<s>
In	O
image	B-Algorithm
processing	I-Algorithm
and	O
computer	B-Application
vision	I-Application
,	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
,	O
also	O
called	O
Perona	O
–	O
Malik	O
diffusion	O
,	O
is	O
a	O
technique	O
aiming	O
at	O
reducing	O
image	B-Algorithm
noise	I-Algorithm
without	O
removing	O
significant	O
parts	O
of	O
the	O
image	O
content	O
,	O
typically	O
edges	O
,	O
lines	O
or	O
other	O
details	O
that	O
are	O
important	O
for	O
the	O
interpretation	O
of	O
the	O
image	O
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
resembles	O
the	O
process	O
that	O
creates	O
a	O
scale	B-Algorithm
space	I-Algorithm
,	O
where	O
an	O
image	O
generates	O
a	O
parameterized	O
family	O
of	O
successively	O
more	O
and	O
more	O
blurred	O
images	O
based	O
on	O
a	O
diffusion	O
process	O
.	O
</s>
<s>
Each	O
of	O
the	O
resulting	O
images	O
in	O
this	O
family	O
are	O
given	O
as	O
a	O
convolution	B-Language
between	O
the	O
image	O
and	O
a	O
2D	O
isotropic	O
Gaussian	O
filter	O
,	O
where	O
the	O
width	O
of	O
the	O
filter	O
increases	O
with	O
the	O
parameter	O
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
is	O
a	O
generalization	O
of	O
this	O
diffusion	O
process	O
:	O
it	O
produces	O
a	O
family	O
of	O
parameterized	O
images	O
,	O
but	O
each	O
resulting	O
image	O
is	O
a	O
combination	O
between	O
the	O
original	O
image	O
and	O
a	O
filter	O
that	O
depends	O
on	O
the	O
local	O
content	O
of	O
the	O
original	O
image	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
is	O
a	O
non-linear	O
and	O
space-variant	O
transformation	O
of	O
the	O
original	O
image	O
.	O
</s>
<s>
In	O
its	O
original	O
formulation	O
,	O
presented	O
by	O
Perona	O
and	O
Malik	O
in	O
1987	O
,	O
the	O
space-variant	O
filter	O
is	O
in	O
fact	O
isotropic	O
but	O
depends	O
on	O
the	O
image	O
content	O
such	O
that	O
it	O
approximates	O
an	O
impulse	O
function	O
close	O
to	O
edges	O
and	O
other	O
structures	O
that	O
should	O
be	O
preserved	O
in	O
the	O
image	O
over	O
the	O
different	O
levels	O
of	O
the	O
resulting	O
scale	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
This	O
formulation	O
was	O
referred	O
to	O
as	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
by	O
Perona	O
and	O
Malik	O
even	O
though	O
the	O
locally	O
adapted	O
filter	O
is	O
isotropic	O
,	O
but	O
it	O
has	O
also	O
been	O
referred	O
to	O
as	O
inhomogeneous	O
and	O
nonlinear	O
diffusion	O
or	O
Perona	O
–	O
Malik	O
diffusion	O
by	O
other	O
authors	O
.	O
</s>
<s>
Such	O
methods	O
are	O
referred	O
to	O
as	O
shape-adapted	B-Algorithm
smoothing	I-Algorithm
or	O
coherence	O
enhancing	O
diffusion	O
.	O
</s>
<s>
Both	O
these	O
cases	O
can	O
be	O
described	O
by	O
a	O
generalization	O
of	O
the	O
usual	O
diffusion	O
equation	O
where	O
the	O
diffusion	O
coefficient	O
,	O
instead	O
of	O
being	O
a	O
constant	O
scalar	O
,	O
is	O
a	O
function	O
of	O
image	O
position	O
and	O
assumes	O
a	O
matrix	B-Architecture
(	O
or	O
tensor	B-Device
)	O
value	O
(	O
see	O
structure	B-Algorithm
tensor	I-Algorithm
)	O
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
is	O
normally	O
implemented	O
by	O
means	O
of	O
an	O
approximation	O
of	O
the	O
generalized	O
diffusion	O
equation	O
:	O
each	O
new	O
image	O
in	O
the	O
family	O
is	O
computed	O
by	O
applying	O
this	O
equation	O
to	O
the	O
previous	O
image	O
.	O
</s>
<s>
Consequently	O
,	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
is	O
an	O
iterative	B-Algorithm
process	O
where	O
a	O
relatively	O
simple	O
set	O
of	O
computation	O
are	O
used	O
to	O
compute	O
each	O
successive	O
image	O
in	O
the	O
family	O
and	O
this	O
process	O
is	O
continued	O
until	O
a	O
sufficient	O
degree	O
of	O
smoothing	O
is	O
obtained	O
.	O
</s>
<s>
where	O
denotes	O
the	O
Laplacian	O
,	O
denotes	O
the	O
gradient	O
,	O
is	O
the	O
divergence	B-Application
operator	O
and	O
is	O
the	O
diffusion	O
coefficient	O
.	O
</s>
<s>
Pietro	O
Perona	O
and	O
Jitendra	O
Malik	O
pioneered	O
the	O
idea	O
of	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
in	O
1990	O
and	O
proposed	O
two	O
functions	O
for	O
the	O
diffusion	O
coefficient	O
:	O
</s>
<s>
Thus	O
by	O
letting	O
the	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
equations	O
are	O
obtained	O
.	O
</s>
<s>
Anisotropic	B-Algorithm
diffusion	I-Algorithm
can	O
be	O
used	O
to	O
remove	O
noise	O
from	O
digital	O
images	O
without	O
blurring	O
edges	O
.	O
</s>
<s>
With	O
a	O
constant	O
diffusion	O
coefficient	O
,	O
the	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
equations	O
reduce	O
to	O
the	O
heat	O
equation	O
which	O
is	O
equivalent	O
to	O
Gaussian	O
blurring	O
.	O
</s>
<s>
Along	O
the	O
same	O
lines	O
as	O
noise	O
removal	O
,	O
anisotropic	B-Algorithm
diffusion	I-Algorithm
can	O
be	O
used	O
in	O
edge	B-Algorithm
detection	I-Algorithm
algorithms	O
.	O
</s>
<s>
By	O
running	O
the	O
diffusion	O
with	O
an	O
edge	O
seeking	O
diffusion	O
coefficient	O
for	O
a	O
certain	O
number	O
of	O
iterations	B-Algorithm
,	O
the	O
image	O
can	O
be	O
evolved	O
towards	O
a	O
piecewise	O
constant	O
image	O
with	O
the	O
boundaries	O
between	O
the	O
constant	O
components	O
being	O
detected	O
as	O
edges	O
.	O
</s>
