is a typical optimiza-
tion problem and many optimization methods have been employed, including
exhaustive search, gradient descent, simplex downhill, Powell's method, simu-
lated annealing, and genetic algorithms [36]. This chapter studies the simplex
downhill optimization since it is reported that it is faster than other algorithms
with similar accuracy [36]. Simplex is also the easiest method to understand and
does not require any derivative calculation.
The simplex downhill method may be trapped at local minimum. Simulated
annealing method can avoid the problem, but it is computationally expensive. To
avoid that we incorporate multiresolution strategies into the iterative process.
