<s>
Mean	B-Algorithm
shift	I-Algorithm
is	O
a	O
non-parametric	B-General_Concept
feature-space	O
mathematical	O
analysis	O
technique	O
for	O
locating	O
the	O
maxima	O
of	O
a	O
density	O
function	O
,	O
a	O
so-called	O
mode-seeking	O
algorithm	O
.	O
</s>
<s>
Application	O
domains	O
include	O
cluster	B-Algorithm
analysis	I-Algorithm
in	O
computer	B-Application
vision	I-Application
and	O
image	B-Algorithm
processing	I-Algorithm
.	O
</s>
<s>
The	O
mean	B-Algorithm
shift	I-Algorithm
procedure	O
is	O
usually	O
credited	O
to	O
work	O
by	O
Fukunaga	O
and	O
Hostetler	O
in	O
1975	O
.	O
</s>
<s>
Mean	B-Algorithm
shift	I-Algorithm
is	O
a	O
procedure	O
for	O
locating	O
the	O
maxima	O
—	O
the	O
modes	O
—	O
of	O
a	O
density	O
function	O
given	O
discrete	O
data	O
sampled	O
from	O
that	O
function	O
.	O
</s>
<s>
Typically	O
a	O
Gaussian	B-Algorithm
kernel	I-Algorithm
on	O
the	O
distance	O
to	O
the	O
current	O
estimate	O
is	O
used	O
,	O
.	O
</s>
<s>
The	O
difference	O
is	O
called	O
mean	B-Algorithm
shift	I-Algorithm
in	O
Fukunaga	O
and	O
Hostetler	O
.	O
</s>
<s>
The	O
mean-shift	B-Algorithm
algorithm	I-Algorithm
now	O
sets	O
,	O
and	O
repeats	O
the	O
estimation	O
until	O
converges	O
.	O
</s>
<s>
Although	O
the	O
mean	B-Algorithm
shift	I-Algorithm
algorithm	O
has	O
been	O
widely	O
used	O
in	O
many	O
applications	O
,	O
a	O
rigid	O
proof	O
for	O
the	O
convergence	O
of	O
the	O
algorithm	O
using	O
a	O
general	O
kernel	O
in	O
a	O
high	O
dimensional	O
space	O
is	O
still	O
not	O
known	O
.	O
</s>
<s>
Aliyari	O
Ghassabeh	O
showed	O
the	O
convergence	O
of	O
the	O
mean	B-Algorithm
shift	I-Algorithm
algorithm	O
in	O
one	O
dimension	O
with	O
a	O
differentiable	O
,	O
convex	O
,	O
and	O
strictly	O
decreasing	O
profile	O
function	O
.	O
</s>
<s>
Gaussian	O
Mean-Shift	B-Algorithm
is	O
an	O
Expectation	B-Algorithm
–	I-Algorithm
maximization	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
where	O
are	O
the	O
input	O
samples	O
and	O
is	O
the	O
kernel	O
function	O
(	O
or	O
Parzen	B-General_Concept
window	I-General_Concept
)	O
.	O
</s>
<s>
This	O
approach	O
is	O
known	O
as	O
kernel	B-General_Concept
density	I-General_Concept
estimation	I-General_Concept
or	O
the	O
Parzen	B-General_Concept
window	I-General_Concept
technique	O
.	O
</s>
<s>
Instead	O
,	O
mean	B-Algorithm
shift	I-Algorithm
uses	O
a	O
variant	O
of	O
what	O
is	O
known	O
in	O
the	O
optimization	O
literature	O
as	O
multiple	O
restart	O
gradient	O
descent	O
.	O
</s>
<s>
Starting	O
at	O
some	O
guess	O
for	O
a	O
local	O
maximum	O
,	O
,	O
which	O
can	O
be	O
a	O
random	O
input	O
data	O
point	O
,	O
mean	B-Algorithm
shift	I-Algorithm
computes	O
the	O
gradient	O
of	O
the	O
density	O
estimate	O
at	O
and	O
takes	O
an	O
uphill	O
step	O
in	O
that	O
direction	O
.	O
</s>
<s>
The	O
two	O
most	O
frequently	O
used	O
kernel	O
profiles	O
for	O
mean	B-Algorithm
shift	I-Algorithm
are	O
:	O
</s>
<s>
Mean-shift	B-Algorithm
is	O
a	O
hill	O
climbing	O
algorithm	O
which	O
involves	O
shifting	O
this	O
kernel	O
iteratively	O
to	O
a	O
higher	O
density	O
region	O
until	O
convergence	O
.	O
</s>
<s>
Every	O
shift	O
is	O
defined	O
by	O
a	O
mean	B-Algorithm
shift	I-Algorithm
vector	O
.	O
</s>
<s>
The	O
mean	B-Algorithm
shift	I-Algorithm
vector	O
always	O
points	O
toward	O
the	O
direction	O
of	O
the	O
maximum	O
increase	O
in	O
the	O
density	O
.	O
</s>
<s>
In	O
this	O
case	O
if	O
a	O
Gaussian	B-Algorithm
kernel	I-Algorithm
is	O
chosen	O
instead	O
of	O
a	O
flat	O
kernel	O
,	O
then	O
every	O
point	O
will	O
first	O
be	O
assigned	O
a	O
weight	O
which	O
will	O
decay	O
exponentially	O
as	O
the	O
distance	O
from	O
the	O
kernel	O
's	O
center	O
increases	O
.	O
</s>
<s>
The	O
mean	B-Algorithm
shift	I-Algorithm
algorithm	O
can	O
be	O
used	O
for	O
visual	O
tracking	O
.	O
</s>
<s>
The	O
simplest	O
such	O
algorithm	O
would	O
create	O
a	O
confidence	O
map	O
in	O
the	O
new	O
image	O
based	O
on	O
the	O
color	O
histogram	O
of	O
the	O
object	O
in	O
the	O
previous	O
image	O
,	O
and	O
use	O
mean	B-Algorithm
shift	I-Algorithm
to	O
find	O
the	O
peak	O
of	O
a	O
confidence	O
map	O
near	O
the	O
object	O
's	O
old	O
position	O
.	O
</s>
<s>
Mean	B-Algorithm
shift	I-Algorithm
is	O
an	O
application-independent	O
tool	O
suitable	O
for	O
real	O
data	O
analysis	O
.	O
</s>
<s>
The	O
bandwidth/window	O
size	O
'	O
h	O
 '	O
has	O
a	O
physical	O
meaning	O
,	O
unlike	O
k-means	B-Algorithm
.	O
</s>
<s>
Variants	O
of	O
the	O
algorithm	O
can	O
be	O
found	O
in	O
machine	O
learning	O
and	O
image	B-Algorithm
processing	I-Algorithm
packages	O
:	O
</s>
<s>
ELKI	B-Language
.	O
</s>
<s>
Java	O
data	O
mining	O
tool	O
with	O
many	O
clustering	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
ImageJ	B-Language
.	O
</s>
<s>
Image	O
filtering	O
using	O
the	O
mean	B-Algorithm
shift	I-Algorithm
filter	O
.	O
</s>
<s>
mlpack	B-Language
.	O
</s>
<s>
Orfeo	B-Language
toolbox	I-Language
.	O
</s>
