<s>
Edge-preserving	B-Algorithm
smoothing	I-Algorithm
or	O
edge-preserving	B-Algorithm
filtering	I-Algorithm
is	O
an	O
image	B-Algorithm
processing	I-Algorithm
technique	O
that	O
smooths	O
away	O
noise	O
or	O
textures	O
while	O
retaining	O
sharp	O
edges	O
.	O
</s>
<s>
Examples	O
are	O
the	O
median	B-Algorithm
,	O
bilateral	B-Algorithm
,	O
guided	B-Algorithm
,	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
,	O
and	O
Kuwahara	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
the	O
motivation	O
for	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
(	O
also	O
called	O
nonuniform	O
or	O
variable	O
conductance	O
diffusion	O
)	O
is	O
that	O
a	O
Gaussian	O
smoothed	O
image	O
is	O
a	O
single	O
time	O
slice	O
of	O
the	O
solution	O
to	O
the	O
heat	O
equation	O
,	O
that	O
has	O
the	O
original	O
image	O
as	O
its	O
initial	O
conditions	O
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
includes	O
a	O
variable	O
conductance	O
term	O
that	O
is	O
determined	O
using	O
the	O
differential	O
structure	O
of	O
the	O
image	O
,	O
such	O
that	O
the	O
heat	O
does	O
not	O
propagate	O
over	O
the	O
edges	O
of	O
the	O
image	O
.	O
</s>
<s>
The	O
edge-preserving	O
filters	O
can	O
conveniently	O
be	O
formulated	O
in	O
a	O
general	O
context	O
of	O
graph-based	O
signal	O
processing	O
,	O
where	O
the	O
graph	O
adjacency	B-Algorithm
matrix	I-Algorithm
is	O
first	O
determined	O
using	O
the	O
differential	O
structure	O
of	O
the	O
image	O
,	O
then	O
the	O
graph	B-Algorithm
Laplacian	I-Algorithm
is	O
formulated	O
(	O
analogous	O
to	O
the	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
operator	O
)	O
,	O
and	O
finally	O
the	O
approximate	O
low-pass	O
filter	O
is	O
constructed	O
to	O
amplify	O
the	O
eigenvectors	O
of	O
the	O
graph	B-Algorithm
Laplacian	I-Algorithm
corresponding	O
to	O
its	O
smallest	O
eigenvalues	O
.	O
</s>
<s>
A	O
repetitive	O
application	O
of	O
the	O
filter	O
may	O
be	O
useful	O
to	O
reduce	O
the	O
noise	O
,	O
leading	O
to	O
the	O
idea	O
of	O
combining	O
the	O
filter	O
with	O
an	O
iterative	B-Algorithm
method	I-Algorithm
,	O
e.g.	O
,	O
the	O
Chebyshev	B-Algorithm
iteration	I-Algorithm
and	O
the	O
conjugate	B-Algorithm
gradient	I-Algorithm
method	I-Algorithm
are	O
proposed	O
in	O
for	O
graph-based	O
image	O
denoising	O
.	O
</s>
<s>
Due	O
to	O
the	O
interpretation	O
of	O
the	O
edge-preserving	O
filters	O
as	O
low-pass	O
graph-based	O
filters	O
,	O
iterative	O
eigenvalue	O
solvers	O
,	O
such	O
as	O
LOBPCG	B-Application
,	O
can	O
be	O
used	O
for	O
denoising	O
;	O
see	O
,	O
e.g.	O
,	O
to	O
accelerate	O
the	O
repeated	O
application	O
of	O
the	O
total	B-Algorithm
variation	I-Algorithm
denoising	I-Algorithm
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
generates	O
small	O
conductance	O
at	O
the	O
location	O
of	O
the	O
edge	O
of	O
the	O
image	O
to	O
prevent	O
the	O
heat	O
flow	O
over	O
the	O
edge	O
,	O
thus	O
making	O
the	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
filter	O
edge-preserving	O
.	O
</s>
<s>
Signal	O
upsampling	B-Algorithm
via	O
the	O
traditional	O
interpolation	O
followed	O
by	O
smoothing	O
for	O
denoising	O
evidently	O
distorts	O
the	O
edges	O
in	O
the	O
original	O
ideal	O
or	O
downsampled	O
signal	O
.	O
</s>
<s>
The	O
edge-preserving	O
interpolation	O
followed	O
by	O
the	O
edge-preserving	O
filters	O
is	O
proposed	O
in	O
e.g.	O
,	O
to	O
upsample	B-Algorithm
a	O
no-flash	O
RGB	O
photo	O
guided	B-Algorithm
using	O
a	O
high	O
resolution	O
flash	O
RGB	O
photo	O
,	O
and	O
a	O
depth	O
image	O
guided	B-Algorithm
using	O
a	O
high	O
resolution	O
RGB	O
photo	O
.	O
</s>
