<s>
A	O
box	B-Algorithm
blur	I-Algorithm
(	O
also	O
known	O
as	O
a	O
box	O
linear	O
filter	O
)	O
is	O
a	O
spatial	O
domain	O
linear	O
filter	O
in	O
which	O
each	O
pixel	O
in	O
the	O
resulting	O
image	O
has	O
a	O
value	O
equal	O
to	O
the	O
average	O
value	O
of	O
its	O
neighboring	O
pixels	O
in	O
the	O
input	O
image	O
.	O
</s>
<s>
Box	B-Algorithm
blurs	I-Algorithm
are	O
frequently	O
used	O
to	O
approximate	O
a	O
Gaussian	B-Error_Name
blur	I-Error_Name
.	O
</s>
<s>
By	O
the	O
central	O
limit	O
theorem	O
,	O
repeated	O
application	O
of	O
a	O
box	B-Algorithm
blur	I-Algorithm
will	O
approximate	O
a	O
Gaussian	B-Error_Name
blur	I-Error_Name
.	O
</s>
<s>
In	O
the	O
frequency	O
domain	O
,	O
a	O
box	B-Algorithm
blur	I-Algorithm
has	O
zeros	O
and	O
negative	O
components	O
.	O
</s>
<s>
has	O
extended	O
Box	B-Algorithm
blur	I-Algorithm
to	O
take	O
a	O
fractional	O
radius	O
:	O
the	O
edges	O
of	O
the	O
1-D	O
filter	O
are	O
expanded	O
with	O
a	O
fraction	O
.	O
</s>
<s>
Mario	O
Klingemann	O
has	O
a	O
"	O
stack	O
blur	O
"	O
that	O
tries	O
to	O
better	O
emulate	O
gaussian	O
's	O
look	O
in	O
one	O
pass	O
by	O
stacking	O
weights	O
:	O
The	O
triangular	O
impulse	O
response	O
it	O
forms	O
decomposes	O
to	O
two	O
rounds	O
of	O
box	B-Algorithm
blur	I-Algorithm
.	O
</s>
<s>
Stacked	O
Integral	B-Algorithm
Image	I-Algorithm
by	O
Bhatia	O
et	O
al	O
.	O
</s>
<s>
takes	O
the	O
weighted	O
average	O
of	O
a	O
few	O
box	B-Algorithm
blurs	I-Algorithm
to	O
fit	O
the	O
gaussian	O
response	O
curve	O
.	O
</s>
<s>
The	O
following	O
pseudocode	O
implements	O
a	O
3x3	O
box	B-Algorithm
blur	I-Algorithm
.	O
</s>
<s>
A	O
number	O
of	O
optimizations	O
can	O
be	O
applied	O
when	O
implementing	O
the	O
box	B-Algorithm
blur	I-Algorithm
of	O
a	O
radius	O
r	O
and	O
N	O
pixels	O
:	O
</s>
<s>
The	O
box	B-Algorithm
blur	I-Algorithm
is	O
a	O
separable	B-Algorithm
filter	I-Algorithm
,	O
so	O
that	O
only	O
two	O
1D	O
passes	O
of	O
averaging	O
pixels	O
will	O
be	O
needed	O
,	O
one	O
horizontal	O
and	O
one	O
vertical	O
,	O
for	O
each	O
pixel	O
.	O
</s>
<s>
A	O
summed-area	B-Algorithm
table	I-Algorithm
can	O
be	O
used	O
similarly	O
.	O
</s>
<s>
When	O
being	O
used	O
in	O
multiple	O
passes	O
to	O
approximate	O
a	O
Gaussian	B-Error_Name
blur	I-Error_Name
,	O
the	O
cascaded	O
integrator	O
–	O
comb	O
filter	O
construction	O
allows	O
for	O
doing	O
the	O
equivalent	O
operation	O
in	O
a	O
single	O
pass	O
.	O
</s>
