<s>
The	O
image	B-Algorithm
segmentation	I-Algorithm
problem	O
is	O
concerned	O
with	O
partitioning	O
an	O
image	O
into	O
multiple	O
regions	O
according	O
to	O
some	O
homogeneity	O
criterion	O
.	O
</s>
<s>
This	O
article	O
is	O
primarily	O
concerned	O
with	O
graph	O
theoretic	O
approaches	O
to	O
image	B-Algorithm
segmentation	I-Algorithm
applying	O
graph	O
partitioning	O
via	O
minimum	O
cut	O
or	O
maximum	O
cut	O
.	O
</s>
<s>
Segmentation-based	B-Algorithm
object	I-Algorithm
categorization	I-Algorithm
can	O
be	O
viewed	O
as	O
a	O
specific	O
case	O
of	O
spectral	B-Algorithm
clustering	I-Algorithm
applied	O
to	O
image	B-Algorithm
segmentation	I-Algorithm
.	O
</s>
<s>
Automatic	O
segmentation	B-Algorithm
of	O
MRI	O
images	O
for	O
identification	O
of	O
cancerous	O
regions	O
.	O
</s>
<s>
In	O
this	O
context	O
,	O
we	O
can	O
formulate	O
the	O
image	B-Algorithm
segmentation	I-Algorithm
problem	O
as	O
a	O
graph	O
partitioning	O
problem	O
that	O
asks	O
for	O
a	O
partition	O
of	O
the	O
vertex	O
set	O
,	O
where	O
,	O
according	O
to	O
some	O
measure	O
,	O
the	O
vertices	O
in	O
any	O
set	O
have	O
high	O
similarity	O
,	O
and	O
the	O
vertices	O
in	O
two	O
different	O
sets	O
have	O
low	O
similarity	O
.	O
</s>
<s>
This	O
is	O
impractical	O
for	O
image	B-Algorithm
segmentation	I-Algorithm
applications	O
where	O
is	O
the	O
number	O
of	O
pixels	O
in	O
the	O
image	O
.	O
</s>
<s>
For	O
image	B-Algorithm
segmentation	I-Algorithm
,	O
the	O
matrix	O
W	O
is	O
typically	O
sparse	O
,	O
with	O
a	O
number	O
of	O
nonzero	O
entries	O
,	O
so	O
such	O
a	O
matrix-vector	O
product	O
takes	O
time	O
.	O
</s>
<s>
For	O
high-resolution	O
images	O
,	O
the	O
second	O
eigenvalue	O
is	O
often	O
ill-conditioned	B-Algorithm
,	O
leading	O
to	O
slow	O
convergence	O
of	O
iterative	O
eigenvalue	O
solvers	O
,	O
such	O
as	O
the	O
Lanczos	O
algorithm	O
.	O
</s>
<s>
Preconditioning	O
is	O
a	O
key	O
technology	O
accelerating	O
the	O
convergence	O
,	O
e.g.	O
,	O
in	O
the	O
matrix-free	O
LOBPCG	B-Application
method	O
.	O
</s>
<s>
scikit-learn	B-Application
uses	O
LOBPCG	B-Application
from	O
SciPy	B-Application
with	O
algebraic	O
multigrid	O
preconditioning	O
for	O
solving	O
the	O
eigenvalue	O
problem	O
for	O
the	O
graph	B-Algorithm
Laplacian	I-Algorithm
to	O
perform	O
image	B-Algorithm
segmentation	I-Algorithm
via	O
spectral	O
graph	O
partitioning	O
as	O
first	O
proposed	O
in	O
and	O
actually	O
tested	O
in	O
and	O
.	O
</s>
<s>
cows	O
,	O
the	O
OBJ	O
CUT	O
algorithm	O
computes	O
a	O
segmentation	B-Algorithm
of	O
the	O
object	O
,	O
that	O
is	O
,	O
it	O
infers	O
a	O
set	O
of	O
labelsm	O
.	O
</s>
<s>
The	O
objective	O
function	O
is	O
minimized	O
using	O
a	O
single	O
MINCUT	B-Algorithm
operation	O
to	O
obtain	O
the	O
segmentation	B-Algorithm
m	O
.	O
</s>
