<s>
Fractal	B-Algorithm
compression	I-Algorithm
is	O
a	O
lossy	B-Algorithm
compression	I-Algorithm
method	O
for	O
digital	B-Algorithm
images	I-Algorithm
,	O
based	O
on	O
fractals	B-Application
.	O
</s>
<s>
Fractal	B-Application
algorithms	O
convert	O
these	O
parts	O
into	O
mathematical	O
data	O
called	O
"	O
fractal	B-Application
codes	O
"	O
which	O
are	O
used	O
to	O
recreate	O
the	O
encoded	O
image	O
.	O
</s>
<s>
Fractal	B-Application
image	O
representation	O
may	O
be	O
described	O
mathematically	O
as	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
(	O
IFS	O
)	O
.	O
</s>
<s>
We	O
begin	O
with	O
the	O
representation	O
of	O
a	O
binary	B-Algorithm
image	I-Algorithm
,	O
where	O
the	O
image	O
may	O
be	O
thought	O
of	O
as	O
a	O
subset	O
of	O
.	O
</s>
<s>
That	O
is	O
,	O
H	O
is	O
an	O
operator	O
mapping	O
sets	O
to	O
sets	O
,	O
and	O
S	O
is	O
the	O
unique	O
set	O
satisfying	O
H(S )	O
=	O
S	O
.	O
The	O
idea	O
is	O
to	O
construct	O
the	O
IFS	O
such	O
that	O
this	O
set	O
S	O
is	O
the	O
input	O
binary	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
So	O
we	O
see	O
the	O
IFS	O
is	O
a	O
fractal	B-Application
representation	O
of	O
S	O
.	O
</s>
<s>
IFS	O
representation	O
can	O
be	O
extended	O
to	O
a	O
grayscale	O
image	O
by	O
considering	O
the	O
image	O
's	O
graph	B-Application
as	O
a	O
subset	O
of	O
.	O
</s>
<s>
A	O
challenging	O
problem	O
of	O
ongoing	O
research	O
in	O
fractal	B-Application
image	O
representation	O
is	O
how	O
to	O
choose	O
the	O
ƒ1	O
,...,	O
ƒN	O
such	O
that	O
its	O
fixed	O
point	O
approximates	O
the	O
input	O
image	O
,	O
and	O
how	O
to	O
do	O
this	O
efficiently	O
.	O
</s>
<s>
A	O
simple	O
approach	O
for	O
doing	O
so	O
is	O
the	O
following	O
partitioned	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
(	O
PIFS	O
)	O
:	O
</s>
<s>
This	O
bottleneck	O
of	O
searching	O
for	O
similar	O
blocks	O
is	O
why	O
PIFS	O
fractal	B-Application
encoding	O
is	O
much	O
slower	O
than	O
for	O
example	O
DCT	B-General_Concept
and	O
wavelet	O
based	O
image	O
representation	O
.	O
</s>
<s>
The	O
initial	O
square	O
partitioning	O
and	O
brute-force	B-Algorithm
search	I-Algorithm
algorithm	O
presented	O
by	O
Jacquin	O
provides	O
a	O
starting	O
point	O
for	O
further	O
research	O
and	O
extensions	O
in	O
many	O
possible	O
directions	O
--	O
different	O
ways	O
of	O
partitioning	O
the	O
image	O
into	O
range	O
blocks	O
of	O
various	O
sizes	O
and	O
shapes	O
;	O
fast	O
techniques	O
for	O
quickly	O
finding	O
a	O
close-enough	O
matching	O
domain	O
block	O
for	O
each	O
range	O
block	O
rather	O
than	O
brute-force	O
searching	O
,	O
such	O
as	O
fast	O
motion	O
estimation	O
algorithms	O
;	O
different	O
ways	O
of	O
encoding	O
the	O
mapping	O
from	O
the	O
domain	O
block	O
to	O
the	O
range	O
block	O
;	O
etc	O
.	O
</s>
<s>
Other	O
researchers	O
attempt	O
to	O
find	O
algorithms	O
to	O
automatically	O
encode	O
an	O
arbitrary	O
image	O
as	O
RIFS	O
(	O
recurrent	O
iterated	B-Algorithm
function	I-Algorithm
systems	I-Algorithm
)	O
or	O
global	O
IFS	O
,	O
rather	O
than	O
PIFS	O
;	O
and	O
algorithms	O
for	O
fractal	B-Application
video	O
compression	O
including	O
motion	B-Algorithm
compensation	I-Algorithm
and	O
three	O
dimensional	O
iterated	B-Algorithm
function	I-Algorithm
systems	I-Algorithm
.	O
</s>
<s>
Fractal	B-Algorithm
image	I-Algorithm
compression	I-Algorithm
has	O
many	O
similarities	O
to	O
vector	B-Algorithm
quantization	I-Algorithm
image	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
With	O
fractal	B-Algorithm
compression	I-Algorithm
,	O
encoding	O
is	O
extremely	O
computationally	O
expensive	O
because	O
of	O
the	O
search	O
used	O
to	O
find	O
the	O
self-similarities	O
.	O
</s>
<s>
While	O
this	O
asymmetry	O
has	O
so	O
far	O
made	O
it	O
impractical	O
for	O
real	O
time	O
applications	O
,	O
when	O
video	O
is	O
archived	O
for	O
distribution	O
from	O
disk	O
storage	O
or	O
file	O
downloads	O
fractal	B-Algorithm
compression	I-Algorithm
becomes	O
more	O
competitive	O
.	O
</s>
<s>
At	O
common	O
compression	O
ratios	O
,	O
up	O
to	O
about	O
50:1	O
,	O
fractal	B-Algorithm
compression	I-Algorithm
provides	O
similar	O
results	O
to	O
DCT-based	B-General_Concept
algorithms	O
such	O
as	O
JPEG	O
.	O
</s>
<s>
At	O
high	O
compression	O
ratios	O
fractal	B-Algorithm
compression	I-Algorithm
may	O
offer	O
superior	O
quality	O
.	O
</s>
<s>
Fractal	B-Application
video	O
compression	O
ratios	O
of	O
25:1	O
–	O
244:1	O
have	O
been	O
achieved	O
in	O
reasonable	O
compression	O
times	O
(	O
2.4	O
to	O
66	O
sec/frame	O
)	O
.	O
</s>
<s>
An	O
inherent	O
feature	O
of	O
fractal	B-Algorithm
compression	I-Algorithm
is	O
that	O
images	O
become	O
resolution	O
independent	O
after	O
being	O
converted	O
to	O
fractal	B-Application
code	O
.	O
</s>
<s>
This	O
is	O
because	O
the	O
iterated	B-Algorithm
function	I-Algorithm
systems	I-Algorithm
in	O
the	O
compressed	O
file	O
scale	O
indefinitely	O
.	O
</s>
<s>
This	O
indefinite	O
scaling	O
property	O
of	O
a	O
fractal	B-Application
is	O
known	O
as	O
"	O
fractal	B-Application
scaling	O
"	O
.	O
</s>
<s>
The	O
resolution	O
independence	O
of	O
a	O
fractal-encoded	O
image	O
can	O
be	O
used	O
to	O
increase	O
the	O
display	O
resolution	O
of	O
an	O
image	O
.	O
</s>
<s>
This	O
process	O
is	O
also	O
known	O
as	O
"	O
fractal	B-Application
interpolation	O
"	O
.	O
</s>
<s>
In	O
fractal	B-Application
interpolation	O
,	O
an	O
image	O
is	O
encoded	O
into	O
fractal	B-Application
codes	O
via	O
fractal	B-Algorithm
compression	I-Algorithm
,	O
and	O
subsequently	O
decompressed	O
at	O
a	O
higher	O
resolution	O
.	O
</s>
<s>
The	O
result	O
is	O
an	O
up-sampled	O
image	O
in	O
which	O
iterated	B-Algorithm
function	I-Algorithm
systems	I-Algorithm
have	O
been	O
used	O
as	O
the	O
interpolant	O
.	O
</s>
<s>
Fractal	B-Application
interpolation	O
maintains	O
geometric	O
detail	O
very	O
well	O
compared	O
to	O
traditional	O
interpolation	O
methods	O
like	O
bilinear	O
interpolation	O
and	O
bicubic	B-Algorithm
interpolation	I-Algorithm
.	O
</s>
<s>
Michael	O
Barnsley	O
led	O
development	O
of	O
fractal	B-Algorithm
compression	I-Algorithm
in	O
1987	O
,	O
and	O
was	O
granted	O
several	O
patents	O
on	O
the	O
technology	O
.	O
</s>
<s>
The	O
most	O
widely	O
known	O
practical	O
fractal	B-Algorithm
compression	I-Algorithm
algorithm	O
was	O
invented	O
by	O
Barnsley	O
and	O
Alan	O
Sloan	O
.	O
</s>
<s>
All	O
methods	O
are	O
based	O
on	O
the	O
fractal	B-Application
transform	O
using	O
iterated	B-Algorithm
function	I-Algorithm
systems	I-Algorithm
.	O
</s>
<s>
Michael	O
Barnsley	O
and	O
Alan	O
Sloan	O
formed	O
Iterated	O
Systems	O
Inc	O
.	O
in	O
1987	O
which	O
was	O
granted	O
over	O
20	O
additional	O
patents	O
related	O
to	O
fractal	B-Algorithm
compression	I-Algorithm
.	O
</s>
<s>
A	O
major	O
breakthrough	O
for	O
Iterated	O
Systems	O
Inc	O
.	O
was	O
the	O
automatic	O
fractal	B-Application
transform	O
process	O
which	O
eliminated	O
the	O
need	O
for	O
human	O
intervention	O
during	O
compression	O
as	O
was	O
the	O
case	O
in	O
early	O
experimentation	O
with	O
fractal	B-Algorithm
compression	I-Algorithm
technology	O
.	O
</s>
<s>
In	O
1992	O
,	O
Iterated	O
Systems	O
Inc	O
.	O
received	O
a	O
US	O
$2.1	O
million	O
government	O
grant	O
to	O
develop	O
a	O
prototype	O
digital	B-Algorithm
image	I-Algorithm
storage	O
and	O
decompression	O
chip	O
using	O
fractal	B-Application
transform	O
image	B-General_Concept
compression	I-General_Concept
technology	O
.	O
</s>
<s>
Fractal	B-Algorithm
image	I-Algorithm
compression	I-Algorithm
has	O
been	O
used	O
in	O
a	O
number	O
of	O
commercial	O
applications	O
:	O
onOne	O
Software	O
,	O
developed	O
under	O
license	O
from	O
Iterated	O
Systems	O
Inc.	O
,	O
Genuine	O
Fractals	B-Application
5	O
which	O
is	O
a	O
Photoshop	B-Operating_System
plugin	O
capable	O
of	O
saving	O
files	O
in	O
compressed	O
FIF	O
(	O
Fractal	B-Application
Image	O
Format	O
)	O
.	O
</s>
<s>
To	O
date	O
the	O
most	O
successful	O
use	O
of	O
still	O
fractal	B-Algorithm
image	I-Algorithm
compression	I-Algorithm
is	O
by	O
Microsoft	O
in	O
its	O
Encarta	B-Application
multimedia	O
encyclopedia	O
,	O
also	O
under	O
license	O
.	O
</s>
<s>
Iterated	O
Systems	O
Inc	O
.	O
supplied	O
a	O
shareware	O
encoder	O
(	O
Fractal	B-Application
Imager	O
)	O
,	O
a	O
stand-alone	O
decoder	O
,	O
a	O
Netscape	O
plug-in	O
decoder	O
and	O
a	O
development	O
package	O
for	O
use	O
under	O
Windows	O
.	O
</s>
<s>
As	O
wavelet-based	O
methods	O
of	O
image	B-General_Concept
compression	I-General_Concept
improved	O
and	O
were	O
more	O
easily	O
licensed	O
by	O
commercial	O
software	O
vendors	O
the	O
adoption	O
of	O
the	O
Fractal	B-Application
Image	O
Format	O
failed	O
to	O
evolve	O
.	O
</s>
<s>
During	O
the	O
1990s	O
Iterated	O
Systems	O
Inc	O
.	O
and	O
its	O
partners	O
expended	O
considerable	O
resources	O
to	O
bring	O
fractal	B-Algorithm
compression	I-Algorithm
to	O
video	O
.	O
</s>
<s>
While	O
compression	O
results	O
were	O
promising	O
,	O
computer	O
hardware	O
of	O
that	O
time	O
lacked	O
the	O
processing	O
power	O
for	O
fractal	B-Application
video	O
compression	O
to	O
be	O
practical	O
beyond	O
a	O
few	O
select	O
usages	O
.	O
</s>
<s>
ClearVideo	O
also	O
known	O
as	O
RealVideo	B-Algorithm
(	O
Fractal	B-Application
)	O
and	O
SoftVideo	O
were	O
early	O
fractal	B-Application
video	O
compression	O
products	O
.	O
</s>
<s>
In	O
1994	O
SoftVideo	O
was	O
licensed	O
to	O
Spectrum	O
Holobyte	O
for	O
use	O
in	O
its	O
CD-ROM	B-Device
games	O
including	O
Falcon	O
Gold	O
and	O
Star	O
Trek	O
:	O
The	O
Next	O
Generation	O
A	O
Final	O
Unity	O
.	O
</s>
<s>
The	O
original	O
ClearVideo	O
1.2	O
decoder	O
driver	O
is	O
still	O
supported	O
by	O
Microsoft	O
in	O
Windows	B-Device
Media	I-Device
Player	I-Device
although	O
the	O
encoder	O
is	O
no	O
longer	O
supported	O
.	O
</s>
<s>
In	O
summary	O
,	O
it	O
is	O
a	O
simple	O
quadtree	O
block-copying	O
system	O
with	O
neither	O
the	O
bandwidth	O
efficiency	O
nor	O
PSNR	O
quality	O
of	O
traditional	O
DCT-based	B-General_Concept
codecs	O
.	O
</s>
<s>
In	O
January	O
2016	O
,	O
TMMI	O
announced	O
that	O
it	O
was	O
abandoning	O
fractal-based	O
technology	O
altogether	O
.	O
</s>
<s>
Research	O
papers	O
between	O
1997	O
and	O
2007	O
discussed	O
possible	O
solutions	O
to	O
improve	O
fractal	B-Application
algorithms	O
and	O
encoding	O
hardware	O
.	O
</s>
<s>
The	O
Netpbm	B-Language
library	O
includes	O
the	O
Fiasco	O
library	O
.	O
</s>
<s>
Femtosoft	O
developed	O
an	O
implementation	O
of	O
fractal	B-Algorithm
image	I-Algorithm
compression	I-Algorithm
in	O
Object	B-Language
Pascal	I-Language
and	O
Java	B-Language
.	O
</s>
