<s>
A	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
or	O
co-occurrence	O
distribution	O
(	O
also	O
referred	O
to	O
as	O
:	O
gray-level	O
co-occurrence	O
matrices	O
GLCMs	O
)	O
is	O
a	O
matrix	B-Architecture
that	O
is	O
defined	O
over	O
an	O
image	B-Algorithm
to	O
be	O
the	O
distribution	O
of	O
co-occurring	O
pixel	B-Algorithm
values	O
(	O
grayscale	O
values	O
,	O
or	O
colors	O
)	O
at	O
a	O
given	O
offset	O
.	O
</s>
<s>
It	O
is	O
used	O
as	O
an	O
approach	O
to	O
texture	O
analysis	O
with	O
various	O
applications	O
especially	O
in	O
medical	O
image	B-Algorithm
analysis	O
.	O
</s>
<s>
Given	O
a	O
grey-level	O
image	B-Algorithm
,	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
computes	O
how	O
often	O
pairs	O
of	O
pixels	B-Algorithm
with	O
a	O
specific	O
value	O
and	O
offset	O
occur	O
in	O
the	O
image	B-Algorithm
.	O
</s>
<s>
The	O
offset	O
,	O
,	O
is	O
a	O
position	O
operator	O
that	O
can	O
be	O
applied	O
to	O
any	O
pixel	B-Algorithm
in	O
the	O
image	B-Algorithm
(	O
ignoring	O
edge	O
effects	O
)	O
:	O
for	O
instance	O
,	O
could	O
indicate	O
"	O
one	O
down	O
,	O
two	O
right	O
"	O
.	O
</s>
<s>
An	O
image	B-Algorithm
with	O
different	O
pixel	B-Algorithm
values	O
will	O
produce	O
a	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
,	O
for	O
the	O
given	O
offset	O
.	O
</s>
<s>
The	O
value	O
of	O
the	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
gives	O
the	O
number	O
of	O
times	O
in	O
the	O
image	B-Algorithm
that	O
the	O
and	O
pixel	B-Algorithm
values	O
occur	O
in	O
the	O
relation	O
given	O
by	O
the	O
offset	O
.	O
</s>
<s>
For	O
an	O
image	B-Algorithm
with	O
different	O
pixel	B-Algorithm
values	O
,	O
the	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
C	O
is	O
defined	O
over	O
an	O
image	B-Algorithm
,	O
parameterized	O
by	O
an	O
offset	O
,	O
as	O
:	O
</s>
<s>
where	O
:	O
and	O
are	O
the	O
pixel	B-Algorithm
values	O
;	O
and	O
are	O
the	O
spatial	O
positions	O
in	O
the	O
image	B-Algorithm
I	O
;	O
the	O
offsets	O
define	O
the	O
spatial	O
relation	O
for	O
which	O
this	O
matrix	B-Architecture
is	O
calculated	O
;	O
and	O
indicates	O
the	O
pixel	B-Algorithm
value	O
at	O
pixel	B-Algorithm
.	O
</s>
<s>
The	O
'	O
value	O
 '	O
of	O
the	O
image	B-Algorithm
originally	O
referred	O
to	O
the	O
grayscale	O
value	O
of	O
the	O
specified	O
pixel	B-Algorithm
,	O
but	O
could	O
be	O
anything	O
,	O
from	O
a	O
binary	O
on/off	O
value	O
to	O
32-bit	O
color	O
and	O
beyond	O
.	O
</s>
<s>
(	O
Note	O
that	O
32-bit	O
color	O
will	O
yield	O
a	O
232×232	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
!	O
)	O
</s>
<s>
Any	O
matrix	B-Architecture
or	O
pair	O
of	O
matrices	O
can	O
be	O
used	O
to	O
generate	O
a	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
,	O
though	O
their	O
most	O
common	O
application	O
has	O
been	O
in	O
measuring	O
texture	O
in	O
images	O
,	O
so	O
the	O
typical	O
definition	O
,	O
as	O
above	O
,	O
assumes	O
that	O
the	O
matrix	B-Architecture
is	O
an	O
image	B-Algorithm
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
to	O
define	O
the	O
matrix	B-Architecture
across	O
two	O
different	O
images	O
.	O
</s>
<s>
Such	O
a	O
matrix	B-Architecture
can	O
then	O
be	O
used	O
for	O
color	B-Algorithm
mapping	I-Algorithm
.	O
</s>
<s>
Whether	O
considering	O
the	O
intensity	O
or	O
grayscale	O
values	O
of	O
the	O
image	B-Algorithm
or	O
various	O
dimensions	O
of	O
color	O
,	O
the	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
can	O
measure	O
the	O
texture	O
of	O
the	O
image	B-Algorithm
.	O
</s>
<s>
Because	O
co-occurrence	O
matrices	O
are	O
typically	O
large	O
and	O
sparse	O
,	O
various	O
metrics	O
of	O
the	O
matrix	B-Architecture
are	O
often	O
taken	O
to	O
get	O
a	O
more	O
useful	O
set	O
of	O
features	O
.	O
</s>
<s>
Texture	O
analysis	O
is	O
often	O
concerned	O
with	O
detecting	O
aspects	O
of	O
an	O
image	B-Algorithm
that	O
are	O
rotationally	O
invariant	O
.	O
</s>
<s>
Texture	O
measures	O
like	O
the	O
co-occurrence	B-Algorithm
matrix	I-Algorithm
,	O
wavelet	B-Algorithm
transforms	I-Algorithm
,	O
and	O
model	B-Algorithm
fitting	I-Algorithm
have	O
found	O
application	O
in	O
medical	O
image	B-Algorithm
analysis	O
in	O
particular	O
.	O
</s>
<s>
Co-occurrence	O
matrices	O
are	O
also	O
used	O
for	O
words	O
processing	O
in	O
natural	B-Language
language	I-Language
processing	I-Language
(	O
NLP	B-Language
)	O
.	O
</s>
