<s>
In	O
digital	B-General_Concept
signal	I-General_Concept
processing	I-General_Concept
,	O
spatial	B-Algorithm
anti-aliasing	I-Algorithm
is	O
a	O
technique	O
for	O
minimizing	O
the	O
distortion	O
artifacts	O
(	O
aliasing	B-Error_Name
)	O
when	O
representing	O
a	O
high-resolution	B-Algorithm
image	O
at	O
a	O
lower	O
resolution	B-Algorithm
.	O
</s>
<s>
Anti-aliasing	O
is	O
used	O
in	O
digital	B-Application
photography	I-Application
,	O
computer	O
graphics	O
,	O
digital	O
audio	O
,	O
and	O
many	O
other	O
applications	O
.	O
</s>
<s>
Anti-aliasing	O
means	O
removing	O
signal	O
components	O
that	O
have	O
a	O
higher	O
frequency	O
than	O
is	O
able	O
to	O
be	O
properly	O
resolved	O
by	O
the	O
recording	O
(	O
or	O
sampling	O
)	O
device	O
.	O
</s>
<s>
This	O
removal	O
is	O
done	O
before	O
(	O
re	O
)	O
sampling	O
at	O
a	O
lower	O
resolution	B-Algorithm
.	O
</s>
<s>
In	O
signal	O
acquisition	O
and	O
audio	O
,	O
anti-aliasing	O
is	O
often	O
done	O
using	O
an	O
analog	O
anti-aliasing	O
filter	O
to	O
remove	O
the	O
out-of-band	O
component	O
of	O
the	O
input	O
signal	O
prior	O
to	O
sampling	O
with	O
an	O
analog-to-digital	O
converter	O
.	O
</s>
<s>
In	O
digital	B-Application
photography	I-Application
,	O
optical	O
anti-aliasing	O
filters	O
made	O
of	O
birefringent	O
materials	O
smooth	O
the	O
signal	O
in	O
the	O
spatial	O
optical	O
domain	O
.	O
</s>
<s>
The	O
anti-aliasing	O
filter	O
essentially	O
blurs	O
the	O
image	O
slightly	O
in	O
order	O
to	O
reduce	O
the	O
resolution	B-Algorithm
to	O
or	O
below	O
that	O
achievable	O
by	O
the	O
digital	O
sensor	O
(	O
the	O
larger	O
the	O
pixel	B-Algorithm
pitch	O
,	O
the	O
lower	O
the	O
achievable	O
resolution	B-Algorithm
at	O
the	O
sensor	O
level	O
)	O
.	O
</s>
<s>
In	O
computer	O
graphics	O
,	O
anti-aliasing	O
improves	O
the	O
appearance	O
of	O
"	O
jagged	O
"	O
polygon	O
edges	O
,	O
or	O
"	O
jaggies	B-Algorithm
"	O
,	O
so	O
they	O
are	O
smoothed	O
out	O
on	O
the	O
screen	O
.	O
</s>
<s>
However	O
,	O
it	O
incurs	O
a	O
performance	O
cost	O
for	O
the	O
graphics	B-Device
card	I-Device
and	O
uses	O
more	O
video	O
memory	O
.	O
</s>
<s>
The	O
level	O
of	O
anti-aliasing	O
determines	O
how	O
smooth	O
polygon	O
edges	O
are	O
(	O
and	O
how	O
much	O
video	O
memory	O
it	O
consumes	O
)	O
.	O
</s>
<s>
In	O
contrast	O
,	O
when	O
anti-aliased	O
the	O
checker-board	O
near	O
the	O
top	O
blends	O
into	O
grey	O
,	O
which	O
is	O
usually	O
the	O
desired	O
effect	O
when	O
the	O
resolution	B-Algorithm
is	O
insufficient	O
to	O
show	O
the	O
detail	O
.	O
</s>
<s>
Multiple	O
methods	O
exist	O
,	O
including	O
the	O
sinc	B-Algorithm
filter	I-Algorithm
,	O
which	O
is	O
considered	O
a	O
better	O
anti-aliasing	O
algorithm	O
.	O
</s>
<s>
When	O
magnified	O
,	O
it	O
can	O
be	O
seen	O
how	O
anti-aliasing	O
interpolates	O
the	O
brightness	O
of	O
the	O
pixels	B-Algorithm
at	O
the	O
boundaries	O
to	O
produce	O
grey	O
pixels	B-Algorithm
since	O
the	O
space	O
is	O
occupied	O
by	O
both	O
black	O
and	O
white	O
tiles	O
.	O
</s>
<s>
These	O
help	O
make	O
the	O
sinc	B-Algorithm
filter	I-Algorithm
antialiased	O
image	O
appear	O
much	O
smoother	O
than	O
the	O
original	O
.	O
</s>
<s>
In	O
a	O
simple	O
diamond	O
image	O
,	O
anti-aliasing	O
blends	O
the	O
boundary	O
pixels	B-Algorithm
;	O
this	O
reduces	O
the	O
aesthetically	O
jarring	O
effect	O
of	O
the	O
sharp	O
,	O
step-like	O
boundaries	O
that	O
appear	O
in	O
the	O
aliased	O
graphic	O
.	O
</s>
<s>
Anti-aliasing	O
is	O
often	O
applied	O
in	O
rendering	O
text	O
on	O
a	O
computer	B-Device
screen	I-Device
,	O
to	O
suggest	O
smooth	O
contours	O
that	O
better	O
emulate	O
the	O
appearance	O
of	O
text	O
produced	O
by	O
conventional	O
ink-and-paper	O
printing	O
.	O
</s>
<s>
Sub-pixel	O
rendering	O
requires	O
special	O
colour-balanced	O
anti-aliasing	O
filters	O
to	O
turn	O
what	O
would	O
be	O
severe	O
colour	O
distortion	O
into	O
barely-noticeable	O
colour	O
fringes	O
.	O
</s>
<s>
Equivalent	O
results	O
can	O
be	O
had	O
by	O
making	O
individual	O
sub-pixels	O
addressable	O
as	O
if	O
they	O
were	O
full	O
pixels	B-Algorithm
,	O
and	O
supplying	O
a	O
hardware-based	O
anti-aliasing	O
filter	O
as	O
is	O
done	O
in	O
the	O
OLPC	B-Application
XO-1	I-Application
laptop	O
's	O
display	B-Device
controller	O
.	O
</s>
<s>
Pixel	B-General_Concept
geometry	I-General_Concept
affects	O
all	O
of	O
this	O
,	O
whether	O
the	O
anti-aliasing	O
and	O
sub-pixel	O
addressing	O
are	O
done	O
in	O
software	O
or	O
hardware	O
.	O
</s>
<s>
The	O
most	O
basic	O
approach	O
to	O
anti-aliasing	O
a	O
pixel	B-Algorithm
is	O
determining	O
what	O
percentage	O
of	O
the	O
pixel	B-Algorithm
is	O
occupied	O
by	O
a	O
given	O
region	O
in	O
the	O
vector	O
graphic	O
-	O
in	O
this	O
case	O
a	O
pixel-sized	O
square	O
,	O
possibly	O
transposed	O
over	O
several	O
pixels	B-Algorithm
-	O
and	O
using	O
that	O
percentage	O
as	O
the	O
colour	O
.	O
</s>
<s>
This	O
method	O
is	O
generally	O
best	O
suited	O
for	O
simple	O
graphics	O
,	O
such	O
as	O
basic	O
lines	O
or	O
curves	O
,	O
and	O
applications	O
that	O
would	O
otherwise	O
have	O
to	O
convert	O
absolute	O
coordinates	O
to	O
pixel-constrained	O
coordinates	O
,	O
such	O
as	O
3D	O
graphics	O
.	O
</s>
<s>
Otherwise	O
,	O
the	O
brightness	O
of	O
each	O
pixel	B-Algorithm
will	O
be	O
equal	O
to	O
the	O
darkest	O
value	O
calculated	O
in	O
time	O
for	O
that	O
location	O
which	O
produces	O
a	O
very	O
bad	O
result	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
one	O
point	O
sets	O
a	O
brightness	O
level	O
of	O
0.90	O
for	O
a	O
given	O
pixel	B-Algorithm
and	O
another	O
point	O
calculated	O
later	O
barely	O
touches	O
that	O
pixel	B-Algorithm
and	O
has	O
a	O
brightness	O
of	O
0.05	O
,	O
the	O
final	O
value	O
set	O
for	O
that	O
pixel	B-Algorithm
should	O
be	O
0.95	O
,	O
not	O
0.05	O
.	O
</s>
<s>
For	O
more	O
sophisticated	O
shapes	O
,	O
the	O
algorithm	O
may	O
be	O
generalized	O
as	O
rendering	O
the	O
shape	O
to	O
a	O
pixel	B-Algorithm
grid	O
with	O
higher	O
resolution	B-Algorithm
than	O
the	O
target	O
display	B-Device
surface	O
(	O
usually	O
a	O
multiple	O
that	O
is	O
a	O
power	O
of	O
2	O
to	O
reduce	O
distortion	O
)	O
,	O
then	O
using	O
bicubic	B-Algorithm
interpolation	I-Algorithm
to	O
determine	O
the	O
average	O
intensity	O
of	O
each	O
real	O
pixel	B-Algorithm
on	O
the	O
display	B-Device
surface	O
.	O
</s>
<s>
The	O
image	O
displayed	O
on	O
the	O
screen	O
is	O
taken	O
as	O
samples	O
,	O
at	O
each	O
(	O
x	O
,	O
y	O
)	O
pixel	B-Algorithm
position	O
,	O
of	O
a	O
filtered	O
version	O
of	O
the	O
signal	O
.	O
</s>
<s>
The	O
most	O
widely	O
accepted	O
analytic	O
tool	O
for	O
such	O
problems	O
is	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
;	O
this	O
decomposes	O
a	O
signal	O
into	O
basis	O
functions	O
of	O
different	O
frequencies	O
,	O
known	O
as	O
frequency	O
components	O
,	O
and	O
gives	O
us	O
the	O
amplitude	B-Application
of	O
each	O
frequency	O
component	O
in	O
the	O
signal	O
.	O
</s>
<s>
The	O
goal	O
of	O
an	O
anti-aliasing	O
filter	O
is	O
to	O
greatly	O
reduce	O
frequencies	O
above	O
a	O
certain	O
limit	O
,	O
known	O
as	O
the	O
Nyquist	O
frequency	O
,	O
so	O
that	O
the	O
signal	O
will	O
be	O
accurately	O
represented	O
by	O
its	O
samples	O
,	O
or	O
nearly	O
so	O
,	O
in	O
accordance	O
with	O
the	O
sampling	O
theorem	O
;	O
there	O
are	O
many	O
different	O
choices	O
of	O
detailed	O
algorithm	O
,	O
with	O
different	O
filter	O
transfer	O
functions	O
.	O
</s>
<s>
Lanczos	B-Algorithm
resampling	I-Algorithm
is	O
based	O
on	O
convolution	O
of	O
the	O
data	O
with	O
a	O
discrete	O
representation	O
of	O
the	O
sinc	O
function	O
.	O
</s>
<s>
If	O
the	O
resolution	B-Algorithm
is	O
not	O
limited	O
by	O
the	O
rectangular	O
sampling	O
rate	O
of	O
either	O
the	O
source	O
or	O
target	O
image	O
,	O
then	O
one	O
should	O
ideally	O
use	O
rotationally	O
symmetrical	O
filter	O
or	O
interpolation	O
functions	O
,	O
as	O
though	O
the	O
data	O
were	O
a	O
two	O
dimensional	O
function	O
of	O
continuous	O
x	O
and	O
y	O
.	O
</s>
<s>
The	O
sinc	O
function	O
of	O
the	O
radius	O
has	O
too	O
long	O
a	O
tail	O
to	O
make	O
a	O
good	O
filter	O
(	O
it	O
is	O
not	O
even	O
square-integrable	B-Algorithm
)	O
.	O
</s>
<s>
A	O
more	O
appropriate	O
analog	O
to	O
the	O
one-dimensional	O
sinc	O
is	O
the	O
two-dimensional	O
Airy	O
disc	O
amplitude	B-Application
,	O
the	O
2D	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
a	O
circular	O
region	O
in	O
2D	O
frequency	O
space	O
,	O
as	O
opposed	O
to	O
a	O
square	O
region	O
.	O
</s>
<s>
Such	O
interpolation	O
would	O
treat	O
diagonal	O
lines	O
differently	O
from	O
horizontal	O
and	O
vertical	O
lines	O
,	O
which	O
is	O
like	O
a	O
weak	O
form	O
of	O
aliasing	B-Error_Name
.	O
</s>
<s>
There	O
are	O
only	O
a	O
handful	O
of	O
primitives	O
used	O
at	O
the	O
lowest	O
level	O
in	O
a	O
real-time	B-General_Concept
rendering	I-General_Concept
engine	O
(	O
either	O
software	O
or	O
hardware	O
accelerated	O
)	O
.	O
</s>
<s>
If	O
one	O
is	O
to	O
draw	O
such	O
a	O
primitive	O
in	O
white	O
against	O
a	O
black	O
background	O
,	O
it	O
is	O
possible	O
to	O
design	O
such	O
a	O
primitive	O
to	O
have	O
fuzzy	O
edges	O
,	O
achieving	O
some	O
sort	O
of	O
anti-aliasing	O
.	O
</s>
<s>
To	O
approximate	O
the	O
uniform	O
averaging	O
algorithm	O
,	O
one	O
may	O
use	O
an	O
extra	O
buffer	O
for	O
sub-pixel	O
data	O
.	O
</s>
<s>
The	O
initial	O
(	O
and	O
least	O
memory-hungry	O
)	O
approach	O
used	O
16	O
extra	O
bits	O
per	O
pixel	B-Algorithm
,	O
in	O
a	O
4	O
×	O
4	O
grid	O
.	O
</s>
<s>
Since	O
this	O
requires	O
that	O
the	O
primitives	O
be	O
in	O
some	O
order	O
,	O
and	O
hence	O
interacts	O
poorly	O
with	O
an	O
application	O
programming	O
interface	O
such	O
as	O
OpenGL	B-Application
,	O
the	O
latest	O
methods	O
simply	O
have	O
two	O
or	O
more	O
full	O
sub-pixels	O
per	O
pixel	B-Algorithm
,	O
including	O
full	O
color	O
information	O
for	O
each	O
sub-pixel	O
.	O
</s>
<s>
Some	O
information	O
may	O
be	O
shared	O
between	O
the	O
sub-pixels	O
(	O
such	O
as	O
the	O
Z-buffer	O
.	O
)	O
</s>
<s>
There	O
is	O
also	O
an	O
approach	O
specialised	O
for	O
texture	O
mapping	O
called	O
mipmapping	B-Data_Structure
,	O
which	O
works	O
by	O
creating	O
lower	O
resolution	B-Algorithm
,	O
pre-filtered	O
versions	O
of	O
the	O
texture	O
map	O
.	O
</s>
<s>
When	O
rendering	O
the	O
image	O
,	O
the	O
appropriate-resolution	O
mipmap	B-Data_Structure
is	O
chosen	O
and	O
hence	O
the	O
texture	O
pixels	B-Algorithm
(	O
texels	O
)	O
are	O
already	O
filtered	O
when	O
they	O
arrive	O
on	O
the	O
screen	O
.	O
</s>
<s>
Mipmapping	B-Data_Structure
is	O
generally	O
combined	O
with	O
various	O
forms	O
of	O
texture	O
filtering	O
in	O
order	O
to	O
improve	O
the	O
final	O
result	O
.	O
</s>
<s>
Because	O
fractals	B-Application
have	O
unlimited	O
detail	O
and	O
no	O
noise	O
other	O
than	O
arithmetic	O
round-off	O
error	O
,	O
they	O
illustrate	O
aliasing	B-Error_Name
more	O
clearly	O
than	O
do	O
photographs	O
or	O
other	O
measured	O
data	O
.	O
</s>
<s>
The	O
escape	O
times	O
,	O
which	O
are	O
converted	O
to	O
colours	O
at	O
the	O
exact	O
centres	O
of	O
the	O
pixels	B-Algorithm
,	O
go	O
to	O
infinity	O
at	O
the	O
border	O
of	O
the	O
set	O
,	O
so	O
colours	O
from	O
centres	O
near	O
borders	O
are	O
unpredictable	O
,	O
due	O
to	O
aliasing	B-Error_Name
.	O
</s>
<s>
This	O
example	O
has	O
edges	O
in	O
about	O
half	O
of	O
its	O
pixels	B-Algorithm
,	O
so	O
it	O
shows	O
much	O
aliasing	B-Error_Name
.	O
</s>
<s>
(	O
Since	O
most	O
modern	O
software	O
anti-aliases	O
,	O
one	O
may	O
have	O
to	O
download	O
the	O
full-size	O
version	O
to	O
see	O
all	O
of	O
the	O
aliasing	B-Error_Name
.	O
)	O
</s>
<s>
The	O
second	O
image	O
is	O
calculated	O
at	O
five	O
times	O
the	O
sampling	O
rate	O
and	O
down-sampled	B-Algorithm
with	O
anti-aliasing	O
.	O
</s>
<s>
Assuming	O
that	O
one	O
would	O
really	O
like	O
something	O
like	O
the	O
average	O
colour	O
over	O
each	O
pixel	B-Algorithm
,	O
this	O
one	O
is	O
getting	O
closer	O
.	O
</s>
<s>
The	O
colours	O
derived	O
from	O
these	O
calculated	O
points	O
have	O
been	O
identified	O
as	O
unusually	O
unrepresentative	O
of	O
their	O
pixels	B-Algorithm
.	O
</s>
<s>
The	O
set	O
changes	O
more	O
rapidly	O
there	O
,	O
so	O
a	O
single	O
point	O
sample	O
is	O
less	O
representative	O
of	O
the	O
whole	O
pixel	B-Algorithm
.	O
</s>
<s>
Finally	O
,	O
"	O
Budding	O
Turbines	O
"	O
is	O
so	O
regular	O
that	O
systematic	O
(	O
Moiré	O
)	O
aliasing	B-Error_Name
can	O
clearly	O
be	O
seen	O
near	O
the	O
main	O
"	O
turbine	O
axis	O
"	O
when	O
it	O
is	O
downsized	O
by	O
taking	O
the	O
nearest	O
pixel	B-Algorithm
.	O
</s>
<s>
The	O
aliasing	B-Error_Name
in	O
the	O
first	O
image	O
appears	O
random	O
because	O
it	O
comes	O
from	O
all	O
levels	O
of	O
detail	O
,	O
below	O
the	O
pixel	B-Algorithm
size	O
.	O
</s>
<s>
When	O
the	O
lower	O
level	O
aliasing	B-Error_Name
is	O
suppressed	O
,	O
to	O
make	O
the	O
third	O
image	O
and	O
then	O
that	O
is	O
down-sampled	B-Algorithm
once	O
more	O
,	O
without	O
anti-aliasing	O
,	O
to	O
make	O
the	O
fifth	O
image	O
,	O
the	O
order	O
on	O
the	O
scale	O
of	O
the	O
third	O
image	O
appears	O
as	O
systematic	O
aliasing	B-Error_Name
in	O
the	O
fifth	O
image	O
.	O
</s>
<s>
Super	B-Algorithm
sampling	I-Algorithm
anti-aliasing	O
(	O
SSAA	O
)	O
,	O
also	O
called	O
full-scene	O
anti-aliasing	O
(	O
FSAA	O
)	O
,	O
is	O
used	O
to	O
avoid	O
aliasing	B-Error_Name
(	O
or	O
"	O
jaggies	B-Algorithm
"	O
)	O
on	O
full-screen	O
images	O
.	O
</s>
<s>
SSAA	O
was	O
the	O
first	O
type	O
of	O
anti-aliasing	O
available	O
with	O
early	O
video	B-Device
cards	I-Device
.	O
</s>
<s>
But	O
due	O
to	O
its	O
tremendous	O
computational	O
cost	O
and	O
the	O
advent	O
of	O
multisample	B-Algorithm
anti-aliasing	I-Algorithm
(	O
MSAA	O
)	O
support	O
on	O
GPUs	B-Architecture
,	O
it	O
is	O
no	O
longer	O
widely	O
used	O
in	O
real	O
time	O
applications	O
.	O
</s>
<s>
However	O
,	O
while	O
useful	O
for	O
photo-like	O
images	O
,	O
a	O
simple	O
anti-aliasing	O
approach	O
(	O
such	O
as	O
super-sampling	B-Algorithm
and	O
then	O
averaging	O
)	O
may	O
actually	O
worsen	O
the	O
appearance	O
of	O
some	O
types	O
of	O
line	O
art	O
or	O
diagrams	O
(	O
making	O
the	O
image	O
appear	O
fuzzy	O
)	O
,	O
especially	O
where	O
most	O
lines	O
are	O
horizontal	O
or	O
vertical	O
.	O
</s>
<s>
In	O
general	O
,	O
super-sampling	B-Algorithm
is	O
a	O
technique	O
of	O
collecting	O
data	O
points	O
at	O
a	O
greater	O
resolution	B-Algorithm
(	O
usually	O
by	O
a	O
power	O
of	O
two	O
)	O
than	O
the	O
final	O
data	O
resolution	B-Algorithm
.	O
</s>
<s>
These	O
data	O
points	O
are	O
then	O
combined	O
(	O
down-sampled	B-Algorithm
)	O
to	O
the	O
desired	O
resolution	B-Algorithm
,	O
often	O
just	O
by	O
a	O
simple	O
average	O
.	O
</s>
<s>
The	O
combined	O
data	O
points	O
have	O
less	O
visible	O
aliasing	B-Error_Name
artifacts	O
(	O
or	O
moiré	O
patterns	O
)	O
.	O
</s>
<s>
Full-scene	O
anti-aliasing	O
by	O
super-sampling	B-Algorithm
usually	O
means	O
that	O
each	O
full	O
frame	O
is	O
rendered	O
at	O
double	O
(	O
2x	O
)	O
or	O
quadruple	O
(	O
4x	O
)	O
the	O
display	B-Device
resolution	B-Algorithm
,	O
and	O
then	O
down-sampled	B-Algorithm
to	O
match	O
the	O
display	B-Device
resolution	B-Algorithm
.	O
</s>
<s>
Thus	O
,	O
a	O
2x	O
FSAA	O
would	O
render	O
4	O
super-sampled	O
pixels	B-Algorithm
for	O
each	O
single	O
pixel	B-Algorithm
of	O
each	O
frame	O
.	O
</s>
<s>
Sometimes	O
FSAA	O
is	O
implemented	O
in	O
hardware	O
in	O
such	O
a	O
way	O
that	O
a	O
graphical	O
application	O
is	O
unaware	O
the	O
images	O
are	O
being	O
super-sampled	O
and	O
then	O
down-sampled	B-Algorithm
before	O
being	O
displayed	O
.	O
</s>
<s>
A	O
graphics	O
rendering	O
system	O
creates	O
an	O
image	O
based	O
on	O
objects	O
constructed	O
of	O
polygonal	O
primitives	O
;	O
the	O
aliasing	B-Error_Name
effects	O
in	O
the	O
image	O
can	O
be	O
reduced	O
by	O
applying	O
an	O
anti-aliasing	O
scheme	O
only	O
to	O
the	O
areas	O
of	O
the	O
image	O
representing	O
silhouette	O
edges	O
of	O
the	O
objects	O
.	O
</s>
<s>
The	O
silhouette	O
edges	O
are	O
anti-aliased	O
by	O
creating	O
anti-aliasing	O
primitives	O
which	O
vary	O
in	O
opacity	O
.	O
</s>
<s>
These	O
anti-aliasing	O
primitives	O
are	O
joined	O
to	O
the	O
silhouetted	O
edges	O
,	O
and	O
create	O
a	O
region	O
in	O
the	O
image	O
where	O
the	O
objects	O
appear	O
to	O
blend	O
into	O
the	O
background	O
.	O
</s>
<s>
The	O
method	O
has	O
some	O
important	O
advantages	O
over	O
classical	O
methods	O
based	O
on	O
the	O
accumulation	O
buffer	O
since	O
it	O
generates	O
full-scene	O
anti-aliasing	O
in	O
only	O
two	O
passes	O
and	O
does	O
not	O
require	O
the	O
use	O
of	O
additional	O
memory	O
required	O
by	O
the	O
accumulation	O
buffer	O
.	O
</s>
<s>
Object-based	O
anti-aliasing	O
was	O
first	O
developed	O
at	O
Silicon	O
Graphics	O
for	O
their	O
Indy	B-Operating_System
workstation	O
.	O
</s>
<s>
Digital	O
images	O
are	O
usually	O
stored	O
in	O
a	O
gamma-compressed	O
format	O
,	O
but	O
most	O
optical	O
anti-aliasing	O
filters	O
are	O
linear	O
.	O
</s>
<s>
So	O
to	O
down-sample	O
an	O
image	O
in	O
a	O
way	O
that	O
would	O
match	O
optical	O
blurring	O
,	O
one	O
should	O
first	O
convert	O
it	O
to	O
a	O
linear	O
format	O
,	O
then	O
apply	O
the	O
anti-aliasing	O
filter	O
,	O
and	O
finally	O
convert	O
it	O
back	O
to	O
a	O
gamma	O
compressed	O
format	O
.	O
</s>
<s>
Using	O
linear	O
arithmetic	O
on	O
a	O
gamma-compressed	O
image	O
results	O
in	O
values	O
which	O
are	O
slightly	O
different	O
from	O
the	O
ideal	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Each	O
pixel	B-Algorithm
is	O
individually	O
distorted	O
,	O
meaning	O
outlines	O
become	O
unsmooth	O
after	O
anti-aliasing	O
.	O
</s>
<s>
Because	O
the	O
conversion	O
to	O
and	O
from	O
a	O
linear	O
format	O
greatly	O
slows	O
down	O
the	O
process	O
,	O
and	O
because	O
the	O
differences	O
are	O
usually	O
subtle	O
,	O
most	O
image	B-Application
editing	I-Application
software	I-Application
,	O
including	O
Final	B-Application
Cut	I-Application
Pro	I-Application
and	O
Adobe	B-Operating_System
Photoshop	I-Operating_System
,	O
process	O
images	O
in	O
the	O
gamma-compressed	O
domain	O
.	O
</s>
<s>
Most	O
modern	O
GPUs	B-Architecture
support	O
storing	O
textures	O
in	O
memory	O
in	O
sRGB	O
format	O
,	O
and	O
can	O
perform	O
transformation	O
to	O
linear	O
space	O
and	O
back	O
transparently	O
,	O
with	O
essentially	O
no	O
loss	O
in	O
performance	O
.	O
</s>
<s>
Important	O
early	O
works	O
in	O
the	O
history	O
of	O
anti-aliasing	O
include	O
:	O
</s>
