<s>
In	O
imaging	O
science	O
,	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
(	O
DoG	O
)	O
is	O
a	O
feature	B-Algorithm
enhancement	O
algorithm	O
that	O
involves	O
the	O
subtraction	O
of	O
one	O
Gaussian	B-Error_Name
blurred	I-Error_Name
version	O
of	O
an	O
original	O
image	O
from	O
another	O
,	O
less	O
blurred	O
version	O
of	O
the	O
original	O
.	O
</s>
<s>
In	O
the	O
simple	O
case	O
of	O
grayscale	O
images	O
,	O
the	O
blurred	O
images	O
are	O
obtained	O
by	O
convolving	B-Language
the	O
original	O
grayscale	O
images	O
with	O
Gaussian	O
kernels	O
having	O
differing	O
width	O
(	O
standard	O
deviations	O
)	O
.	O
</s>
<s>
obtained	O
by	O
subtracting	O
the	O
image	O
convolved	B-Language
with	O
the	O
Gaussian	O
of	O
variance	O
from	O
the	O
image	O
convolved	B-Language
with	O
a	O
Gaussian	O
of	O
narrower	O
variance	O
,	O
with	O
.	O
</s>
<s>
which	O
represents	O
an	O
image	O
convolved	B-Language
by	O
the	O
difference	O
of	O
two	O
Gaussians	O
,	O
which	O
approximates	O
a	O
Mexican	O
hat	O
function	O
.	O
</s>
<s>
The	O
relation	O
between	O
the	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
operator	O
and	O
the	O
Laplacian	O
of	O
the	O
Gaussian	O
operator	O
(	O
the	O
Mexican	O
hat	O
wavelet	O
)	O
is	O
explained	O
in	O
appendix	O
A	O
in	O
Lindeberg	O
(	O
2015	O
)	O
.	O
</s>
<s>
As	O
a	O
feature	B-Algorithm
enhancement	O
algorithm	O
,	O
the	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
can	O
be	O
utilized	O
to	O
increase	O
the	O
visibility	O
of	O
edges	O
and	O
other	O
detail	O
present	O
in	O
a	O
digital	O
image	O
.	O
</s>
<s>
A	O
wide	O
variety	O
of	O
alternative	O
edge	B-Algorithm
sharpening	I-Algorithm
filters	I-Algorithm
operate	O
by	O
enhancing	O
high	O
frequency	O
detail	O
,	O
but	O
because	O
random	O
noise	O
also	O
has	O
a	O
high	O
spatial	O
frequency	O
,	O
many	O
of	O
these	O
sharpening	O
filters	O
tend	O
to	O
enhance	O
noise	O
,	O
which	O
can	O
be	O
an	O
undesirable	O
artifact	O
.	O
</s>
<s>
The	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
algorithm	O
removes	O
high	O
frequency	O
detail	O
that	O
often	O
includes	O
random	O
noise	O
,	O
rendering	O
this	O
approach	O
one	O
of	O
the	O
most	O
suitable	O
for	O
processing	O
images	O
with	O
a	O
high	O
degree	O
of	O
noise	O
.	O
</s>
<s>
When	O
utilized	O
for	O
image	O
enhancement	O
,	O
the	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
algorithm	O
is	O
typically	O
applied	O
when	O
the	O
size	O
ratio	O
of	O
kernel	O
(	O
2	O
)	O
to	O
kernel	O
(	O
1	O
)	O
is	O
4:1	O
or	O
5:1	O
.	O
</s>
<s>
Differences	O
of	O
Gaussians	O
have	O
also	O
been	O
used	O
for	O
blob	B-Algorithm
detection	I-Algorithm
in	O
the	O
scale-invariant	B-Algorithm
feature	I-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
In	O
fact	O
,	O
the	O
DoG	O
as	O
the	O
difference	O
of	O
two	O
Multivariate	O
normal	O
distribution	O
has	O
always	O
a	O
total	O
null	O
sum	O
and	O
convolving	B-Language
it	O
with	O
a	O
uniform	O
signal	O
generates	O
no	O
response	O
.	O
</s>
<s>
It	O
may	O
easily	O
be	O
used	O
in	O
recursive	O
schemes	O
and	O
is	O
used	O
as	O
an	O
operator	O
in	O
real-time	O
algorithms	O
for	O
blob	B-Algorithm
detection	I-Algorithm
and	O
automatic	O
scale	O
selection	O
.	O
</s>
<s>
In	O
its	O
operation	O
,	O
the	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
algorithm	O
is	O
believed	O
to	O
mimic	O
how	O
neural	O
processing	O
in	O
the	O
retina	O
of	O
the	O
eye	O
extracts	O
details	O
from	O
images	O
destined	O
for	O
transmission	O
to	O
the	O
brain	O
.	O
</s>
