<s>
In	O
computer	O
graphics	O
and	O
digital	B-Algorithm
imaging	I-Algorithm
,	O
image	B-Algorithm
scaling	I-Algorithm
refers	O
to	O
the	O
resizing	O
of	O
a	O
digital	O
image	O
.	O
</s>
<s>
In	O
video	O
technology	O
,	O
the	O
magnification	O
of	O
digital	O
material	O
is	O
known	O
as	O
upscaling	O
or	O
resolution	B-Algorithm
enhancement	I-Algorithm
.	O
</s>
<s>
When	O
scaling	O
a	O
vector	O
graphic	O
image	O
,	O
the	O
graphic	O
primitives	O
that	O
make	O
up	O
the	O
image	O
can	O
be	O
scaled	O
using	O
geometric	O
transformations	O
,	O
with	O
no	O
loss	O
of	O
image	B-Algorithm
quality	I-Algorithm
.	O
</s>
<s>
When	O
scaling	O
a	O
raster	B-Algorithm
graphics	I-Algorithm
image	O
,	O
a	O
new	O
image	O
with	O
a	O
higher	O
or	O
lower	O
number	O
of	O
pixels	O
must	O
be	O
generated	O
.	O
</s>
<s>
From	O
the	O
standpoint	O
of	O
digital	B-General_Concept
signal	I-General_Concept
processing	I-General_Concept
,	O
the	O
scaling	O
of	O
raster	B-Algorithm
graphics	I-Algorithm
is	O
a	O
two-dimensional	O
example	O
of	O
sample-rate	O
conversion	O
,	O
the	O
conversion	O
of	O
a	O
discrete	O
signal	O
from	O
a	O
sampling	O
rate	O
(	O
in	O
this	O
case	O
the	O
local	O
sampling	O
rate	O
)	O
to	O
another	O
.	O
</s>
<s>
Image	B-Algorithm
scaling	I-Algorithm
can	O
be	O
interpreted	O
as	O
a	O
form	O
of	O
image	B-Algorithm
resampling	I-Algorithm
or	O
image	B-Algorithm
reconstruction	I-Algorithm
from	O
the	O
view	O
of	O
the	O
Nyquist	O
sampling	O
theorem	O
.	O
</s>
<s>
According	O
to	O
the	O
theorem	O
,	O
downsampling	O
to	O
a	O
smaller	O
image	O
from	O
a	O
higher-resolution	O
original	O
can	O
only	O
be	O
carried	O
out	O
after	O
applying	O
a	O
suitable	O
2D	O
anti-aliasing	O
filter	O
to	O
prevent	O
aliasing	O
artifacts	O
.	O
</s>
<s>
An	O
image	B-Algorithm
size	I-Algorithm
can	O
be	O
changed	O
in	O
several	O
ways	O
.	O
</s>
<s>
One	O
of	O
the	O
simpler	O
ways	O
of	O
increasing	O
image	B-Algorithm
size	I-Algorithm
is	O
nearest-neighbor	O
interpolation	B-Algorithm
,	O
replacing	O
every	O
pixel	O
with	O
the	O
nearest	O
pixel	O
in	O
the	O
output	O
;	O
for	O
upscaling	O
this	O
means	O
multiple	O
pixels	O
of	O
the	O
same	O
color	O
will	O
be	O
present	O
.	O
</s>
<s>
This	O
can	O
preserve	O
sharp	O
details	O
in	O
pixel	O
art	O
,	O
but	O
also	O
introduce	O
jaggedness	B-Algorithm
in	O
previously	O
smooth	O
images	O
.	O
</s>
<s>
Bilinear	O
interpolation	B-Algorithm
works	O
by	O
interpolating	B-Algorithm
pixel	O
color	O
values	O
,	O
introducing	O
a	O
continuous	O
transition	O
into	O
the	O
output	O
even	O
where	O
the	O
original	O
material	O
has	O
discrete	O
transitions	O
.	O
</s>
<s>
Although	O
this	O
is	O
desirable	O
for	O
continuous-tone	O
images	O
,	O
this	O
algorithm	O
reduces	O
contrast	B-Device
(	O
sharp	O
edges	O
)	O
in	O
a	O
way	O
that	O
may	O
be	O
undesirable	O
for	O
line	O
art	O
.	O
</s>
<s>
Bicubic	B-Algorithm
interpolation	I-Algorithm
yields	O
substantially	O
better	O
results	O
,	O
with	O
an	O
increase	O
in	O
computational	O
cost	O
.	O
</s>
<s>
Sinc	O
resampling	B-Algorithm
in	O
theory	O
provides	O
the	O
best	O
possible	O
reconstruction	O
for	O
a	O
perfectly	O
bandlimited	O
signal	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
assumptions	O
behind	O
sinc	O
resampling	B-Algorithm
are	O
not	O
completely	O
met	O
by	O
real-world	O
digital	O
images	O
.	O
</s>
<s>
Lanczos	B-Algorithm
resampling	I-Algorithm
,	O
an	O
approximation	O
to	O
the	O
sinc	O
method	O
,	O
yields	O
better	O
results	O
.	O
</s>
<s>
Bicubic	B-Algorithm
interpolation	I-Algorithm
can	O
be	O
regarded	O
as	O
a	O
computationally	O
efficient	O
approximation	O
to	O
Lanczos	B-Algorithm
resampling	I-Algorithm
.	O
</s>
<s>
One	O
weakness	O
of	O
bilinear	O
,	O
bicubic	B-Algorithm
and	O
related	O
algorithms	O
is	O
that	O
they	O
sample	O
a	O
specific	O
number	O
of	O
pixels	O
.	O
</s>
<s>
Another	O
solution	O
to	O
the	O
downscale	O
problem	O
of	O
bi-sampling	O
scaling	O
are	O
mipmaps	B-Data_Structure
.	O
</s>
<s>
A	O
mipmap	B-Data_Structure
is	O
a	O
prescaled	O
set	O
of	O
downscale	O
copies	O
.	O
</s>
<s>
When	O
downscaling	O
the	O
nearest	O
larger	O
mipmap	B-Data_Structure
is	O
used	O
as	O
the	O
origin	O
,	O
to	O
ensure	O
no	O
scaling	O
below	O
the	O
useful	O
threshold	O
of	O
bilinear	O
scaling	O
is	O
used	O
.	O
</s>
<s>
It	O
is	O
standard	O
in	O
many	O
frameworks	O
such	O
as	O
OpenGL	B-Application
.	O
</s>
<s>
Simple	O
interpolation	B-Algorithm
based	O
on	O
Fourier	B-Algorithm
transform	I-Algorithm
pads	O
the	O
frequency	O
domain	O
with	O
zero	O
components	O
(	O
a	O
smooth	O
window-based	O
approach	O
would	O
reduce	O
the	O
ringing	B-Algorithm
)	O
.	O
</s>
<s>
Besides	O
the	O
good	O
conservation	O
(	O
or	O
recovery	O
)	O
of	O
details	O
,	O
notable	O
is	O
the	O
ringing	B-Algorithm
and	O
the	O
circular	O
bleeding	O
of	O
content	O
from	O
the	O
left	O
border	O
to	O
right	O
border	O
(	O
and	O
the	O
other	O
way	O
around	O
)	O
.	O
</s>
<s>
Edge-directed	O
interpolation	B-Algorithm
algorithms	O
aim	O
to	O
preserve	O
edges	O
in	O
the	O
image	O
after	O
scaling	O
,	O
unlike	O
other	O
algorithms	O
,	O
which	O
can	O
introduce	O
staircase	O
artifacts	O
.	O
</s>
<s>
Examples	O
of	O
algorithms	O
for	O
this	O
task	O
include	O
New	O
Edge-Directed	O
Interpolation	B-Algorithm
(	O
NEDI	O
)	O
,	O
Edge-Guided	O
Image	O
Interpolation	B-Algorithm
(	O
EGGI	O
)	O
,	O
Iterative	O
Curvature-Based	O
Interpolation	B-Algorithm
(	O
ICBI	O
)	O
,	O
and	O
Directional	B-Algorithm
Cubic	I-Algorithm
Convolution	I-Algorithm
Interpolation	I-Algorithm
(	O
DCCI	O
)	O
.	O
</s>
<s>
A	O
2013	O
analysis	O
found	O
that	O
DCCI	O
had	O
the	O
best	O
scores	O
in	O
PSNR	O
and	O
SSIM	B-Algorithm
on	O
a	O
series	O
of	O
test	O
images	O
.	O
</s>
<s>
For	O
magnifying	O
computer	O
graphics	O
with	O
low	B-Algorithm
resolution	I-Algorithm
and/or	O
few	O
colors	O
(	O
usually	O
from	O
2	O
to	O
256	O
colors	O
)	O
,	O
better	O
results	O
can	O
be	O
achieved	O
by	O
hqx	B-Algorithm
or	O
other	O
pixel-art	B-Algorithm
scaling	I-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Vectorization	O
first	O
creates	O
a	O
resolution-independent	O
vector	O
representation	O
of	O
the	O
graphic	O
to	O
be	O
scaled	O
.	O
</s>
<s>
Then	O
the	O
resolution-independent	O
version	O
is	O
rendered	O
as	O
a	O
raster	B-Algorithm
image	I-Algorithm
at	O
the	O
desired	O
resolution	B-Algorithm
.	O
</s>
<s>
This	O
technique	O
is	O
used	O
by	O
Adobe	B-Language
Illustrator	I-Language
,	O
Live	O
Trace	O
,	O
and	O
Inkscape	B-Application
.	O
</s>
<s>
Scalable	B-Application
Vector	I-Application
Graphics	I-Application
are	O
well	O
suited	O
to	O
simple	O
geometric	O
images	O
,	O
while	O
photographs	O
do	O
not	O
fare	O
well	O
with	O
vectorization	O
due	O
to	O
their	O
complexity	O
.	O
</s>
<s>
Programs	O
that	O
use	O
this	O
method	O
include	O
waifu2x	B-Algorithm
,	O
Imglarger	O
and	O
Neural	O
Enhance	O
.	O
</s>
<s>
Image	B-Algorithm
scaling	I-Algorithm
is	O
used	O
in	O
,	O
among	O
other	O
applications	O
,	O
web	B-Application
browsers	I-Application
,	O
image	B-Application
editors	I-Application
,	O
image	O
and	O
file	O
viewers	O
,	O
software	O
magnifiers	O
,	O
digital	O
zoom	O
,	O
the	O
process	O
of	O
generating	O
thumbnail	O
images	O
and	O
when	O
outputting	O
images	O
through	O
screens	O
or	O
printers	O
.	O
</s>
<s>
This	O
application	O
is	O
the	O
magnification	O
of	O
images	O
for	O
home	O
theaters	O
for	O
HDTV-ready	O
output	O
devices	O
from	O
PAL-Resolution	O
content	O
,	O
for	O
example	O
from	O
a	O
DVD	O
player	O
.	O
</s>
<s>
As	O
pixel-art	O
graphics	O
are	O
usually	O
low-resolution	O
,	O
they	O
rely	O
on	O
careful	O
placing	O
of	O
individual	O
pixels	O
,	O
often	O
with	O
a	O
limited	O
palette	O
of	O
colors	O
.	O
</s>
<s>
This	O
results	O
in	O
graphics	O
that	O
rely	O
on	O
stylized	O
visual	O
cues	O
to	O
define	O
complex	O
shapes	O
with	O
little	O
resolution	B-Algorithm
,	O
down	O
to	O
individual	O
pixels	O
.	O
</s>
<s>
Since	O
a	O
typical	O
application	O
is	O
to	O
improve	O
the	O
appearance	O
of	O
fourth-generation	B-Application
and	O
earlier	O
video	O
games	O
on	O
arcade	O
and	O
console	O
emulators	O
,	O
many	O
are	O
designed	O
to	O
run	O
in	O
real	O
time	O
for	O
small	O
input	O
images	O
at	O
60	O
frames	O
per	O
second	O
.	O
</s>
<s>
On	O
fast	O
hardware	O
,	O
these	O
algorithms	O
are	O
suitable	O
for	O
gaming	O
and	O
other	O
real-time	B-General_Concept
image	O
processing	O
.	O
</s>
<s>
Scaling	O
art	O
algorithms	O
have	O
been	O
implemented	O
in	O
a	O
wide	O
range	O
of	O
emulators	O
such	O
as	O
HqMAME	O
and	O
DOSBox	B-Application
,	O
as	O
well	O
as	O
2D	O
game	O
engines	O
and	O
game	O
engine	O
recreations	O
such	O
as	O
ScummVM	B-Device
.	O
</s>
<s>
Such	O
filters	O
are	O
currently	O
used	O
in	O
commercial	O
emulators	O
on	O
Xbox	B-Application
Live	I-Application
,	O
Virtual	B-Application
Console	I-Application
,	O
and	O
PSN	B-Device
to	O
allow	O
classic	O
low-resolution	O
games	O
to	O
be	O
more	O
visually	O
appealing	O
on	O
modern	O
HD	O
displays	O
.	O
</s>
<s>
Recently	O
released	O
games	O
that	O
incorporate	O
these	O
filters	O
include	O
Sonic	B-Application
's	I-Application
Ultimate	I-Application
Genesis	I-Application
Collection	I-Application
,	O
Castlevania	B-Application
:	I-Application
The	I-Application
Dracula	I-Application
X	I-Application
Chronicles	I-Application
,	O
Castlevania	B-Application
:	I-Application
Symphony	I-Application
of	I-Application
the	I-Application
Night	I-Application
,	O
and	O
Akumajō	B-Application
Dracula	I-Application
X	I-Application
Chi	I-Application
no	I-Application
Rondo	I-Application
.	O
</s>
<s>
A	O
number	O
of	O
companies	O
have	O
developed	O
techniques	O
to	O
upscale	O
video	O
frames	O
in	O
real-time	B-General_Concept
,	O
such	O
as	O
when	O
they	O
are	O
drawn	O
on	O
screen	O
in	O
a	O
video	O
game	O
.	O
</s>
<s>
Nvidia	O
's	O
deep	B-Device
learning	I-Device
super	I-Device
sampling	I-Device
(	O
DLSS	B-Device
)	O
uses	O
deep	B-Algorithm
learning	I-Algorithm
to	O
upsample	O
lower-resolution	O
images	O
to	O
a	O
higher	O
resolution	B-Algorithm
for	O
display	O
on	O
higher-resolution	O
computer	O
monitors	O
.	O
</s>
<s>
AMD	O
's	O
FidelityFX	O
Super	O
Resolution	B-Algorithm
1.0	O
(	O
FSR	O
)	O
does	O
not	O
employ	O
machine	O
learning	O
,	O
instead	O
using	O
traditional	O
hand-written	O
algorithms	O
to	O
achieve	O
spatial	O
upscaling	O
on	O
traditional	O
shading	O
units	O
.	O
</s>
<s>
FSR	O
standardized	O
presets	O
are	O
not	O
enforced	O
,	O
and	O
some	O
titles	O
such	O
as	O
Dota	B-Application
2	I-Application
offer	O
resolution	B-Algorithm
sliders	O
.	O
</s>
