<s>
Thinning	B-Algorithm
is	O
the	O
transformation	O
of	O
a	O
digital	B-Algorithm
image	I-Algorithm
into	O
a	O
simplified	O
,	O
but	O
topologically	O
equivalent	O
image	O
.	O
</s>
<s>
It	O
is	O
a	O
type	O
of	O
topological	B-Algorithm
skeleton	I-Algorithm
,	O
but	O
computed	O
using	O
mathematical	B-Algorithm
morphology	I-Algorithm
operators	O
.	O
</s>
<s>
where	O
denotes	O
the	O
set-theoretical	O
difference	O
and	O
denotes	O
the	O
hit-or-miss	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
The	O
thinning	B-Algorithm
of	O
an	O
image	O
A	O
is	O
obtained	O
by	O
cyclically	O
iterating	O
until	O
convergence	O
:	O
</s>
<s>
Thickening	O
is	O
the	O
dual	O
of	O
thinning	B-Algorithm
that	O
is	O
used	O
to	O
grow	O
selected	O
regions	O
of	O
foreground	O
pixels	O
.	O
</s>
<s>
where	O
denotes	O
the	O
set-theoretical	O
difference	O
and	O
denotes	O
the	O
hit-or-miss	B-Algorithm
transform	I-Algorithm
,	O
and	O
is	O
the	O
structural	O
element	O
and	O
is	O
the	O
image	O
being	O
operated	O
on	O
.	O
</s>
