<s>
In	O
computer	B-Application
vision	I-Application
,	O
rigid	B-Algorithm
motion	I-Algorithm
segmentation	I-Algorithm
is	O
the	O
process	O
of	O
separating	O
regions	O
,	O
features	O
,	O
or	O
trajectories	B-Application
from	O
a	O
video	O
sequence	O
into	O
coherent	O
subsets	O
of	O
space	O
and	O
time	O
.	O
</s>
<s>
The	O
goal	O
of	O
this	O
segmentation	B-Algorithm
is	O
to	O
differentiate	O
and	O
extract	O
the	O
meaningful	O
rigid	B-Algorithm
motion	I-Algorithm
from	O
the	O
background	O
and	O
analyze	O
it	O
.	O
</s>
<s>
Image	B-Algorithm
segmentation	I-Algorithm
techniques	O
labels	O
the	O
pixels	B-Algorithm
to	O
be	O
a	O
part	O
of	O
pixels	B-Algorithm
with	O
certain	O
characteristics	O
at	O
a	O
particular	O
time	O
.	O
</s>
<s>
Here	O
,	O
the	O
pixels	B-Algorithm
are	O
segmented	O
depending	O
on	O
its	O
relative	O
movement	O
over	O
a	O
period	O
of	O
time	O
i.e.	O
</s>
<s>
There	O
is	O
no	O
consistent	O
way	O
to	O
classify	O
motion	O
segmentation	B-Algorithm
due	O
to	O
its	O
large	O
variation	O
in	O
literature	O
.	O
</s>
<s>
Depending	O
on	O
the	O
segmentation	B-Algorithm
criterion	O
used	O
in	O
the	O
algorithm	O
it	O
can	O
be	O
broadly	O
classified	O
into	O
the	O
following	O
categories	O
:	O
image	O
difference	O
,	O
statistical	O
methods	O
,	O
wavelets	O
,	O
layering	O
,	O
optical	O
flow	O
and	O
factorization	O
.	O
</s>
<s>
Rigid	B-Algorithm
motion	I-Algorithm
segmentation	I-Algorithm
has	O
found	O
an	O
increase	O
in	O
its	O
application	O
over	O
the	O
recent	O
past	O
with	O
rise	O
in	O
surveillance	O
and	O
video	O
editing	O
.	O
</s>
<s>
If	O
this	O
transformation	O
preserves	O
size	O
and	O
shape	O
of	O
the	O
object	O
it	O
is	O
known	O
as	O
a	O
Rigid	B-Algorithm
Transformation	I-Algorithm
.	O
</s>
<s>
We	O
define	O
rigid	B-Algorithm
transformation	I-Algorithm
mathematically	O
as	O
:	O
</s>
<s>
This	O
motion	O
(	O
3-D	O
)	O
in	O
time	O
when	O
captured	O
by	O
a	O
camera	O
(	O
2-D	O
)	O
corresponds	O
to	O
change	O
of	O
pixels	B-Algorithm
in	O
the	O
subsequent	O
frames	O
of	O
the	O
video	O
sequence	O
.	O
</s>
<s>
This	O
transformation	O
is	O
also	O
known	O
as	O
2-D	O
rigid	O
body	O
motion	O
or	O
the	O
2-D	O
Euclidean	B-Algorithm
transformation	I-Algorithm
.	O
</s>
<s>
X	O
→	O
original	O
pixel	B-Algorithm
co-ordinate	O
.	O
</s>
<s>
X'→	O
transformed	O
pixel	B-Algorithm
co-ordinate	O
.	O
</s>
<s>
Thus	O
the	O
car	O
is	O
said	O
to	O
have	O
a	O
rigid	B-Algorithm
motion	I-Algorithm
.	O
</s>
<s>
Image	B-Algorithm
segmentation	I-Algorithm
techniques	O
are	O
interested	O
in	O
segmenting	O
out	O
different	O
parts	O
of	O
the	O
image	O
as	O
per	O
the	O
region	O
of	O
interest	O
.	O
</s>
<s>
As	O
videos	O
are	O
sequences	O
of	O
images	O
,	O
motion	O
segmentation	B-Algorithm
aims	O
at	O
decomposing	O
a	O
video	O
in	O
moving	O
objects	O
and	O
background	O
by	O
segmenting	O
the	O
objects	O
that	O
undergo	O
different	O
motion	O
patterns	O
.	O
</s>
<s>
The	O
analysis	O
of	O
these	O
spatial	O
and	O
temporal	O
changes	O
occurring	O
in	O
the	O
image	O
sequence	O
by	O
separating	O
visual	B-Algorithm
features	I-Algorithm
from	O
the	O
scenes	O
into	O
different	O
groups	O
lets	O
us	O
extract	O
visual	O
information	O
.	O
</s>
<s>
In	O
the	O
simplest	O
case	O
motion	O
segmentation	B-Algorithm
can	O
mean	O
extracting	O
moving	O
objects	O
from	O
a	O
stationary	O
camera	O
but	O
the	O
camera	O
can	O
also	O
move	O
which	O
introduces	O
the	O
relative	O
motion	O
of	O
the	O
static	O
background	O
.	O
</s>
<s>
Depending	O
upon	O
the	O
type	O
of	O
visual	B-Algorithm
features	I-Algorithm
that	O
are	O
extracted	O
,	O
motion	O
segmentation	B-Algorithm
algorithms	O
can	O
be	O
broadly	O
divided	O
into	O
two	O
categories	O
.	O
</s>
<s>
The	O
first	O
is	O
known	O
as	O
direct	O
motion	O
segmentation	B-Algorithm
that	O
uses	O
pixel	B-Algorithm
intensities	O
from	O
the	O
image	O
.	O
</s>
<s>
There	O
are	O
a	O
number	O
of	O
requirements	O
to	O
design	O
a	O
good	O
motion	O
segmentation	B-Algorithm
algorithm	O
.	O
</s>
<s>
In	O
case	O
of	O
view-based	O
segmentation	B-Algorithm
techniques	O
described	O
below	O
,	O
this	O
happens	O
because	O
the	O
single	O
fundamental	B-General_Concept
matrix	I-General_Concept
assumption	O
is	O
violated	O
as	O
each	O
motion	O
will	O
now	O
be	O
represented	O
by	O
means	O
of	O
a	O
new	O
fundamental	B-General_Concept
matrix	I-General_Concept
corresponding	O
to	O
that	O
motion	O
.	O
</s>
<s>
As	O
mentioned	O
earlier	O
that	O
there	O
is	O
no	O
particular	O
way	O
to	O
distinguish	O
Motion	O
Segmentation	B-Algorithm
techniques	O
but	O
depending	O
on	O
the	O
basis	O
of	O
the	O
segmentation	B-Algorithm
criterion	O
used	O
in	O
the	O
algorithm	O
it	O
can	O
be	O
broadly	O
classified	O
as	O
follows	O
:	O
</s>
<s>
The	O
algorithm	O
first	O
considers	O
two	O
frames	O
at	O
a	O
time	O
and	O
then	O
computes	O
the	O
pixel	B-Algorithm
by	O
pixel	B-Algorithm
intensity	O
difference	O
.	O
</s>
<s>
On	O
this	O
computation	O
it	O
thresholds	B-Algorithm
the	O
intensity	O
difference	O
and	O
maps	O
the	O
changes	O
onto	O
a	O
contour	O
.	O
</s>
<s>
Motion	O
segmentation	B-Algorithm
can	O
be	O
seen	O
as	O
a	O
classification	O
problem	O
where	O
each	O
pixel	B-Algorithm
has	O
to	O
be	O
classified	O
as	O
background	O
or	O
foreground	O
.	O
</s>
<s>
Such	O
classifications	O
are	O
modeled	O
under	O
statistic	O
theory	O
and	O
can	O
be	O
used	O
in	O
segmentation	B-Algorithm
algorithms	O
.	O
</s>
<s>
a	O
posteriori	O
probability	O
(	O
MAP	O
)	O
,	O
Particle	B-Algorithm
Filter	I-Algorithm
(	O
PF	O
)	O
and	O
Expectation	B-Algorithm
Maximization	I-Algorithm
(	O
EM	O
)	O
.	O
</s>
<s>
MAP	O
uses	O
Bayes	O
 '	O
Rule	O
for	O
implementation	O
where	O
a	O
particular	O
pixel	B-Algorithm
has	O
to	O
be	O
classified	O
under	O
predefined	O
classes	O
.	O
</s>
<s>
The	O
EM	B-Algorithm
algorithm	I-Algorithm
is	O
also	O
an	O
iterative	O
estimation	O
method	O
.	O
</s>
<s>
Optical	O
flow	O
(	O
OF	O
)	O
helps	O
in	O
determining	O
the	O
relative	O
pixel	B-Algorithm
velocity	O
of	O
points	O
within	O
an	O
image	O
sequence	O
.	O
</s>
<s>
Like	O
image	O
difference	O
,	O
it	O
is	O
also	O
an	O
old	O
concept	O
used	O
for	O
segmentation	B-Algorithm
.	O
</s>
<s>
For	O
complicated	O
scenarios	O
,	O
particularly	O
when	O
the	O
camera	O
itself	O
is	O
moving	O
,	O
OF	O
provides	O
a	O
basis	O
for	O
estimating	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
where	O
outliers	O
represent	O
other	O
objects	O
moving	O
independently	O
in	O
the	O
scene	O
.	O
</s>
<s>
Such	O
techniques	O
are	O
used	O
in	O
stereo	B-Algorithm
vision	I-Algorithm
where	O
it	O
is	O
needed	O
to	O
compute	O
the	O
depth	O
distance	O
.	O
</s>
<s>
As	O
humans	O
also	O
use	O
layer	O
based	O
segmentation	B-Algorithm
,	O
this	O
method	O
is	O
a	O
natural	O
solution	O
to	O
occlusion	O
problems	O
but	O
it	O
is	O
very	O
complex	O
with	O
requirement	O
of	O
manual	O
tuning	O
.	O
</s>
<s>
This	O
technique	O
factorized	O
the	O
trajectory	B-Application
matrix	O
W	O
,	O
determined	O
after	O
the	O
tracking	O
of	O
different	O
features	O
over	O
the	O
sequence	O
into	O
two	O
matrices	O
:	O
motion	O
and	O
structure	O
using	O
Singular	O
Value	O
Decomposition	O
.	O
</s>
<s>
The	O
two-view	O
based	O
approaches	O
are	O
usually	O
based	O
on	O
epipolar	B-Algorithm
geometry	I-Algorithm
.	O
</s>
<s>
Consider	O
two	O
perspective	O
camera	O
views	O
of	O
a	O
rigid	O
body	O
and	O
find	O
its	O
feature	B-Algorithm
correspondences	O
.	O
</s>
<s>
These	O
correspondences	O
are	O
seen	O
to	O
satisfy	O
either	O
an	O
epipolar	B-Algorithm
constraint	I-Algorithm
for	O
a	O
general	O
rigid-body	O
or	O
a	O
homography	B-Algorithm
constraint	O
for	O
a	O
planar	O
object	O
.	O
</s>
<s>
Hence	O
in	O
a	O
sequence	O
we	O
expect	O
to	O
see	O
more	O
than	O
one	O
type	O
of	O
motion	O
,	O
described	O
by	O
multiple	O
epipolar	B-Algorithm
constraints	I-Algorithm
and	O
homographies	B-Algorithm
.	O
</s>
<s>
The	O
view	O
based	O
algorithms	O
are	O
sensitive	O
to	O
outliers	O
but	O
recent	O
approaches	O
deal	O
with	O
outliers	O
by	O
using	O
random	B-Algorithm
sample	I-Algorithm
consensus	I-Algorithm
(	O
RANSAC	B-Algorithm
)	O
and	O
enhanced	O
Dirichlet	B-General_Concept
process	I-General_Concept
mixture	O
models	O
.	O
</s>
<s>
These	O
approaches	O
use	O
only	O
two	O
frames	O
for	O
motion	O
segmentation	B-Algorithm
even	O
if	O
multiple	O
frames	O
are	O
available	O
as	O
they	O
cannot	O
use	O
multi	O
frame	O
information	O
.	O
</s>
<s>
Multiview-based	O
approaches	O
utilize	O
the	O
trajectory	B-Application
of	O
feature	B-Algorithm
points	O
unlike	O
two-view	O
based	O
approaches	O
.	O
</s>
<s>
Motion	O
segmentation	B-Algorithm
is	O
a	O
field	O
under	O
research	O
as	O
there	O
are	O
many	O
issues	O
which	O
provide	O
scope	O
of	O
improvement	O
.	O
</s>
<s>
One	O
of	O
the	O
major	O
problems	O
is	O
of	O
feature	B-Algorithm
detection	O
and	O
finding	B-Algorithm
correspondences	I-Algorithm
.	O
</s>
<s>
There	O
are	O
strong	O
feature	B-Algorithm
detection	O
algorithms	O
but	O
they	O
still	O
give	O
false	O
positives	O
which	O
can	O
lead	O
to	O
unexpected	O
correspondences	O
.	O
</s>
<s>
Finding	O
these	O
pixel	B-Algorithm
or	O
feature	B-Algorithm
correspondences	O
is	O
a	O
difficult	O
task	O
.	O
</s>
<s>
These	O
mismatched	O
feature	B-Algorithm
points	O
from	O
the	O
objects	O
and	O
the	O
background	O
often	O
introduce	O
outliers	O
.	O
</s>
<s>
Most	O
algorithms	O
perform	O
2-D	O
motion	O
segmentation	B-Algorithm
by	O
assuming	O
the	O
motions	O
in	O
the	O
scene	O
can	O
be	O
modeled	O
by	O
2-D	O
affine	O
motion	O
models	O
.	O
</s>
<s>
Measurement	O
of	O
3-D	O
feature	B-Algorithm
correspondences	O
in	O
the	O
images	O
can	O
be	O
noisy	O
in	O
terms	O
of	O
pixel	B-Algorithm
coordinates	O
.	O
</s>
<s>
Motion	O
segmentation	B-Algorithm
has	O
many	O
important	O
applications	O
.	O
</s>
<s>
With	O
segmentation	B-Algorithm
,	O
it	O
is	O
possible	O
to	O
eliminate	O
the	O
redundancy	O
related	O
to	O
the	O
repetition	O
of	O
the	O
same	O
visual	O
patterns	O
in	O
successive	O
images	O
.	O
</s>
