Rough

Fuzzy Clustering: An
Application to Medical Imagery
Sushmita Mitra
Center for Soft Computing Research
Indian Statistical Institute, Kolkata, INDIA
Bishal Barman
Electrical Engineering Department
S. V. National Institute of Technology, Surat, INDIA
Rough and Rough

Fuzzy Sets
Rough
Set
Theory
–
Z
.
Pawlak
(
1990
–
91
)
Idea
of
Approximation
Spaces
Handles
vagueness,
uncertainty
and
incompleteness
in
information
systems
Rough

Fuzzy
and
Fuzzy

Rough
Sets
–
Dubois
and
Prade
(
1990
)
Uncertainty
modeling
through
Upper
and
Lower
Approximations
Hybridized
Rough

Fuzzy
modeling
through
Upper

Lower
Approximations
and
membership
values
Brief Overview
Novel
Application
of
Rough

Fuzzy
(RF)
Clustering
(For
Synthetic
as
well
as
CT
scan
images
of
the
brain)
RF
Clustering
simultaneously
handles
overlap
of
clusters
(Fuzzy)
and
uncertainty
involved
in
class
boundary
(Rough)
Number
of
clusters
was
optimized
via
cluster
validity
indices
Main
objective
was
the
diagnosis
of
the
extent
of
brain
infarction
in
CT
scan
images
Rough Clustering Algorithms
Rough
and
Fuzzy
sets
incorporated
in
c

means
framework
to
give
Rough
c

means
(RCM)
and
Fuzzy
c

means
(FCM)
RCM
views
each
cluster
as
an
interval
or
rough
set
U
Cluster
prototypes
in
the
RCM
algorithm
defined
as
:
Rough

Fuzzy
c

means (RFCM)
Rough

Fuzzy
c

means (RFCM)
–
Mitra, S., Banka, H., Pedrycz, W.:
Rough

fuzzy collaborative clustering.
IEEE Transactions on Systems,
Man, and Cybernetics, Part

B,
36, (2006), 795
–
805
Algorithm outlined as:
RFCM Continued…
Salient Features of the hybridized
algorithm (RFCM)
Fuzzy
membership
enables
efficient
handling
of
overlapping
partitions
while
Rough
set
deals
with
uncertainty,
vagueness
and
incompleteness
in
data
in
terms
of
upper
and
lower
approximation
Incorporation
of
membership
in
the
RCM
framework
enhances
the
robustness
of
the
algorithm
Previously,
in
RCM,
one
never
had
the
idea
of
how
similar
a
sample
was
to
the
given
cluster
in
the
absence
of
any
similarity
index
.
RFCM
solves
this
problem
with
the
help
of
membership
values
Maximizes
the
use
of
both
Fuzzy
and
Rough
sets
for
effective
approach
in
Knowledge
Discovery
Cluster Validation
Partitive
clustering
requires
pre

specification
of
the
number
of
clusters
To
evaluate
the
goodness
of
clustering,
we
employed
three
cluster
validity
indices
Davies

Bouldin
Index
Xie

Beni
Index
Silhouette
Statistic
Davies

Bouldin Index
Xie

Beni Index
Silhouette Statistic
Silhouette Index,
S
, computes for each point a width
depending on its membership in any cluster
a
i
is the average distance between point
i
and all
other points in its own cluster and
b
i
is the minimum
of the average dissimilarities between
i
and points in
other clusters
RESULTS
Synthetic
Data
32
points
with
2
clusters
3
outliers
to
test
the
ability
of
the
algorithms
to
resist
a
bias
in
the
estimation
of
cluster
prototypes
Results
obtained
for
the
Hard
c

means
(HCM)
or
the
k

means,
Fuzzy
c

means
(FCM),
Rough
c

means
(RCM)
and
Rough

Fuzzy
c

means
(RFCM)
Original Scatter Plot of X

32
Hard
c

means (HCM) or
k

means
Fuzzy
c

means (FCM)
Rough
c

means (RCM)
Rough

Fuzzy
c

means (RFCM)
Scatter Plot and RFCM result for another
synthetic data with 45 points (X

45)
Scatter Plot and RFCM result for another
synthetic data with 70 points (X

70)
Cluster Validity Indices for X

32 ( 2
Clusters)
CT Scan Image Segmentation
Segmentation
–
Process
of
partitioning
an
image
into
some
non

overlapping
meaningful
regions
Segmentation
here
via
Pixel
Clustering
Study
consists
of
cases
of
Vascular
Infarction
of
the
Human
Brain
Partitioning
into
five
regions
–
Gray
matter
(GM),
White
matter
(WM),
Infarcted
region,
Skull
and
the
backround
Fresh case of Vascular Insult (Original
Image)
1.
Infarction is on the
left side..
2.
The left side is
compressing the right
side
3.
Dilation of the blood
ventricles
4.
Severe edema
5.
Division of brain into
gray matter, white
matter and the
cerebrospinal fluid
(CSF)
6.
The third ventricle is
not visible here due
to severe edema
from the right
ventricle side
7.
Cause: Cholesterol
Deposit, Blockage
Segmentation Result (HCM)
Segmentation Result (FCM)
Segmentation Result (RCM)
Segmentation Result (RFCM)
White Matter
Gray Matter
Cerebrospinal
Fluid
Infarcted
Region
Comparative Analysis (HCM, FCM, RCM
& RFCM respectively)
RFCM: Much Crisper
segmentation of White matter,
Gray matter and CSF.
HCM (Noisy)
FCM (Noisy)
RCM
(Noisy)
Skull
GM
WM
CSF
Chronic Infarction (Original Image)
1.
Patient suffering
from vascular insult
2.
Right and left
should have been
symmetric (the most
definite metric for
comparison)
3.
Right side is dark
because it has not
received blood
supply for a very
long time
4.
Due to this the
blood ventricles
have dilated and
have undergone
liquefaction (water)
5.
Parenchyma is
infarcted
6.
Arteries were
blocked due to high
cholesterol levels
7.
Happens due to
normal old age
Chronic Infarction (RFCM Segmentation
result)
White
Matter
Gray
Matter
Cerebrospinal
Fluid
Infarcted
Region
Skull
Subtle Case of Infarction (Original Image)
1.
The third ventricle
has dilated
2.
Edema from below
3.
Blockage of arteries,
no blood supply from
a long time
4.
Dilation of left and
right ventricles due to
this as passage from
below is blocked
5.
Problem modeling
same. although the
infarction here is
petty difficult to
locate
6.
Tough problem of
segmentation for
infarction
7.
Cause: Cholesterol
deposit, Blockage
Subtle Case of Infarction (RFCM
Segmentation result)
Cerebrospinal
Fluid
White
Matter
Uniform
merging of
Gray Matter
and the
Infarcted
region
Conclusion
In
the
absence
of
an
accurate
index
to
test
the
accuracy
of
segmentation
results
in
CT
scan
imagery,
we
resorted
to
expert
domain
knowledge
36
frames
of
each
case
of
infarction
was
studied
and
results
verified
by
an
experienced
radiologist
RFCM
produced
the
best
result
as
verified
by
expert
radiologist
Results
promise
to
provide
a
helpful
second
opinion
to
radiologists
in
case
of
Computer

Aided
Diagnostic
(CAD)
QUESTIONS ?
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