<s>
Edge	B-Algorithm
detection	I-Algorithm
includes	O
a	O
variety	O
of	O
mathematical	O
methods	O
that	O
aim	O
at	O
identifying	O
edges	O
,	O
curves	O
in	O
a	O
digital	B-Algorithm
image	I-Algorithm
at	O
which	O
the	O
image	O
brightness	O
changes	O
sharply	O
or	O
,	O
more	O
formally	O
,	O
has	O
discontinuities	O
.	O
</s>
<s>
The	O
same	O
problem	O
of	O
finding	O
discontinuities	O
in	O
one-dimensional	O
signals	O
is	O
known	O
as	O
step	B-Algorithm
detection	I-Algorithm
and	O
the	O
problem	O
of	O
finding	O
signal	O
discontinuities	O
over	O
time	O
is	O
known	O
as	O
change	B-General_Concept
detection	I-General_Concept
.	O
</s>
<s>
Edge	B-Algorithm
detection	I-Algorithm
is	O
a	O
fundamental	O
tool	O
in	O
image	B-Algorithm
processing	I-Algorithm
,	O
machine	B-General_Concept
vision	I-General_Concept
and	O
computer	B-Application
vision	I-Application
,	O
particularly	O
in	O
the	O
areas	O
of	O
feature	O
detection	O
and	O
feature	B-Algorithm
extraction	I-Algorithm
.	O
</s>
<s>
Thus	O
,	O
applying	O
an	O
edge	B-Algorithm
detection	I-Algorithm
algorithm	O
to	O
an	O
image	O
may	O
significantly	O
reduce	O
the	O
amount	O
of	O
data	O
to	O
be	O
processed	O
and	O
may	O
therefore	O
filter	O
out	O
information	O
that	O
may	O
be	O
regarded	O
as	O
less	O
relevant	O
,	O
while	O
preserving	O
the	O
important	O
structural	O
properties	O
of	O
an	O
image	O
.	O
</s>
<s>
If	O
the	O
edge	B-Algorithm
detection	I-Algorithm
step	O
is	O
successful	O
,	O
the	O
subsequent	O
task	O
of	O
interpreting	O
the	O
information	O
contents	O
in	O
the	O
original	O
image	O
may	O
therefore	O
be	O
substantially	O
simplified	O
.	O
</s>
<s>
Edge	B-Algorithm
detection	I-Algorithm
is	O
one	O
of	O
the	O
fundamental	O
steps	O
in	O
image	B-Algorithm
processing	I-Algorithm
,	O
image	O
analysis	O
,	O
image	O
pattern	O
recognition	O
,	O
and	O
computer	B-Application
vision	I-Application
techniques	O
.	O
</s>
<s>
In	O
contrast	O
a	O
line	O
(	O
as	O
can	O
be	O
extracted	O
by	O
a	O
ridge	O
detector	O
)	O
can	O
be	O
a	O
small	O
number	O
of	O
pixels	B-Algorithm
of	O
a	O
different	O
color	O
on	O
an	O
otherwise	O
unchanging	O
background	O
.	O
</s>
<s>
To	O
illustrate	O
why	O
edge	B-Algorithm
detection	I-Algorithm
is	O
not	O
a	O
trivial	O
task	O
,	O
consider	O
the	O
problem	O
of	O
detecting	O
edges	O
in	O
the	O
following	O
one-dimensional	O
signal	O
.	O
</s>
<s>
Here	O
,	O
we	O
may	O
intuitively	O
say	O
that	O
there	O
should	O
be	O
an	O
edge	O
between	O
the	O
4th	O
and	O
5th	O
pixels	B-Algorithm
.	O
</s>
<s>
If	O
the	O
intensity	O
difference	O
were	O
smaller	O
between	O
the	O
4th	O
and	O
the	O
5th	O
pixels	B-Algorithm
and	O
if	O
the	O
intensity	O
differences	O
between	O
the	O
adjacent	O
neighboring	O
pixels	B-Algorithm
were	O
higher	O
,	O
it	O
would	O
not	O
be	O
as	O
easy	O
to	O
say	O
that	O
there	O
should	O
be	O
an	O
edge	O
in	O
the	O
corresponding	O
region	O
.	O
</s>
<s>
Hence	O
,	O
to	O
firmly	O
state	O
a	O
specific	O
threshold	O
on	O
how	O
large	O
the	O
intensity	O
change	O
between	O
two	O
neighbouring	O
pixels	B-Algorithm
must	O
be	O
for	O
us	O
to	O
say	O
that	O
there	O
should	O
be	O
an	O
edge	O
between	O
these	O
pixels	B-Algorithm
is	O
not	O
always	O
simple	O
.	O
</s>
<s>
Indeed	O
,	O
this	O
is	O
one	O
of	O
the	O
reasons	O
why	O
edge	B-Algorithm
detection	I-Algorithm
may	O
be	O
a	O
non-trivial	O
problem	O
unless	O
the	O
objects	O
in	O
the	O
scene	O
are	O
particularly	O
simple	O
and	O
the	O
illumination	O
conditions	O
can	O
be	O
well	O
controlled	O
(	O
see	O
for	O
example	O
,	O
the	O
edges	O
extracted	O
from	O
the	O
image	O
with	O
the	O
girl	O
above	O
)	O
.	O
</s>
<s>
There	O
are	O
many	O
methods	O
for	O
edge	B-Algorithm
detection	I-Algorithm
,	O
but	O
most	O
of	O
them	O
can	O
be	O
grouped	O
into	O
two	O
categories	O
,	O
search-based	O
and	O
zero-crossing	B-Algorithm
based	O
.	O
</s>
<s>
The	O
search-based	O
methods	O
detect	O
edges	O
by	O
first	O
computing	O
a	O
measure	O
of	O
edge	O
strength	O
,	O
usually	O
a	O
first-order	O
derivative	B-Algorithm
expression	O
such	O
as	O
the	O
gradient	O
magnitude	O
,	O
and	O
then	O
searching	O
for	O
local	O
directional	O
maxima	O
of	O
the	O
gradient	O
magnitude	O
using	O
a	O
computed	O
estimate	O
of	O
the	O
local	O
orientation	O
of	O
the	O
edge	O
,	O
usually	O
the	O
gradient	O
direction	O
.	O
</s>
<s>
The	O
zero-crossing	B-Algorithm
based	O
methods	O
search	O
for	O
zero	B-Algorithm
crossings	I-Algorithm
in	O
a	O
second-order	O
derivative	B-Algorithm
expression	O
computed	O
from	O
the	O
image	O
in	O
order	O
to	O
find	O
edges	O
,	O
usually	O
the	O
zero-crossings	B-Algorithm
of	O
the	O
Laplacian	O
or	O
the	O
zero-crossings	B-Algorithm
of	O
a	O
non-linear	O
differential	O
expression	O
.	O
</s>
<s>
As	O
a	O
pre-processing	O
step	O
to	O
edge	B-Algorithm
detection	I-Algorithm
,	O
a	O
smoothing	O
stage	O
,	O
typically	O
Gaussian	B-Error_Name
smoothing	I-Error_Name
,	O
is	O
almost	O
always	O
applied	O
(	O
see	O
also	O
noise	B-Algorithm
reduction	O
)	O
.	O
</s>
<s>
The	O
edge	B-Algorithm
detection	I-Algorithm
methods	O
that	O
have	O
been	O
published	O
mainly	O
differ	O
in	O
the	O
types	O
of	O
smoothing	O
filters	O
that	O
are	O
applied	O
and	O
the	O
way	O
the	O
measures	O
of	O
edge	O
strength	O
are	O
computed	O
.	O
</s>
<s>
As	O
many	O
edge	B-Algorithm
detection	I-Algorithm
methods	O
rely	O
on	O
the	O
computation	O
of	O
image	O
gradients	O
,	O
they	O
also	O
differ	O
in	O
the	O
types	O
of	O
filters	O
used	O
for	O
computing	O
gradient	O
estimates	O
in	O
the	O
x	O
-	O
and	O
y-directions	O
.	O
</s>
<s>
A	O
survey	O
of	O
a	O
number	O
of	O
different	O
edge	B-Algorithm
detection	I-Algorithm
methods	O
can	O
be	O
found	O
in	O
(	O
Ziou	O
and	O
Tabbone	O
1998	O
)	O
;	O
see	O
also	O
the	O
encyclopedia	O
articles	O
on	O
edge	B-Algorithm
detection	I-Algorithm
in	O
Encyclopedia	O
of	O
Mathematics	O
and	O
Encyclopedia	O
of	O
Computer	O
Science	O
and	O
Engineering	O
.	O
</s>
<s>
He	O
also	O
showed	O
that	O
this	O
filter	O
can	O
be	O
well	O
approximated	O
by	O
first-order	O
derivatives	B-Algorithm
of	O
Gaussians	O
.	O
</s>
<s>
Looking	O
for	O
the	O
zero	B-Algorithm
crossing	I-Algorithm
of	O
the	O
2nd	B-Algorithm
derivative	I-Algorithm
along	O
the	O
gradient	O
direction	O
was	O
first	O
proposed	O
by	O
Haralick	O
.	O
</s>
<s>
It	O
took	O
less	O
than	O
two	O
decades	O
to	O
find	O
a	O
modern	O
geometric	O
variational	O
meaning	O
for	O
that	O
operator	O
that	O
links	O
it	O
to	O
the	O
Marr	B-Algorithm
–	I-Algorithm
Hildreth	I-Algorithm
(	O
zero	B-Algorithm
crossing	I-Algorithm
of	O
the	O
Laplacian	O
)	O
edge	O
detector	O
.	O
</s>
<s>
Although	O
his	O
work	O
was	O
done	O
in	O
the	O
early	O
days	O
of	O
computer	B-Application
vision	I-Application
,	O
the	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
(	O
including	O
its	O
variations	O
)	O
is	O
still	O
a	O
state-of-the-art	O
edge	O
detector	O
.	O
</s>
<s>
This	O
method	O
uses	O
no	O
brightness	O
of	O
the	O
image	O
but	O
only	O
the	O
intensities	O
of	O
the	O
color	O
channels	O
which	O
is	O
important	O
for	O
detecting	O
an	O
edge	O
between	O
two	O
adjacent	O
pixels	B-Algorithm
of	O
equal	O
brightness	O
but	O
different	O
colors	O
.	O
</s>
<s>
In	O
each	O
horizontal	O
line	O
six	O
consequent	O
adjacent	O
pixels	B-Algorithm
are	O
considered	O
and	O
five	O
color	O
difference	O
between	O
each	O
two	O
adjacent	O
pixels	B-Algorithm
are	O
calculated	O
.	O
</s>
<s>
Each	O
color	O
difference	O
is	O
the	O
sum	O
of	O
absolute	O
differences	O
of	O
the	O
intensities	O
of	O
the	O
color	O
channels	O
Red	O
,	O
Green	O
,	O
and	O
Blue	O
of	O
the	O
corresponding	O
adjacent	O
pixels	B-Algorithm
.	O
</s>
<s>
Certain	O
conditions	O
for	O
the	O
values	O
and	O
signs	O
of	O
the	O
five	O
color	O
differences	O
are	O
specified	O
in	O
such	O
way	O
that	O
if	O
the	O
conditions	O
are	O
fulfilled	O
,	O
then	O
a	O
short	O
vertical	O
stroke	O
is	O
put	O
between	O
the	O
third	O
and	O
the	O
fourth	O
of	O
the	O
six	O
pixels	B-Algorithm
as	O
the	O
label	O
of	O
the	O
edge	O
.	O
</s>
<s>
In	O
this	O
case	O
a	O
short	O
horizontal	O
stroke	O
is	O
put	O
between	O
the	O
third	O
and	O
the	O
fourth	O
of	O
the	O
six	O
subsequent	O
pixels	B-Algorithm
.	O
</s>
<s>
This	O
method	O
is	O
robust	O
and	O
very	O
fast	O
and	O
,	O
what	O
is	O
more	O
important	O
,	O
it	O
can	O
detect	O
edges	O
between	O
adjacent	O
pixels	B-Algorithm
of	O
equal	O
brightness	O
’s	O
if	O
the	O
color	O
difference	O
between	O
these	O
pixels	B-Algorithm
is	O
greater	O
than	O
the	O
threshold	O
.	O
</s>
<s>
The	O
Canny	O
–	O
Deriche	O
detector	O
was	O
derived	O
from	O
similar	O
mathematical	O
criteria	O
as	O
the	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
,	O
although	O
starting	O
from	O
a	O
discrete	O
viewpoint	O
and	O
then	O
leading	O
to	O
a	O
set	O
of	O
recursive	O
filters	O
for	O
image	O
smoothing	O
instead	O
of	O
exponential	O
filters	O
or	O
Gaussian	O
filters	O
.	O
</s>
<s>
The	O
differential	O
edge	O
detector	O
described	O
below	O
can	O
be	O
seen	O
as	O
a	O
reformulation	O
of	O
Canny	O
's	O
method	O
from	O
the	O
viewpoint	O
of	O
differential	O
invariants	O
computed	O
from	O
a	O
scale	B-Algorithm
space	I-Algorithm
representation	I-Algorithm
leading	O
to	O
a	O
number	O
of	O
advantages	O
in	O
terms	O
of	O
both	O
theoretical	O
analysis	O
and	O
sub-pixel	O
implementation	O
.	O
</s>
<s>
In	O
that	O
aspect	O
,	O
Log	B-Algorithm
Gabor	I-Algorithm
filter	I-Algorithm
have	O
been	O
shown	O
to	O
be	O
a	O
good	O
choice	O
to	O
extract	O
boundaries	O
in	O
natural	O
scenes	O
.	O
</s>
<s>
The	O
well-known	O
and	O
earlier	O
Sobel	B-Algorithm
operator	I-Algorithm
is	O
based	O
on	O
the	O
following	O
filters	O
:	O
</s>
<s>
Given	O
such	O
estimates	O
of	O
first-order	O
image	B-Algorithm
derivatives	I-Algorithm
,	O
the	O
gradient	O
magnitude	O
is	O
then	O
computed	O
as	O
:	O
</s>
<s>
Other	O
first-order	O
difference	O
operators	O
for	O
estimating	O
image	O
gradient	O
have	O
been	O
proposed	O
in	O
the	O
Prewitt	B-Algorithm
operator	I-Algorithm
,	O
Roberts	B-Algorithm
cross	I-Algorithm
,	O
Kayyali	O
operator	O
and	O
Frei	O
–	O
Chen	O
operator	O
.	O
</s>
<s>
The	O
lower	O
the	O
threshold	O
,	O
the	O
more	O
edges	O
will	O
be	O
detected	O
,	O
and	O
the	O
result	O
will	O
be	O
increasingly	O
susceptible	O
to	O
noise	B-Algorithm
and	O
detecting	O
edges	O
of	O
irrelevant	O
features	O
in	O
the	O
image	O
.	O
</s>
<s>
For	O
edges	O
detected	O
with	O
non-maximum	O
suppression	O
however	O
,	O
the	O
edge	O
curves	O
are	O
thin	O
by	O
definition	O
and	O
the	O
edge	O
pixels	B-Algorithm
can	O
be	O
linked	O
into	O
edge	O
polygon	O
by	O
an	O
edge	O
linking	O
(	O
edge	O
tracking	O
)	O
procedure	O
.	O
</s>
<s>
On	O
a	O
discrete	O
grid	O
,	O
the	O
non-maximum	O
suppression	O
stage	O
can	O
be	O
implemented	O
by	O
estimating	O
the	O
gradient	O
direction	O
using	O
first-order	O
derivatives	B-Algorithm
,	O
then	O
rounding	O
off	O
the	O
gradient	O
direction	O
to	O
multiples	O
of	O
45	O
degrees	O
,	O
and	O
finally	O
comparing	O
the	O
values	O
of	O
the	O
gradient	O
magnitude	O
in	O
the	O
estimated	O
gradient	O
direction	O
.	O
</s>
<s>
A	O
commonly	O
used	O
approach	O
to	O
handle	O
the	O
problem	O
of	O
appropriate	O
thresholds	O
for	O
thresholding	B-Algorithm
is	O
by	O
using	O
thresholding	B-Algorithm
with	O
hysteresis	O
.	O
</s>
<s>
Once	O
we	O
have	O
a	O
start	O
point	O
,	O
we	O
then	O
trace	O
the	O
path	O
of	O
the	O
edge	O
through	O
the	O
image	O
pixel	B-Algorithm
by	O
pixel	B-Algorithm
,	O
marking	O
an	O
edge	O
whenever	O
we	O
are	O
above	O
the	O
lower	O
threshold	O
.	O
</s>
<s>
This	O
approach	O
makes	O
the	O
assumption	O
that	O
edges	O
are	O
likely	O
to	O
be	O
in	O
continuous	O
curves	O
,	O
and	O
allows	O
us	O
to	O
follow	O
a	O
faint	O
section	O
of	O
an	O
edge	O
we	O
have	O
previously	O
seen	O
,	O
without	O
meaning	O
that	O
every	O
noisy	O
pixel	B-Algorithm
in	O
the	O
image	O
is	O
marked	O
down	O
as	O
an	O
edge	O
.	O
</s>
<s>
Still	O
,	O
however	O
,	O
we	O
have	O
the	O
problem	O
of	O
choosing	O
appropriate	O
thresholding	B-Algorithm
parameters	O
,	O
and	O
suitable	O
thresholding	B-Algorithm
values	O
may	O
vary	O
over	O
the	O
image	O
.	O
</s>
<s>
This	O
technique	O
is	O
employed	O
after	O
the	O
image	O
has	O
been	O
filtered	O
for	O
noise	B-Algorithm
(	O
using	O
median	O
,	O
Gaussian	O
filter	O
etc	O
.	O
</s>
<s>
This	O
removes	O
all	O
the	O
unwanted	O
points	O
and	O
if	O
applied	O
carefully	O
,	O
results	O
in	O
one	O
pixel	B-Algorithm
thick	O
edge	O
elements	O
.	O
</s>
<s>
If	O
Hough	B-Algorithm
transforms	I-Algorithm
are	O
used	O
to	O
detect	O
lines	O
and	O
ellipses	O
,	O
then	O
thinning	O
could	O
give	O
much	O
better	O
results	O
.	O
</s>
<s>
8	O
connectivity	O
is	O
preferred	O
,	O
where	O
all	O
the	O
immediate	O
pixels	B-Algorithm
surrounding	O
a	O
particular	O
pixel	B-Algorithm
are	O
considered	O
.	O
</s>
<s>
Some	O
edge-detection	O
operators	O
are	O
instead	O
based	O
upon	O
second-order	O
derivatives	B-Algorithm
of	O
the	O
intensity	O
.	O
</s>
<s>
This	O
essentially	O
captures	O
the	O
rate	B-Algorithm
of	I-Algorithm
change	I-Algorithm
in	O
the	O
intensity	O
gradient	O
.	O
</s>
<s>
Thus	O
,	O
in	O
the	O
ideal	O
continuous	O
case	O
,	O
detection	O
of	O
zero-crossings	B-Algorithm
in	O
the	O
second	O
derivative	B-Algorithm
captures	O
local	O
maxima	O
in	O
the	O
gradient	O
.	O
</s>
<s>
The	O
early	O
Marr	B-Algorithm
–	I-Algorithm
Hildreth	I-Algorithm
operator	O
is	O
based	O
on	O
the	O
detection	O
of	O
zero-crossings	B-Algorithm
of	O
the	O
Laplacian	O
operator	O
applied	O
to	O
a	O
Gaussian-smoothed	O
image	O
.	O
</s>
<s>
A	O
more	O
refined	O
second-order	O
edge	B-Algorithm
detection	I-Algorithm
approach	O
which	O
automatically	O
detects	O
edges	O
with	O
sub-pixel	O
accuracy	O
,	O
uses	O
the	O
following	O
differential	O
approach	O
of	O
detecting	O
zero-crossings	B-Algorithm
of	O
the	O
second-order	O
directional	O
derivative	B-Algorithm
in	O
the	O
gradient	O
direction	O
:	O
</s>
<s>
while	O
the	O
second-order	O
directional	O
derivative	B-Algorithm
in	O
the	O
-direction	O
of	O
should	O
be	O
negative	O
,	O
i.e.	O
,	O
</s>
<s>
where	O
denote	O
partial	O
derivatives	B-Algorithm
computed	O
from	O
a	O
scale	B-Algorithm
space	I-Algorithm
representation	I-Algorithm
obtained	O
by	O
smoothing	O
the	O
original	O
image	O
with	O
a	O
Gaussian	O
kernel	O
.	O
</s>
<s>
In	O
this	O
way	O
,	O
the	O
edges	O
will	O
be	O
automatically	O
obtained	O
as	O
continuous	O
curves	O
with	O
sub-pixel	O
accuracy	O
.	O
</s>
<s>
Hysteresis	O
thresholding	B-Algorithm
can	O
also	O
be	O
applied	O
to	O
these	O
differential	O
and	O
subpixel	O
edge	O
segments	O
.	O
</s>
<s>
In	O
practice	O
,	O
first-order	O
derivative	B-Algorithm
approximations	O
can	O
be	O
computed	O
by	O
central	O
differences	O
as	O
described	O
above	O
,	O
while	O
second-order	O
derivatives	B-Algorithm
can	O
be	O
computed	O
from	O
the	O
scale	B-Algorithm
space	I-Algorithm
representation	I-Algorithm
according	O
to	O
:	O
</s>
<s>
Higher-order	O
derivatives	B-Algorithm
for	O
the	O
third-order	O
sign	O
condition	O
can	O
be	O
obtained	O
in	O
an	O
analogous	O
fashion	O
.	O
</s>
<s>
A	O
recent	O
development	O
in	O
edge	B-Algorithm
detection	I-Algorithm
techniques	O
takes	O
a	O
frequency	O
domain	O
approach	O
to	O
finding	O
edge	O
locations	O
.	O
</s>
<s>
Phase	B-Algorithm
congruency	I-Algorithm
(	O
also	O
known	O
as	O
phase	O
coherence	O
)	O
methods	O
attempt	O
to	O
find	O
locations	O
in	O
an	O
image	O
where	O
all	O
sinusoids	O
in	O
the	O
frequency	O
domain	O
are	O
in	O
phase	O
.	O
</s>
<s>
A	O
roof	O
edge	O
,	O
is	O
a	O
discontinuity	O
in	O
the	O
first	O
order	O
derivative	B-Algorithm
of	O
a	O
grey-level	O
profile	O
.	O
</s>
<s>
The	O
phase	B-Algorithm
stretch	I-Algorithm
transform	I-Algorithm
or	O
PST	O
is	O
a	O
physics-inspired	O
computational	O
approach	O
to	O
signal	O
and	O
image	B-Algorithm
processing	I-Algorithm
.	O
</s>
<s>
PST	O
performs	O
similar	O
functionality	O
as	O
phase	O
contrast	O
microscopy	O
but	O
on	O
digital	B-Algorithm
images	I-Algorithm
.	O
</s>
<s>
PST	O
is	O
also	O
applicable	O
to	O
digital	B-Algorithm
images	I-Algorithm
as	O
well	O
as	O
temporal	O
,	O
time	O
series	O
,	O
data	O
.	O
</s>
<s>
To	O
increase	O
the	O
precision	O
of	O
edge	B-Algorithm
detection	I-Algorithm
,	O
several	O
subpixel	O
techniques	O
had	O
been	O
proposed	O
,	O
including	O
curve-fitting	O
,	O
moment-based	O
,	O
reconstructive	O
,	O
and	O
partial	O
area	O
effect	O
methods	O
.	O
</s>
<s>
Curve	O
fitting	O
methods	O
are	O
computationally	O
simple	O
but	O
are	O
easily	O
affected	O
by	O
noise	B-Algorithm
.	O
</s>
<s>
Moment-based	O
methods	O
use	O
an	O
integral-based	O
approach	O
to	O
reduce	O
the	O
effect	O
of	O
noise	B-Algorithm
,	O
but	O
may	O
require	O
more	O
computations	O
in	O
some	O
cases	O
.	O
</s>
<s>
Reconstructive	O
methods	O
use	O
horizontal	O
gradients	O
or	O
vertical	O
gradients	O
to	O
build	O
a	O
curve	O
and	O
find	O
the	O
peak	O
of	O
the	O
curve	O
as	O
the	O
sub-pixel	O
edge	O
.	O
</s>
<s>
Partial	O
area	O
effect	O
methods	O
are	O
based	O
on	O
the	O
hypothesis	O
that	O
each	O
pixel	B-Algorithm
value	O
depends	O
on	O
the	O
area	O
at	O
both	O
sides	O
of	O
the	O
edge	O
inside	O
that	O
pixel	B-Algorithm
,	O
producing	O
accurate	O
individual	O
estimation	O
for	O
every	O
edge	O
pixel	B-Algorithm
.	O
</s>
