<s>
The	O
point	B-General_Concept
distribution	I-General_Concept
model	I-General_Concept
is	O
a	O
model	O
for	O
representing	O
the	O
mean	O
geometry	O
of	O
a	O
shape	O
and	O
some	O
statistical	O
modes	O
of	O
geometric	O
variation	O
inferred	O
from	O
a	O
training	O
set	O
of	O
shapes	O
.	O
</s>
<s>
The	O
point	B-General_Concept
distribution	I-General_Concept
model	I-General_Concept
concept	O
has	O
been	O
developed	O
by	O
Cootes	O
,	O
Taylor	O
et	O
al	O
.	O
</s>
<s>
and	O
became	O
a	O
standard	O
in	O
computer	B-Application
vision	I-Application
for	O
the	O
statistical	O
study	O
of	O
shape	O
and	O
for	O
segmentation	B-Algorithm
of	O
medical	B-Application
images	I-Application
where	O
shape	O
priors	O
really	O
help	O
interpretation	O
of	O
noisy	O
and	O
low-contrasted	O
pixels/voxels	O
.	O
</s>
<s>
The	O
latter	O
point	O
leads	O
to	O
active	B-General_Concept
shape	I-General_Concept
models	I-General_Concept
(	O
ASM	O
)	O
and	O
active	B-General_Concept
appearance	I-General_Concept
models	I-General_Concept
(	O
AAM	O
)	O
.	O
</s>
<s>
Point	B-General_Concept
distribution	I-General_Concept
models	I-General_Concept
rely	O
on	O
landmark	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
Principal	B-Application
component	I-Application
analysis	I-Application
(	O
PCA	O
)	O
,	O
for	O
instance	O
,	O
is	O
a	O
relevant	O
tool	O
for	O
studying	O
correlations	O
of	O
movement	O
between	O
groups	O
of	O
landmarks	O
among	O
the	O
training	O
set	O
population	O
.	O
</s>
<s>
These	O
landmarks	O
are	O
aligned	O
using	O
the	O
generalized	B-Algorithm
procrustes	I-Algorithm
analysis	I-Algorithm
,	O
which	O
minimizes	O
the	O
least	O
squared	O
error	O
between	O
the	O
points	O
.	O
</s>
<s>
where	O
is	O
defined	O
as	O
the	O
mean	O
shape	O
across	O
all	O
training	O
images	O
,	O
and	O
is	O
a	O
vector	O
of	O
scaling	O
values	O
for	O
each	O
principal	B-Application
component	I-Application
.	O
</s>
<s>
To	O
ensure	O
that	O
the	O
new	O
shapes	O
are	O
all	O
within	O
the	O
variation	O
seen	O
in	O
the	O
training	O
set	O
,	O
it	O
is	O
common	O
to	O
only	O
allow	O
each	O
element	O
of	O
to	O
be	O
within	O
3	O
standard	O
deviations	O
,	O
where	O
the	O
standard	O
deviation	O
of	O
a	O
given	O
principal	B-Application
component	I-Application
is	O
defined	O
as	O
the	O
square	O
root	O
of	O
its	O
corresponding	O
eigenvalue	O
.	O
</s>
<s>
PDM	O
's	O
can	O
be	O
extended	O
to	O
any	O
arbitrary	O
number	O
of	O
dimensions	O
,	O
but	O
are	O
typically	O
used	O
in	O
2D	O
image	O
and	O
3D	O
volume	O
applications	O
(	O
where	O
each	O
landmark	B-General_Concept
point	I-General_Concept
is	O
or	O
)	O
.	O
</s>
