<s>
Image	B-Algorithm
registration	I-Algorithm
is	O
the	O
process	O
of	O
transforming	O
different	O
sets	O
of	O
data	O
into	O
one	O
coordinate	O
system	O
.	O
</s>
<s>
It	O
is	O
used	O
in	O
computer	B-Application
vision	I-Application
,	O
medical	B-Application
imaging	I-Application
,	O
military	O
automatic	B-Algorithm
target	I-Algorithm
recognition	I-Algorithm
,	O
and	O
compiling	O
and	O
analyzing	O
images	O
and	O
data	O
from	O
satellites	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
or	O
image	O
alignment	O
algorithms	O
can	O
be	O
classified	O
into	O
intensity-based	O
and	O
feature-based	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
involves	O
spatially	O
transforming	O
the	O
source/moving	O
image(s )	O
to	O
align	O
with	O
the	O
target	O
image	O
.	O
</s>
<s>
Intensity-based	O
methods	O
compare	O
intensity	O
patterns	O
in	O
images	O
via	O
correlation	O
metrics	O
,	O
while	O
feature-based	O
methods	O
find	O
correspondence	B-Algorithm
between	O
image	B-Algorithm
features	I-Algorithm
such	O
as	O
points	O
,	O
lines	O
,	O
and	O
contours	O
.	O
</s>
<s>
Feature-based	O
methods	O
establish	O
a	O
correspondence	B-Algorithm
between	O
a	O
number	O
of	O
especially	O
distinct	O
points	O
in	O
images	O
.	O
</s>
<s>
Knowing	O
the	O
correspondence	B-Algorithm
between	O
a	O
number	O
of	O
points	O
in	O
images	O
,	O
a	O
geometrical	O
transformation	O
is	O
then	O
determined	O
to	O
map	O
the	O
target	O
image	O
to	O
the	O
reference	O
images	O
,	O
thereby	O
establishing	O
point-by-point	O
correspondence	B-Algorithm
between	O
the	O
reference	O
and	O
target	O
images	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
algorithms	O
can	O
also	O
be	O
classified	O
according	O
to	O
the	O
transformation	O
models	O
they	O
use	O
to	O
relate	O
the	O
target	O
image	O
space	O
to	O
the	O
reference	O
image	O
space	O
.	O
</s>
<s>
The	O
first	O
broad	O
category	O
of	O
transformation	O
models	O
includes	O
linear	B-Architecture
transformations	I-Architecture
,	O
which	O
include	O
rotation	O
,	O
scaling	O
,	O
translation	O
,	O
and	O
other	O
affine	O
transforms	O
.	O
</s>
<s>
Linear	B-Architecture
transformations	I-Architecture
are	O
global	O
in	O
nature	O
,	O
thus	O
,	O
they	O
cannot	O
model	O
local	O
geometric	O
differences	O
between	O
images	O
.	O
</s>
<s>
Nonrigid	O
transformations	O
include	O
radial	B-Algorithm
basis	I-Algorithm
functions	I-Algorithm
(	O
thin-plate	B-Algorithm
or	O
surface	O
splines	O
,	O
multiquadrics	O
,	O
and	O
compactly-supported	O
transformations	O
)	O
,	O
physical	O
continuum	O
models	O
(	O
viscous	O
fluids	O
)	O
,	O
and	O
large	O
deformation	O
models	O
(	O
diffeomorphisms	O
)	O
.	O
</s>
<s>
It	O
is	O
a	O
part	O
of	O
the	O
SPM	O
and	O
AIR	B-Algorithm
programs	O
.	O
</s>
<s>
Alternatively	O
,	O
many	O
advanced	O
methods	O
for	O
spatial	B-Algorithm
normalization	I-Algorithm
are	O
building	O
on	O
structure	O
preserving	O
transformations	O
homeomorphisms	O
and	O
diffeomorphisms	O
since	O
they	O
carry	O
smooth	O
submanifolds	O
smoothly	O
during	O
transformation	O
.	O
</s>
<s>
Diffeomorphisms	O
are	O
generated	O
in	O
the	O
modern	O
field	O
of	O
Computational	B-Algorithm
Anatomy	I-Algorithm
based	O
on	O
flows	O
since	O
diffeomorphisms	O
are	O
not	O
additive	O
although	O
they	O
form	O
a	O
group	O
,	O
but	O
a	O
group	O
under	O
the	O
law	O
of	O
function	O
composition	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
flows	O
which	O
generalize	O
the	O
ideas	O
of	O
additive	O
groups	O
allow	O
for	O
generating	O
large	B-Algorithm
deformations	I-Algorithm
that	O
preserve	O
topology	O
,	O
providing	O
1-1	O
and	O
onto	O
transformations	O
.	O
</s>
<s>
Computational	O
methods	O
for	O
generating	O
such	O
transformation	O
are	O
often	O
called	O
LDDMM	O
which	O
provide	O
flows	O
of	O
diffeomorphisms	O
as	O
the	O
main	O
computational	O
tool	O
for	O
connecting	O
coordinate	O
systems	O
corresponding	O
to	O
the	O
geodesic	O
flows	O
of	O
Computational	B-Algorithm
Anatomy	I-Algorithm
.	O
</s>
<s>
Some	O
of	O
the	O
feature	O
matching	O
algorithms	O
are	O
outgrowths	O
of	O
traditional	O
techniques	O
for	O
performing	O
manual	O
image	B-Algorithm
registration	I-Algorithm
,	O
in	O
which	O
an	O
operator	O
chooses	O
corresponding	O
control	B-Algorithm
points	I-Algorithm
(	O
CP	O
)	O
in	O
images	O
.	O
</s>
<s>
When	O
the	O
number	O
of	O
control	B-Algorithm
points	I-Algorithm
exceeds	O
the	O
minimum	O
required	O
to	O
define	O
the	O
appropriate	O
transformation	O
model	O
,	O
iterative	O
algorithms	O
like	O
RANSAC	B-Algorithm
can	O
be	O
used	O
to	O
robustly	O
estimate	O
the	O
parameters	O
of	O
a	O
particular	O
transformation	O
type	O
(	O
e.g.	O
</s>
<s>
Applying	O
the	O
phase	B-General_Concept
correlation	I-General_Concept
method	O
to	O
a	O
pair	O
of	O
images	O
produces	O
a	O
third	O
image	O
which	O
contains	O
a	O
single	O
peak	O
.	O
</s>
<s>
Unlike	O
many	O
spatial-domain	O
algorithms	O
,	O
the	O
phase	B-General_Concept
correlation	I-General_Concept
method	O
is	O
resilient	O
to	O
noise	O
,	O
occlusions	O
,	O
and	O
other	O
defects	O
typical	O
of	O
medical	O
or	O
satellite	O
images	O
.	O
</s>
<s>
Additionally	O
,	O
the	O
phase	B-General_Concept
correlation	I-General_Concept
uses	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
to	O
compute	O
the	O
cross-correlation	O
between	O
the	O
two	O
images	O
,	O
generally	O
resulting	O
in	O
large	O
performance	O
gains	O
.	O
</s>
<s>
Due	O
to	O
properties	O
of	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
,	O
the	O
rotation	O
and	O
scaling	O
parameters	O
can	O
be	O
determined	O
in	O
a	O
manner	O
invariant	O
to	O
translation	O
.	O
</s>
<s>
Multi-modality	O
registration	O
methods	O
are	O
often	O
used	O
in	O
medical	B-Application
imaging	I-Application
as	O
images	O
of	O
a	O
subject	O
are	O
frequently	O
obtained	O
from	O
different	O
scanners	O
.	O
</s>
<s>
Examples	O
include	O
registration	O
of	O
brain	O
CT/MRI	O
images	O
or	O
whole	O
body	O
PET/CT	O
images	O
for	O
tumor	O
localization	O
,	O
registration	O
of	O
contrast-enhanced	O
CT	O
images	O
against	O
non-contrast-enhanced	O
CT	O
images	O
for	O
segmentation	O
of	O
specific	O
parts	O
of	O
the	O
anatomy	O
,	O
and	O
registration	O
of	O
ultrasound	B-Application
and	O
CT	O
images	O
for	O
prostate	O
localization	O
in	O
radiotherapy	O
.	O
</s>
<s>
Image	O
similarities	O
are	O
broadly	O
used	O
in	O
medical	B-Application
imaging	I-Application
.	O
</s>
<s>
Measure	O
matching	O
which	O
are	O
pointsets	O
or	O
landmarks	O
without	O
correspondence	B-Algorithm
,	O
Curve	O
matching	O
and	O
Surface	O
matching	O
via	O
mathematical	O
currents	O
and	O
varifolds	O
.	O
</s>
<s>
A	O
confident	O
registration	O
with	O
a	O
measure	O
of	O
uncertainty	O
is	O
critical	O
for	O
many	O
change	B-General_Concept
detection	I-General_Concept
applications	O
such	O
as	O
medical	O
diagnostics	O
.	O
</s>
<s>
In	O
remote	B-Application
sensing	I-Application
applications	O
where	O
a	O
digital	O
image	O
pixel	O
may	O
represent	O
several	O
kilometers	O
of	O
spatial	O
distance	O
(	O
such	O
as	O
NASA	O
's	O
LANDSAT	O
imagery	O
)	O
,	O
an	O
uncertain	O
image	B-Algorithm
registration	I-Algorithm
can	O
mean	O
that	O
a	O
solution	O
could	O
be	O
several	O
kilometers	O
from	O
ground	O
truth	O
.	O
</s>
<s>
Several	O
notable	O
papers	O
have	O
attempted	O
to	O
quantify	O
uncertainty	O
in	O
image	B-Algorithm
registration	I-Algorithm
in	O
order	O
to	O
compare	O
results	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
has	O
applications	O
in	O
remote	B-Application
sensing	I-Application
(	O
cartography	O
updating	O
)	O
,	O
and	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
Due	O
to	O
the	O
vast	O
range	O
of	O
applications	O
to	O
which	O
image	B-Algorithm
registration	I-Algorithm
can	O
be	O
applied	O
,	O
it	O
is	O
impossible	O
to	O
develop	O
a	O
general	O
method	O
that	O
is	O
optimized	O
for	O
all	O
uses	O
.	O
</s>
<s>
Medical	B-Application
image	I-Application
registration	O
(	O
for	O
data	O
of	O
the	O
same	O
patient	O
taken	O
at	O
different	O
points	O
in	O
time	O
such	O
as	O
change	B-General_Concept
detection	I-General_Concept
or	O
tumor	O
monitoring	O
)	O
often	O
additionally	O
involves	O
elastic	O
(	O
also	O
known	O
as	O
nonrigid	O
)	O
registration	O
to	O
cope	O
with	O
deformation	O
of	O
the	O
subject	O
(	O
due	O
to	O
breathing	O
,	O
anatomical	O
changes	O
,	O
and	O
so	O
forth	O
)	O
.	O
</s>
<s>
Nonrigid	O
registration	O
of	O
medical	B-Application
images	I-Application
can	O
also	O
be	O
used	O
to	O
register	O
a	O
patient	O
's	O
data	O
to	O
an	O
anatomical	O
atlas	O
,	O
such	O
as	O
the	O
Talairach	O
atlas	O
for	O
neuroimaging	O
.	O
</s>
<s>
Using	O
control	B-Algorithm
points	I-Algorithm
(	O
automatically	O
or	O
manually	O
entered	O
)	O
,	O
the	O
computer	O
performs	O
transformations	O
on	O
one	O
image	O
to	O
make	O
major	O
features	O
align	O
with	O
a	O
second	O
or	O
multiple	O
images	O
.	O
</s>
<s>
In	O
cryo-TEM	O
instability	O
causes	O
specimen	O
drift	O
and	O
many	O
fast	O
acquisitions	O
with	O
accurate	O
image	B-Algorithm
registration	I-Algorithm
is	O
required	O
to	O
preserve	O
high	O
resolution	O
and	O
obtain	O
high	O
signal	O
to	O
noise	O
images	O
.	O
</s>
<s>
For	O
low	O
SNR	O
data	O
,	O
the	O
best	O
image	B-Algorithm
registration	I-Algorithm
is	O
achieved	O
by	O
cross-correlating	O
all	O
permutations	O
of	O
images	O
in	O
an	O
image	O
stack	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
is	O
an	O
essential	O
part	O
of	O
panoramic	O
image	O
creation	O
.	O
</s>
