<s>
Pyramid	B-Algorithm
,	O
or	O
pyramid	B-Algorithm
representation	O
,	O
is	O
a	O
type	O
of	O
multi-scale	O
signal	O
representation	O
developed	O
by	O
the	O
computer	B-Application
vision	I-Application
,	O
image	B-Algorithm
processing	I-Algorithm
and	O
signal	O
processing	O
communities	O
,	O
in	O
which	O
a	O
signal	O
or	O
an	O
image	O
is	O
subject	O
to	O
repeated	O
smoothing	B-Application
and	O
subsampling	B-Algorithm
.	O
</s>
<s>
Pyramid	B-Algorithm
representation	O
is	O
a	O
predecessor	O
to	O
scale-space	B-Algorithm
representation	I-Algorithm
and	O
multiresolution	O
analysis	O
.	O
</s>
<s>
There	O
are	O
two	O
main	O
types	O
of	O
pyramids	B-Algorithm
:	O
lowpass	O
and	O
bandpass	O
.	O
</s>
<s>
A	O
lowpass	O
pyramid	B-Algorithm
is	O
made	O
by	O
smoothing	B-Application
the	O
image	O
with	O
an	O
appropriate	O
smoothing	B-Application
filter	O
and	O
then	O
subsampling	B-Algorithm
the	O
smoothed	B-Application
image	O
,	O
usually	O
by	O
a	O
factor	O
of	O
2	O
along	O
each	O
coordinate	O
direction	O
.	O
</s>
<s>
Each	O
cycle	O
of	O
this	O
process	O
results	O
in	O
a	O
smaller	O
image	O
with	O
increased	O
smoothing	B-Application
,	O
but	O
with	O
decreased	O
spatial	O
sampling	O
density	O
(	O
that	O
is	O
,	O
decreased	O
image	O
resolution	O
)	O
.	O
</s>
<s>
If	O
illustrated	O
graphically	O
,	O
the	O
entire	O
multi-scale	O
representation	O
will	O
look	O
like	O
a	O
pyramid	B-Algorithm
,	O
with	O
the	O
original	O
image	O
on	O
the	O
bottom	O
and	O
each	O
cycle	O
's	O
resulting	O
smaller	O
image	O
stacked	O
one	O
atop	O
the	O
other	O
.	O
</s>
<s>
A	O
bandpass	O
pyramid	B-Algorithm
is	O
made	O
by	O
forming	O
the	O
difference	O
between	O
images	O
at	O
adjacent	O
levels	O
in	O
the	O
pyramid	B-Algorithm
and	O
performing	O
image	O
interpolation	O
between	O
adjacent	O
levels	O
of	O
resolution	O
,	O
to	O
enable	O
computation	O
of	O
pixelwise	O
differences	O
.	O
</s>
<s>
A	O
variety	O
of	O
different	O
smoothing	B-Application
kernels	B-Algorithm
have	O
been	O
proposed	O
for	O
generating	O
pyramids	B-Algorithm
.	O
</s>
<s>
Among	O
the	O
suggestions	O
that	O
have	O
been	O
given	O
,	O
the	O
binomial	O
kernels	B-Algorithm
arising	O
from	O
the	O
binomial	O
coefficients	O
stand	O
out	O
as	O
a	O
particularly	O
useful	O
and	O
theoretically	O
well-founded	O
class	O
.	O
</s>
<s>
If	O
motivated	O
by	O
specific	O
requirements	O
,	O
intermediate	O
scale	O
levels	O
may	O
also	O
be	O
generated	O
where	O
the	O
subsampling	B-Algorithm
stage	O
is	O
sometimes	O
left	O
out	O
,	O
leading	O
to	O
an	O
oversampled	O
or	O
hybrid	O
pyramid	B-Algorithm
.	O
</s>
<s>
With	O
the	O
increasing	O
computational	O
efficiency	O
of	O
CPUs	B-Device
available	O
today	O
,	O
it	O
is	O
in	O
some	O
situations	O
also	O
feasible	O
to	O
use	O
wider	O
supported	O
Gaussian	O
filters	O
as	O
smoothing	B-Application
kernels	B-Algorithm
in	O
the	O
pyramid	B-Algorithm
generation	O
steps	O
.	O
</s>
<s>
In	O
a	O
Gaussian	O
pyramid	B-Algorithm
,	O
subsequent	O
images	O
are	O
weighted	O
down	O
using	O
a	O
Gaussian	O
average	O
(	O
Gaussian	B-Error_Name
blur	I-Error_Name
)	O
and	O
scaled	O
down	O
.	O
</s>
<s>
Each	O
pixel	O
containing	O
a	O
local	O
average	O
corresponds	O
to	O
a	O
neighborhood	O
pixel	O
on	O
a	O
lower	O
level	O
of	O
the	O
pyramid	B-Algorithm
.	O
</s>
<s>
A	O
Laplacian	O
pyramid	B-Algorithm
is	O
very	O
similar	O
to	O
a	O
Gaussian	O
pyramid	B-Algorithm
but	O
saves	O
the	O
difference	O
image	O
of	O
the	O
blurred	O
versions	O
between	O
each	O
levels	O
.	O
</s>
<s>
This	O
technique	O
can	O
be	O
used	O
in	O
image	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
A	O
steerable	O
pyramid	B-Algorithm
,	O
developed	O
by	O
Simoncelli	O
and	O
others	O
,	O
is	O
an	O
implementation	O
of	O
a	O
multi-scale	O
,	O
multi-orientation	O
band-pass	O
filter	O
bank	O
used	O
for	O
applications	O
including	O
image	B-General_Concept
compression	I-General_Concept
,	O
texture	O
synthesis	O
,	O
and	O
object	O
recognition	O
.	O
</s>
<s>
It	O
can	O
be	O
thought	O
of	O
as	O
an	O
orientation	O
selective	O
version	O
of	O
a	O
Laplacian	O
pyramid	B-Algorithm
,	O
in	O
which	O
a	O
bank	O
of	O
steerable	B-Algorithm
filters	I-Algorithm
are	O
used	O
at	O
each	O
level	O
of	O
the	O
pyramid	B-Algorithm
instead	O
of	O
a	O
single	O
Laplacian	O
or	O
Gaussian	O
filter	O
.	O
</s>
<s>
In	O
the	O
early	O
days	O
of	O
computer	B-Application
vision	I-Application
,	O
pyramids	B-Algorithm
were	O
used	O
as	O
the	O
main	O
type	O
of	O
multi-scale	O
representation	O
for	O
computing	O
multi-scale	O
image	O
features	O
from	O
real-world	O
image	O
data	O
.	O
</s>
<s>
More	O
recent	O
techniques	O
include	O
scale-space	B-Algorithm
representation	I-Algorithm
,	O
which	O
has	O
been	O
popular	O
among	O
some	O
researchers	O
due	O
to	O
its	O
theoretical	O
foundation	O
,	O
the	O
ability	O
to	O
decouple	O
the	O
subsampling	B-Algorithm
stage	O
from	O
the	O
multi-scale	O
representation	O
,	O
the	O
more	O
powerful	O
tools	O
for	O
theoretical	O
analysis	O
as	O
well	O
as	O
the	O
ability	O
to	O
compute	O
a	O
representation	O
at	O
any	O
desired	O
scale	O
,	O
thus	O
avoiding	O
the	O
algorithmic	O
problems	O
of	O
relating	O
image	O
representations	O
at	O
different	O
resolution	O
.	O
</s>
<s>
Nevertheless	O
,	O
pyramids	B-Algorithm
are	O
still	O
frequently	O
used	O
for	O
expressing	O
computationally	O
efficient	O
approximations	O
to	O
scale-space	B-Algorithm
representation	I-Algorithm
.	O
</s>
<s>
Levels	O
of	O
a	O
Laplacian	O
pyramid	B-Algorithm
can	O
be	O
added	O
to	O
or	O
removed	O
from	O
the	O
original	O
image	O
to	O
amplify	O
or	O
reduce	O
detail	O
at	O
different	O
scales	O
.	O
</s>
<s>
However	O
,	O
detail	O
manipulation	O
of	O
this	O
form	O
is	O
known	O
to	O
produce	O
halo	O
artifacts	O
in	O
many	O
cases	O
,	O
leading	O
to	O
the	O
development	O
of	O
alternatives	O
such	O
as	O
the	O
bilateral	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Some	O
image	B-General_Concept
compression	I-General_Concept
file	O
formats	O
use	O
the	O
Adam7	B-Algorithm
algorithm	I-Algorithm
or	O
some	O
other	O
interlacing	O
technique	O
.	O
</s>
<s>
These	O
can	O
be	O
seen	O
as	O
a	O
kind	O
of	O
image	B-Algorithm
pyramid	I-Algorithm
.	O
</s>
