<s>
Boundary	B-Algorithm
tracing	I-Algorithm
,	O
also	O
known	O
as	O
contour	O
tracing	O
,	O
of	O
a	O
binary	O
digital	B-Algorithm
region	I-Algorithm
can	O
be	O
thought	O
of	O
as	O
a	B-Algorithm
segmentation	I-Algorithm
technique	I-Algorithm
that	O
identifies	O
the	O
boundary	O
pixels	O
of	O
the	O
digital	B-Algorithm
region	I-Algorithm
.	O
</s>
<s>
Boundary	B-Algorithm
tracing	I-Algorithm
is	O
an	O
important	O
first	O
step	O
in	O
the	B-General_Concept
analysis	I-General_Concept
of	I-General_Concept
that	I-General_Concept
region	I-General_Concept
.	O
</s>
<s>
However	O
,	O
a	O
digital	B-Algorithm
image	I-Algorithm
is	O
no	O
topological	O
space	O
.	O
</s>
<s>
Therefore	O
,	O
it	O
is	O
impossible	O
to	O
define	O
the	O
notion	O
of	O
a	O
boundary	O
in	O
a	O
digital	B-Algorithm
image	I-Algorithm
mathematically	O
exactly	O
.	O
</s>
<s>
Most	O
publications	O
about	O
tracing	O
the	O
boundary	O
of	O
a	O
subset	O
S	O
of	O
a	O
digital	B-Algorithm
image	I-Algorithm
I	O
describe	O
algorithms	O
which	O
find	O
a	O
set	O
of	O
pixels	O
belonging	O
to	O
S	O
and	O
having	O
in	O
their	O
direct	O
neighborhood	O
pixels	O
belonging	O
both	O
to	O
S	O
and	O
to	O
its	O
complement	O
I	O
-	O
S	O
.	O
According	O
to	O
this	O
definition	O
the	O
boundary	O
of	O
a	O
subset	O
S	O
is	O
different	O
from	O
the	O
boundary	O
of	O
the	O
complement	O
I	O
–	O
S	O
which	O
is	O
a	O
topological	O
paradox	O
.	O
</s>
<s>
To	O
define	O
the	O
boundary	O
correctly	O
it	O
is	O
necessary	O
to	O
introduce	O
a	O
topological	O
space	O
corresponding	O
to	O
the	O
given	O
digital	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
It	O
contains	O
cells	O
of	O
three	O
dimensions	O
:	O
the	O
two-dimensional	O
cells	O
corresponding	O
to	O
pixels	O
of	O
the	O
digital	B-Algorithm
image	I-Algorithm
,	O
the	O
one-dimensional	O
cells	O
or	O
“	O
cracks	O
”	O
representing	O
short	O
lines	O
lying	O
between	O
two	O
adjacent	O
pixels	O
,	O
and	O
the	O
zero-dimensional	O
cells	O
or	O
“	O
points	O
”	O
corresponding	O
to	O
the	O
corners	O
of	O
pixels	O
.	O
</s>
<s>
Algorithms	O
used	O
for	O
boundary	B-Algorithm
tracing	I-Algorithm
:	O
</s>
<s>
An	O
extension	O
of	O
boundary	B-Algorithm
tracing	I-Algorithm
for	O
segmentation	B-Algorithm
of	O
traced	O
boundary	O
into	O
open	O
and	O
closed	O
sub-section	O
is	O
described	O
at	O
.	O
</s>
