Biomedical Engineering Reference
In-Depth Information
Fig. 2.5
Multi-Level: The central coronal slice in y-direction is shown for different resolution
levels. The different levels of a CT scan are shown in the
left column
and corresponding PET
images are shown in the
right column
.(
a
)Level3(22
×
22
×
6) (
b
)Level3(22
×
22
×
6) (
c
)Level
4(44
×
44
×
12) (
d
)Level4(44
×
44
×
12) (
e
)Level5(88
×
88
×
24) (
f
)Level5(88
×
88
×
24)
(
g
) Level 6 (175
×
175
×
47) (
h
) Level 6 (175
×
175
×
47)
Algorithm 2.1
Multi-level image registration
Input:
Template image
T
and reference image
R
Output:
Transformation
y
y
minLevel
←
1
// initialize transformation with identity
for
level
=
minLevel
→
maxLevel
do
T
← T
// down-sampling of template image
level
// down-sampling of reference image
y
level
←
argmin
J
(
y
level
)
// update motion by minimizing the functional
if
level
<
maxLevel
then
y
level
+
1
←
y
level
// prolongate transformation to next level
end if
end for
y
←
y
maxLevel
// output final transformation
R
← R
level
We will meet the general multi-level idea again in optical flow motion esti-
mation in Sect.
2.2
, as it allows to estimate large deformations with optical flow.
However, the approach presented here still differs from the optimize-then-discretize
approach that is typically used in optical flow, cf. Sect.
2.2
. Most importantly, the
discretization used here guarantees that the solution fulfills the properties assumed
in the theory on each discretization level and that large steps can be taken in the
numerical optimization. Also optimization techniques are well understood and clear
rules for stopping [
55
], step lengths [
1
,
100
], etc. exist.
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