Application to Medical Imagery

savagelizardAI and Robotics

Nov 25, 2013 (3 years and 10 months ago)

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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 ?