<s>
The	O
structural	B-Algorithm
similarity	I-Algorithm
index	O
measure	O
(	O
SSIM	B-Algorithm
)	O
is	O
a	O
method	O
for	O
predicting	O
the	O
perceived	O
quality	O
of	O
digital	O
television	O
and	O
cinematic	O
pictures	O
,	O
as	O
well	O
as	O
other	O
kinds	O
of	O
digital	O
images	O
and	O
videos	O
.	O
</s>
<s>
SSIM	B-Algorithm
is	O
used	O
for	O
measuring	O
the	O
similarity	O
between	O
two	O
images	O
.	O
</s>
<s>
The	O
SSIM	B-Algorithm
index	I-Algorithm
is	O
a	O
full	O
reference	O
metric	O
;	O
in	O
other	O
words	O
,	O
the	O
measurement	O
or	O
prediction	O
of	O
image	B-Algorithm
quality	I-Algorithm
is	O
based	O
on	O
an	O
initial	O
uncompressed	O
or	O
distortion-free	O
image	O
as	O
reference	O
.	O
</s>
<s>
SSIM	B-Algorithm
is	O
a	O
perception-based	O
model	O
that	O
considers	O
image	O
degradation	O
as	O
perceived	O
change	O
in	O
structural	O
information	O
,	O
while	O
also	O
incorporating	O
important	O
perceptual	O
phenomena	O
,	O
including	O
both	O
luminance	O
masking	O
and	O
contrast	O
masking	O
terms	O
.	O
</s>
<s>
The	O
difference	O
with	O
other	O
techniques	O
such	O
as	O
MSE	B-Algorithm
or	O
PSNR	O
is	O
that	O
these	O
approaches	O
estimate	O
absolute	O
errors	O
.	O
</s>
<s>
The	O
predecessor	O
of	O
SSIM	B-Algorithm
was	O
called	O
Universal	O
Quality	O
Index	O
(	O
UQI	O
)	O
,	O
or	O
Wang	O
–	O
Bovik	O
Index	O
,	O
which	O
was	O
developed	O
by	O
Zhou	O
Wang	O
and	O
Alan	O
Bovik	O
in	O
2001	O
.	O
</s>
<s>
This	O
evolved	O
,	O
through	O
their	O
collaboration	O
with	O
Hamid	O
Sheikh	O
and	O
Eero	O
Simoncelli	O
,	O
into	O
the	O
current	O
version	O
of	O
SSIM	B-Algorithm
,	O
which	O
was	O
published	O
in	O
April	O
2004	O
in	O
the	O
IEEE	O
Transactions	O
on	O
Image	O
Processing	O
.	O
</s>
<s>
In	O
addition	O
to	O
defining	O
the	O
SSIM	B-Algorithm
quality	O
index	O
,	O
the	O
paper	O
provides	O
a	O
general	O
context	O
for	O
developing	O
and	O
evaluating	O
perceptual	O
quality	O
measures	O
,	O
including	O
connections	O
to	O
human	O
visual	O
neurobiology	O
and	O
perception	O
,	O
and	O
direct	O
validation	O
of	O
the	O
index	O
against	O
human	O
subject	O
ratings	O
.	O
</s>
<s>
SSIM	B-Algorithm
subsequently	O
found	O
strong	O
adoption	O
in	O
the	O
image	O
processing	O
community	O
and	O
in	O
the	O
television	O
and	O
social	O
media	O
industries	O
.	O
</s>
<s>
The	O
2004	O
SSIM	B-Algorithm
paper	O
has	O
been	O
cited	O
over	O
40,000	O
times	O
according	O
to	O
Google	B-Library
Scholar	I-Library
,	O
making	O
it	O
one	O
of	O
the	O
highest	O
cited	O
papers	O
in	O
the	O
image	O
processing	O
and	O
video	O
engineering	O
fields	O
.	O
</s>
<s>
Because	O
of	O
its	O
high	O
adoption	O
by	O
the	O
television	O
industry	O
,	O
the	O
authors	O
of	O
the	O
original	O
SSIM	B-Algorithm
paper	O
were	O
each	O
accorded	O
a	O
Primetime	O
Engineering	O
Emmy	O
Award	O
in	O
2015	O
by	O
the	O
Television	O
Academy	O
.	O
</s>
<s>
The	O
SSIM	B-Algorithm
index	I-Algorithm
is	O
calculated	O
on	O
various	O
windows	O
of	O
an	O
image	O
.	O
</s>
<s>
The	O
SSIM	B-Algorithm
formula	O
is	O
based	O
on	O
three	O
comparison	O
measurements	O
between	O
the	O
samples	O
of	O
and	O
:	O
luminance	O
(	O
)	O
,	O
contrast	O
(	O
)	O
and	O
structure	O
(	O
)	O
.	O
</s>
<s>
SSIM	B-Algorithm
is	O
then	O
a	O
weighted	O
combination	O
of	O
those	O
comparative	O
measures	O
:	O
</s>
<s>
SSIM	B-Algorithm
satisfies	O
the	O
identity	O
of	O
indiscernibles	O
,	O
and	O
symmetry	O
properties	O
,	O
but	O
not	O
the	O
triangle	O
inequality	O
or	O
non-negativity	O
,	O
and	O
thus	O
is	O
not	O
a	O
distance	O
function	O
.	O
</s>
<s>
However	O
,	O
under	O
certain	O
conditions	O
,	O
SSIM	B-Algorithm
may	O
be	O
converted	O
to	O
a	O
normalized	O
root	O
MSE	B-Algorithm
measure	O
,	O
which	O
is	O
a	O
distance	O
function	O
.	O
</s>
<s>
The	O
square	O
of	O
such	O
a	O
function	O
is	O
not	O
convex	O
,	O
but	O
is	O
locally	O
convex	O
and	O
quasiconvex	O
,	O
making	O
SSIM	B-Algorithm
a	O
feasible	O
target	O
for	O
optimization	O
.	O
</s>
<s>
In	O
order	O
to	O
evaluate	O
the	O
image	B-Algorithm
quality	I-Algorithm
,	O
this	O
formula	O
is	O
usually	O
applied	O
only	O
on	O
luma	O
,	O
although	O
it	O
may	O
also	O
be	O
applied	O
on	O
color	O
(	O
e.g.	O
,	O
RGB	O
)	O
values	O
or	O
chromatic	O
(	O
e.g.	O
</s>
<s>
The	O
resultant	O
SSIM	B-Algorithm
index	I-Algorithm
is	O
a	O
decimal	O
value	O
between	O
-1	O
and	O
1	O
,	O
where	O
1	O
indicates	O
perfect	O
similarity	O
,	O
0	O
indicates	O
no	O
similarity	O
,	O
and	O
-1	O
indicates	O
perfect	O
anti-correlation	O
.	O
</s>
<s>
The	O
window	O
can	O
be	O
displaced	O
pixel-by-pixel	O
on	O
the	O
image	O
to	O
create	O
an	O
SSIM	B-Algorithm
quality	O
map	O
of	O
the	O
image	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
video	B-Device
quality	I-Device
assessment	O
,	O
the	O
authors	O
propose	O
to	O
use	O
only	O
a	O
subgroup	O
of	O
the	O
possible	O
windows	O
to	O
reduce	O
the	O
complexity	O
of	O
the	O
calculation	O
.	O
</s>
<s>
A	O
more	O
advanced	O
form	O
of	O
SSIM	B-Algorithm
,	O
called	O
Multiscale	O
SSIM	B-Algorithm
(	O
MS-SSIM	O
)	O
is	O
conducted	O
over	O
multiple	O
scales	O
through	O
a	O
process	O
of	O
multiple	O
stages	O
of	O
sub-sampling	O
,	O
reminiscent	O
of	O
multiscale	O
processing	O
in	O
the	O
early	O
vision	O
system	O
.	O
</s>
<s>
It	O
has	O
been	O
shown	O
to	O
perform	O
equally	O
well	O
or	O
better	O
than	O
SSIM	B-Algorithm
on	O
different	O
subjective	O
image	O
and	O
video	O
databases	O
.	O
</s>
<s>
(	O
3-SSIM	O
)	O
is	O
a	O
form	O
of	O
SSIM	B-Algorithm
that	O
takes	O
into	O
account	O
the	O
fact	O
that	O
the	O
human	O
eye	O
can	O
see	O
differences	O
more	O
precisely	O
on	O
textured	O
or	O
edge	O
regions	O
than	O
on	O
smooth	O
regions	O
.	O
</s>
<s>
The	O
resulting	O
metric	O
is	O
calculated	O
as	O
a	O
weighted	O
average	O
of	O
SSIM	B-Algorithm
for	O
three	O
categories	O
of	O
regions	O
:	O
edges	O
,	O
textures	O
,	O
and	O
smooth	O
regions	O
.	O
</s>
<s>
This	O
suggests	O
that	O
edge	O
regions	O
play	O
a	O
dominant	O
role	O
in	O
image	B-Algorithm
quality	I-Algorithm
perception	O
.	O
</s>
<s>
The	O
authors	O
of	O
3-SSIM	O
have	O
also	O
extended	O
the	O
model	O
into	O
(	O
4-SSIM	O
)	O
.	O
</s>
<s>
Structural	O
dissimilarity	O
(	O
DSSIM	O
)	O
may	O
be	O
derived	O
from	O
SSIM	B-Algorithm
,	O
though	O
it	O
does	O
not	O
constitute	O
a	O
distance	O
function	O
as	O
the	O
triangle	O
inequality	O
is	O
not	O
necessarily	O
satisfied	O
.	O
</s>
<s>
It	O
is	O
worth	O
noting	O
that	O
the	O
original	O
version	O
SSIM	B-Algorithm
was	O
designed	O
to	O
measure	O
the	O
quality	O
of	O
still	O
images	O
.	O
</s>
<s>
A	O
common	O
practice	O
is	O
to	O
calculate	O
the	O
average	O
SSIM	B-Algorithm
value	O
over	O
all	O
frames	O
in	O
the	O
video	O
sequence	O
.	O
</s>
<s>
However	O
,	O
several	O
temporal	O
variants	O
of	O
SSIM	B-Algorithm
have	O
been	O
developed	O
.	O
</s>
<s>
The	O
complex	O
wavelet	O
transform	O
variant	O
of	O
the	O
SSIM	B-Algorithm
(	O
CW-SSIM	O
)	O
is	O
designed	O
to	O
deal	O
with	O
issues	O
of	O
image	O
scaling	O
,	O
translation	O
and	O
rotation	O
.	O
</s>
<s>
Instead	O
of	O
giving	O
low	O
scores	O
to	O
images	O
with	O
such	O
conditions	O
,	O
the	O
CW-SSIM	O
takes	O
advantage	O
of	O
the	O
complex	O
wavelet	O
transform	O
and	O
therefore	O
yields	O
higher	O
scores	O
to	O
said	O
images	O
.	O
</s>
<s>
The	O
CW-SSIM	O
is	O
defined	O
as	O
follows	O
:	O
</s>
<s>
Like	O
the	O
SSIM	B-Algorithm
,	O
the	O
CW-SSIM	O
has	O
a	O
maximum	O
value	O
of	O
1	O
.	O
</s>
<s>
The	O
maximum	O
value	O
of	O
1	O
indicates	O
that	O
the	O
two	O
signals	O
are	O
perfectly	O
structurally	O
similar	O
while	O
a	O
value	O
of	O
0	O
indicates	O
no	O
structural	B-Algorithm
similarity	I-Algorithm
.	O
</s>
<s>
The	O
SSIMPLUS	O
index	O
is	O
based	O
on	O
SSIM	B-Algorithm
and	O
is	O
a	O
commercially	O
available	O
tool	O
.	O
</s>
<s>
It	O
extends	O
SSIM	B-Algorithm
's	O
capabilities	O
,	O
mainly	O
to	O
target	O
video	O
applications	O
.	O
</s>
<s>
According	O
to	O
its	O
authors	O
,	O
SSIMPLUS	O
achieves	O
higher	O
accuracy	O
and	O
higher	O
speed	O
than	O
other	O
image	O
and	O
video	B-Device
quality	I-Device
metrics	I-Device
.	O
</s>
<s>
In	O
order	O
to	O
further	O
investigate	O
the	O
standard	O
discrete	O
SSIM	B-Algorithm
from	O
a	O
theoretical	O
perspective	O
,	O
the	O
continuous	O
SSIM	B-Algorithm
(	O
cSSIM	O
)	O
has	O
been	O
introduced	O
and	O
studied	O
in	O
the	O
context	O
of	O
Radial	O
basis	O
function	O
interpolation	O
.	O
</s>
<s>
The	O
r*	O
cross-correlation	O
metric	O
is	O
based	O
on	O
the	O
variance	O
metrics	O
of	O
SSIM	B-Algorithm
.	O
</s>
<s>
SSIM	B-Algorithm
has	O
also	O
been	O
used	O
on	O
the	O
gradient	O
of	O
images	O
,	O
making	O
it	O
"	O
G-SSIM	O
"	O
.	O
</s>
<s>
G-SSIM	O
is	O
especially	O
useful	O
on	O
blurred	O
images	O
.	O
</s>
<s>
For	O
example	O
,	O
4-G-r*	O
is	O
a	O
combination	O
of	O
4-SSIM	O
,	O
G-SSIM	O
,	O
and	O
r*	O
.	O
</s>
<s>
It	O
is	O
able	O
to	O
reflect	O
radiologist	O
preference	O
for	O
images	O
much	O
better	O
than	O
other	O
SSIM	B-Algorithm
variants	O
tested	O
.	O
</s>
<s>
SSIM	B-Algorithm
has	O
applications	O
in	O
a	O
variety	O
of	O
different	O
problems	O
.	O
</s>
<s>
Image	B-General_Concept
Compression	I-General_Concept
:	O
In	O
lossy	O
image	B-General_Concept
compression	I-General_Concept
,	O
information	O
is	O
deliberately	O
discarded	O
to	O
decrease	O
the	O
storage	O
space	O
of	O
images	O
and	O
video	O
.	O
</s>
<s>
The	O
MSE	B-Algorithm
is	O
typically	O
used	O
in	O
such	O
compression	O
schemes	O
.	O
</s>
<s>
According	O
to	O
its	O
authors	O
,	O
using	O
SSIM	B-Algorithm
instead	O
of	O
MSE	B-Algorithm
is	O
suggested	O
to	O
produce	O
better	O
results	O
for	O
the	O
decompressed	O
images	O
.	O
</s>
<s>
Image	B-Algorithm
Restoration	I-Algorithm
:	O
Image	B-Algorithm
restoration	I-Algorithm
focuses	O
on	O
solving	O
the	O
problem	O
where	O
is	O
the	O
blurry	O
image	O
that	O
should	O
be	O
restored	O
,	O
is	O
the	O
blur	O
kernel	O
,	O
is	O
the	O
additive	O
noise	O
and	O
is	O
the	O
original	O
image	O
we	O
wish	O
to	O
recover	O
.	O
</s>
<s>
However	O
,	O
the	O
Wiener	O
filter	O
design	O
is	O
based	O
on	O
the	O
MSE	B-Algorithm
.	O
</s>
<s>
Using	O
an	O
SSIM	B-Algorithm
variant	O
,	O
specifically	O
Stat-SSIM	O
,	O
is	O
claimed	O
to	O
produce	O
better	O
visual	O
results	O
,	O
according	O
to	O
the	O
algorithm	O
's	O
authors	O
.	O
</s>
<s>
Pattern	O
Recognition	O
:	O
Since	O
SSIM	B-Algorithm
mimics	O
aspects	O
of	O
human	O
perception	O
,	O
it	O
could	O
be	O
used	O
for	O
recognizing	O
patterns	O
.	O
</s>
<s>
When	O
faced	O
with	O
issues	O
like	O
image	O
scaling	O
,	O
translation	O
and	O
rotation	O
,	O
the	O
algorithm	O
's	O
authors	O
claim	O
that	O
it	O
is	O
better	O
to	O
use	O
CW-SSIM	O
,	O
which	O
is	O
insensitive	O
to	O
these	O
variations	O
and	O
may	O
be	O
directly	O
applied	O
by	O
template	O
matching	O
without	O
using	O
any	O
training	O
sample	O
.	O
</s>
<s>
Since	O
data-driven	O
pattern	O
recognition	O
approaches	O
may	O
produce	O
better	O
performance	O
when	O
a	O
large	O
amount	O
of	O
data	O
is	O
available	O
for	O
training	O
,	O
the	O
authors	O
suggest	O
using	O
CW-SSIM	O
in	O
data-driven	O
approaches	O
.	O
</s>
<s>
Due	O
to	O
its	O
popularity	O
,	O
SSIM	B-Algorithm
is	O
often	O
compared	O
to	O
other	O
metrics	O
,	O
including	O
more	O
simple	O
metrics	O
such	O
as	O
MSE	B-Algorithm
and	O
PSNR	O
,	O
and	O
other	O
perceptual	O
image	O
and	O
video	B-Device
quality	I-Device
metrics	I-Device
.	O
</s>
<s>
SSIM	B-Algorithm
has	O
been	O
repeatedly	O
shown	O
to	O
significantly	O
outperform	O
MSE	B-Algorithm
and	O
its	O
derivates	O
in	O
accuracy	O
,	O
including	O
research	O
by	O
its	O
own	O
authors	O
and	O
others	O
.	O
</s>
<s>
A	O
paper	O
by	O
Dosselmann	O
and	O
Yang	O
claims	O
that	O
the	O
performance	O
of	O
SSIM	B-Algorithm
is	O
"	O
much	O
closer	O
to	O
that	O
of	O
the	O
MSE	B-Algorithm
"	O
than	O
usually	O
assumed	O
.	O
</s>
<s>
While	O
they	O
do	O
not	O
dispute	O
the	O
advantage	O
of	O
SSIM	B-Algorithm
over	O
MSE	B-Algorithm
,	O
they	O
state	O
an	O
analytical	O
and	O
functional	O
dependency	O
between	O
the	O
two	O
metrics	O
.	O
</s>
<s>
According	O
to	O
their	O
research	O
,	O
SSIM	B-Algorithm
has	O
been	O
found	O
to	O
correlate	O
as	O
well	O
as	O
MSE-based	O
methods	O
on	O
subjective	O
databases	O
other	O
than	O
the	O
databases	O
from	O
SSIM	B-Algorithm
's	O
creators	O
.	O
</s>
<s>
As	O
an	O
example	O
,	O
they	O
cite	O
Reibman	O
and	O
Poole	O
,	O
who	O
found	O
that	O
MSE	B-Algorithm
outperformed	O
SSIM	B-Algorithm
on	O
a	O
database	O
containing	O
packet-loss	O
–	O
impaired	O
video	O
.	O
</s>
<s>
In	O
another	O
paper	O
,	O
an	O
analytical	O
link	O
between	O
PSNR	O
and	O
SSIM	B-Algorithm
was	O
identified	O
.	O
</s>
