<s>
In	O
mathematical	B-Algorithm
morphology	I-Algorithm
,	O
a	O
structuring	B-Algorithm
element	I-Algorithm
is	O
a	O
shape	O
,	O
used	O
to	O
probe	O
or	O
interact	O
with	O
a	O
given	O
image	O
,	O
with	O
the	O
purpose	O
of	O
drawing	O
conclusions	O
on	O
how	O
this	O
shape	O
fits	O
or	O
misses	O
the	O
shapes	O
in	O
the	O
image	O
.	O
</s>
<s>
It	O
is	O
typically	O
used	O
in	O
morphological	B-Algorithm
operations	I-Algorithm
,	O
such	O
as	O
dilation	B-Algorithm
,	O
erosion	B-Algorithm
,	O
opening	B-Algorithm
,	O
and	O
closing	B-Algorithm
,	O
as	O
well	O
as	O
the	O
hit-or-miss	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
choice	O
of	O
a	O
certain	O
structuring	B-Algorithm
element	I-Algorithm
for	O
a	O
particular	O
morphological	O
operation	O
influences	O
the	O
information	O
one	O
can	O
obtain	O
.	O
</s>
<s>
There	O
are	O
two	O
main	O
characteristics	O
that	O
are	O
directly	O
related	O
to	O
structuring	B-Algorithm
elements	I-Algorithm
:	O
</s>
<s>
For	O
example	O
,	O
the	O
structuring	B-Algorithm
element	I-Algorithm
can	O
be	O
a	O
"	O
ball	O
"	O
or	O
a	O
line	O
;	O
convex	O
or	O
a	O
ring	O
,	O
etc	O
.	O
</s>
<s>
By	O
choosing	O
a	O
particular	O
structuring	B-Algorithm
element	I-Algorithm
,	O
one	O
sets	O
a	O
way	O
of	O
differentiating	O
some	O
objects	O
(	O
or	O
parts	O
of	O
objects	O
)	O
from	O
others	O
,	O
according	O
to	O
their	O
shape	O
or	O
spatial	O
orientation	O
.	O
</s>
<s>
For	O
example	O
,	O
one	O
structuring	B-Algorithm
element	I-Algorithm
can	O
be	O
a	O
square	O
or	O
a	O
square	O
.	O
</s>
<s>
Setting	O
the	O
size	O
of	O
the	O
structuring	B-Algorithm
element	I-Algorithm
is	O
similar	O
to	O
setting	O
the	O
observation	O
scale	O
,	O
and	O
setting	O
the	O
criterion	O
to	O
differentiate	O
image	O
objects	O
or	O
features	O
according	O
to	O
size	O
.	O
</s>
<s>
Structuring	B-Algorithm
elements	I-Algorithm
are	O
particular	O
cases	O
of	O
binary	B-Algorithm
images	I-Algorithm
,	O
usually	O
being	O
small	O
and	O
simple	O
.	O
</s>
<s>
In	O
mathematical	B-Algorithm
morphology	I-Algorithm
,	O
binary	B-Algorithm
images	I-Algorithm
are	O
subsets	O
of	O
a	O
Euclidean	O
space	O
Rd	O
or	O
the	O
integer	O
grid	O
Zd	O
,	O
for	O
some	O
dimension	O
d	O
.	O
Here	O
are	O
some	O
examples	O
of	O
widely	O
used	O
structuring	B-Algorithm
elements	I-Algorithm
(	O
denoted	O
by	O
B	O
)	O
:	O
</s>
<s>
In	O
the	O
discrete	O
case	O
,	O
a	O
structuring	B-Algorithm
element	I-Algorithm
can	O
also	O
be	O
represented	O
as	O
a	O
set	O
of	O
pixels	B-Algorithm
on	O
a	O
grid	O
,	O
assuming	O
the	O
values	O
1	O
(	O
if	O
the	O
pixel	B-Algorithm
belongs	O
to	O
the	O
structuring	B-Algorithm
element	I-Algorithm
)	O
or	O
0	O
(	O
otherwise	O
)	O
.	O
</s>
<s>
When	O
used	O
by	O
a	O
hit-or-miss	B-Algorithm
transform	I-Algorithm
,	O
usually	O
the	O
structuring	B-Algorithm
element	I-Algorithm
is	O
a	O
composite	O
of	O
two	O
disjoint	O
sets	O
(	O
two	O
simple	O
structuring	B-Algorithm
elements	I-Algorithm
)	O
,	O
one	O
associated	O
to	O
the	O
foreground	O
,	O
and	O
one	O
associated	O
to	O
the	O
background	O
of	O
the	O
image	O
to	O
be	O
probed	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
an	O
alternative	O
representation	O
of	O
the	O
composite	O
structuring	B-Algorithm
element	I-Algorithm
is	O
as	O
a	O
set	O
of	O
pixels	B-Algorithm
which	O
are	O
either	O
set	O
(	O
1	O
,	O
associated	O
to	O
the	O
foreground	O
)	O
,	O
not	O
set	O
(	O
0	O
,	O
associated	O
to	O
the	O
background	O
)	O
or	O
"	O
do	O
n't	O
care	O
"	O
.	O
</s>
