<s>
In	O
digital	B-Algorithm
image	I-Algorithm
processing	I-Algorithm
,	O
morphological	B-Algorithm
skeleton	I-Algorithm
is	O
a	O
skeleton	B-Algorithm
(	O
or	O
medial	O
axis	O
)	O
representation	O
of	O
a	O
shape	O
or	O
binary	B-Algorithm
image	I-Algorithm
,	O
computed	O
by	O
means	O
of	O
morphological	B-Algorithm
operators	I-Algorithm
.	O
</s>
<s>
Morphological	B-Algorithm
skeletons	I-Algorithm
are	O
of	O
two	O
kinds	O
:	O
</s>
<s>
Those	O
computed	O
by	O
means	O
of	O
the	O
hit-or-miss	B-Algorithm
transform	I-Algorithm
,	O
which	O
preserve	O
the	O
shape	O
's	O
topology	B-Architecture
.	O
</s>
<s>
In	O
(	O
Lantuéjoul	O
1977	O
)	O
,	O
Lantuéjoul	O
derived	O
the	O
following	O
morphological	O
formula	O
for	O
the	O
skeleton	B-Algorithm
of	O
a	O
continuous	O
binary	B-Algorithm
image	I-Algorithm
:	O
</s>
<s>
where	O
and	O
are	O
the	O
morphological	B-Algorithm
erosion	I-Algorithm
and	O
opening	B-Algorithm
,	O
respectively	O
,	O
is	O
an	O
open	O
ball	O
of	O
radius	B-Protocol
,	O
and	O
is	O
the	O
closure	O
of	O
.	O
</s>
<s>
Let	O
,	O
,	O
be	O
a	O
family	O
of	O
shapes	O
,	O
where	O
B	O
is	O
a	O
structuring	B-Algorithm
element	I-Algorithm
,	O
</s>
<s>
The	O
variable	O
n	O
is	O
called	O
the	O
size	O
of	O
the	O
structuring	B-Algorithm
element	I-Algorithm
.	O
</s>
<s>
For	O
a	O
discrete	O
binary	B-Algorithm
image	I-Algorithm
,	O
the	O
skeleton	B-Algorithm
S(X )	O
is	O
the	O
union	O
of	O
the	O
skeleton	B-Algorithm
subsets	O
,	O
,	O
where	O
:	O
</s>
<s>
The	O
original	O
shape	O
X	O
can	O
be	O
reconstructed	O
from	O
the	O
set	O
of	O
skeleton	B-Algorithm
subsets	O
as	O
follows	O
:	O
</s>
<s>
Each	O
skeleton	B-Algorithm
subset	O
consists	O
of	O
the	O
centers	O
of	O
all	O
maximal	O
disks	O
of	O
size	O
n	O
.	O
</s>
<s>
Morphological	O
Skeletonization	O
can	O
be	O
considered	O
as	O
a	O
controlled	O
erosion	B-Algorithm
process	O
.	O
</s>
<s>
This	O
can	O
allow	O
quick	O
and	O
accurate	O
image	B-Algorithm
processing	I-Algorithm
on	O
an	O
otherwise	O
large	O
and	O
memory	O
intensive	O
operation	O
.	O
</s>
<s>
The	O
image	O
to	O
the	O
right	O
shows	O
the	O
extent	O
of	O
what	O
skeleton	B-Algorithm
morphology	O
can	O
accomplish	O
.	O
</s>
