<s>
In	O
neuroimaging	B-Algorithm
,	O
spatial	B-Algorithm
normalization	I-Algorithm
is	O
an	O
image	B-Algorithm
processing	I-Algorithm
step	O
,	O
more	O
specifically	O
an	O
image	B-Algorithm
registration	I-Algorithm
method	O
.	O
</s>
<s>
Human	O
brains	O
differ	O
in	O
size	O
and	O
shape	O
,	O
and	O
one	O
goal	O
of	O
spatial	B-Algorithm
normalization	I-Algorithm
is	O
to	O
deform	O
human	O
brain	B-Algorithm
scans	I-Algorithm
so	O
one	O
location	O
in	O
one	O
subject	O
's	O
brain	B-Algorithm
scan	I-Algorithm
corresponds	O
to	O
the	O
same	O
location	O
in	O
another	O
subject	O
's	O
brain	B-Algorithm
scan	I-Algorithm
.	O
</s>
<s>
It	O
is	O
often	O
performed	O
in	O
research-based	O
functional	B-Algorithm
neuroimaging	I-Algorithm
where	O
one	O
wants	O
to	O
find	O
common	O
brain	O
activation	O
across	O
multiple	O
human	O
subjects	O
.	O
</s>
<s>
The	O
brain	B-Algorithm
scan	I-Algorithm
can	O
be	O
obtained	O
from	O
magnetic	O
resonance	O
imaging	O
(	O
MRI	O
)	O
or	O
positron	B-Application
emission	I-Application
tomography	I-Application
(	O
PET	O
)	O
scanners	O
.	O
</s>
<s>
There	O
are	O
two	O
steps	O
in	O
the	O
spatial	B-Algorithm
normalization	I-Algorithm
process	O
:	O
</s>
<s>
The	O
estimation	O
of	O
the	O
warp-field	O
can	O
be	O
performed	O
in	O
one	O
modality	O
,	O
e.g.	O
,	O
MRI	O
,	O
and	O
be	O
applied	O
in	O
another	O
modality	O
,	O
e.g.	O
,	O
PET	O
,	O
if	O
MRI	O
and	O
PET	B-Application
scans	I-Application
exist	O
for	O
the	O
same	O
subject	O
and	O
they	O
are	O
coregistered	B-Algorithm
.	O
</s>
<s>
Spatial	B-Algorithm
normalization	I-Algorithm
typically	O
employs	O
a	O
3-dimensional	O
nonrigid	O
transformation	O
model	O
(	O
a	O
"	O
warp-field	O
"	O
)	O
for	O
warping	O
a	O
brain	B-Algorithm
scan	I-Algorithm
to	O
a	O
template	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
diffeomorphic	O
flows	O
,	O
also	O
called	O
diffeomorphic	O
mapping	O
.	O
</s>
<s>
However	O
,	O
such	O
transformations	O
via	O
diffeomorphisms	O
are	O
not	O
additive	O
,	O
although	O
they	O
form	O
a	O
group	O
with	O
function	O
composition	O
and	O
acting	O
non-linearly	O
on	O
the	O
images	O
via	O
group	B-Algorithm
action	I-Algorithm
.	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>
