<s>
A	O
bilateral	B-Algorithm
filter	I-Algorithm
is	O
a	O
non-linear	O
,	O
edge-preserving	B-Algorithm
,	O
and	O
noise-reducing	O
smoothing	B-Application
filter	B-Algorithm
for	I-Algorithm
images	I-Algorithm
.	O
</s>
<s>
is	O
the	O
range	O
kernel	O
for	O
smoothing	B-Application
differences	O
in	O
intensities	O
(	O
this	O
function	O
can	O
be	O
a	O
Gaussian	O
function	O
)	O
;	O
</s>
<s>
is	O
the	O
spatial	O
(	O
or	O
domain	O
)	O
kernel	O
for	O
smoothing	B-Application
differences	O
in	O
coordinates	O
(	O
this	O
function	O
can	O
be	O
a	O
Gaussian	O
function	O
)	O
.	O
</s>
<s>
where	O
σd	O
and	O
σr	O
are	O
smoothing	B-Application
parameters	O
,	O
and	O
I(i, j )	O
and	O
I(k, l )	O
are	O
the	O
intensity	O
of	O
pixels	O
and	O
respectively	O
.	O
</s>
<s>
As	O
the	O
range	O
parameter	O
σr	O
increases	O
,	O
the	O
bilateral	B-Algorithm
filter	I-Algorithm
gradually	O
approaches	O
Gaussian	O
convolution	B-Language
more	O
closely	O
because	O
the	O
range	O
Gaussian	O
widens	O
and	O
flattens	O
,	O
which	O
means	O
that	O
it	O
becomes	O
nearly	O
constant	O
over	O
the	O
intensity	O
interval	O
of	O
the	O
image	O
.	O
</s>
<s>
The	O
bilateral	B-Algorithm
filter	I-Algorithm
in	O
its	O
direct	O
form	O
can	O
introduce	O
several	O
types	O
of	O
image	O
artifacts	O
:	O
</s>
<s>
There	O
exist	O
several	O
extensions	O
to	O
the	O
filter	O
that	O
deal	O
with	O
these	O
artifacts	O
,	O
like	O
the	O
scaled	O
bilateral	B-Algorithm
filter	I-Algorithm
that	O
uses	O
downscaled	O
image	O
for	O
computing	O
the	O
weights	O
.	O
</s>
<s>
Adobe	B-Operating_System
Photoshop	I-Operating_System
implements	O
a	O
bilateral	B-Algorithm
filter	I-Algorithm
in	O
its	O
surface	O
blur	O
tool	O
.	O
</s>
<s>
GIMP	B-Application
implements	O
a	O
bilateral	B-Algorithm
filter	I-Algorithm
in	O
its	O
Filters	O
→	O
Blur	O
tools	O
;	O
and	O
it	O
is	O
called	O
Selective	O
Gaussian	B-Error_Name
Blur	I-Error_Name
.	O
</s>
<s>
The	O
free	O
G'MIC	B-Language
plugin	O
Repair	O
→	O
Smooth	O
 [ bilateral ] 	O
for	O
GIMP	B-Application
adds	O
more	O
control	O
.	O
</s>
<s>
A	O
simple	O
trick	O
to	O
efficiently	O
implement	O
a	O
bilateral	B-Algorithm
filter	I-Algorithm
is	O
to	O
exploit	O
Poisson-disk	O
subsampling	O
.	O
</s>
<s>
that	O
was	O
introduced	O
as	O
an	O
edge	O
preserving	O
selective	O
smoothing	B-Application
mechanism	O
before	O
the	O
bilateral	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Other	O
edge-preserving	B-Algorithm
smoothing	I-Algorithm
filters	O
include	O
:	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
,	O
weighted	O
least	O
squares	O
,	O
edge-avoiding	O
wavelets	O
,	O
geodesic	O
editing	O
,	O
guided	O
filtering	O
,	O
iterative	O
guided	O
filtering	O
and	O
domain	O
transforms	O
.	O
</s>
