Sclera Segmentation using Spatial Kernel Fuzzy Clustering Methods

M. S. Maheshan

1a

, B. S. Harish

1b

and S. V. Aruna Kumar

2c

1

Department of Information Science and Engineering, JSS Science and Technology University, Mysuru, Karnataka, India

2

Socia-Lab, University Beira Interior, Convento de Sto. António, Covilhã, Portugal

Keywords: Clustering, Fuzzy C Means, Sclera, Segmentation.

Abstract: Biometrics is one of the domain that is gaining lot of importance in the present digital industry. Biometrics

are getting integrated in different devices and reaching the end users at a very affordable cost. Among various

biometric traits, Sclera is one such trait that is getting popular in the research community for its distinct nature

of authenticating and identification of individuals. The recognition system using sclera trait purely depends

on efficient segmentation of sclera image. Segmentation process is considered to be significant in image

processing system because of better visualization. The segmentation can be done using region based, edge

based, threshold based and also clustering based techniques. This paper concentrates on clustering based

technique by proposing a variant of conventional Fuzzy C Means (FCM) algorithm. Though the Fuzzy C

Means presents outstanding results in many applications, unfortunately it is sensitive to noise and ignore

neighbourhood information. Thus to alleviate these limitations this paper presents Generalized Spatial Kernel

Fuzzy C Means (GSK-FCM) clustering algorithms for sclera segmentation. To evaluate the proposed methods,

experimentation are conducted on Sclera Segmentation and Recognition Benchmarking Competition (SSRBC

2015) dataset. The result of the experiments reveals that the proposed methods outperform the other variants

of FCM.

1 INTRODUCTION

In today’s mobile based tech industry, biometric

based technological platforms are the front runners in

applying technologies to various devices. Biometric

has lately received a lot of attraction in popular media

including commercial applications. The requirement

to validate ourselves to machines is always increasing

in today’s networked society, which in turn helps in

closing the gap between the humans and the machines

to secure the transactions and networks. Biometric

deals with identification of persons based on their

biological or behavioural distinctiveness (Jain et al.,

2000). Amongst the various biometric traits available,

this paper presents about sclera segmentation. Sclera

which is the white part of the eye that surrounds the

cornea, occupies more than 80% of the surface area

of the eyeball. This trait when compared to other

traditional traits is hard to spoof as the optic nerves of

the sclera region are very unique and random

including the identical twins. In addition the patterns

a

https://orcid.org/0000-0002-3330-8795

b

https://orcid.org/0000-0001-5495-0640

c

https://orcid.org/0000-0002-8953-2921

of these nerves remain factual till the life-time of a

person (Joussen, 2001). Sclera segmentation is a

significant procedure in sclera recognition process.

Segmentation partition the image into its

constituent’s parts and groups the uniform pixels into

clusters. Segmentation techniques have been used in

wide range of medical image processing such as

thresholding (Otsu, 1979), region growing (Adams et

al., 1994; Beveridge et al., 1989) and clustering (Ng

et al., 2006; Chen et al., 1998; Wang el al., 2006;

Hadjahmadi et al., 2008). Clustering has been

extensively applied in numerous fields’ such as

geology, taxonomy, medical image processing,

engineering systems. Among various clustering

techniques the most widely used techniques include

the k-means, fuzzy c-means (Wang el al., 2006) and

their variants. The traditional fuzzy c-means

clustering algorithm is found to comprise the pixel

attributes. This process was found to fail in providing

efficient results in the presence of corrupted noise in

the image. Therefore, from the existing research it is

Maheshan, M., Harish, B. and Kumar, S.

Sclera Segmentation using Spatial Kernel Fuzzy Clustering Methods.

DOI: 10.5220/0008935704330439

In Proceedings of the 9th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2020), pages 433-439

ISBN: 978-989-758-397-1; ISSN: 2184-4313

Copyright

c

2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

433

observed that the significance to improve the

performance of the standard FCM is essential.

Recently, several researchers have developed

diverse methods by modifying the objective function

or membership function of standard FCM method

(Liew et al., 2001; Ahmed et al., 2001). Also, it was

seen that traditional FCM, which uses Euclidean

distance is used to determine the distance between

cluster center and data. The above algorithm was

found to be limited in revealing non-Euclidean

structure of the input data. To overcome this problem,

researchers modified the existing approaches in such

a way that it improves the performance. Further,

several researchers developed a novel FCM method

where kernel function is employed to determine the

distance between center of the cluster and data pixel

(Chen et al., 2002). For better result, a hybrid

technique is proposed which provide new robust

clustering algorithm. In this technique, kernelized

fuzzy logic is incorporated with spatial constraint

which results in new clustering method called

SKFCM. By introducing the higher and lower

elimination of non-required data belonging to one

cluster can be removed. Since FCM failed to handle

the small differences between clusters and as it is

sensitive to noise, FCM algorithm was derived into

KFCM which is based on kernel method. Due to the

limitations of this algorithm a robust generalized

spatial kernel fuzzy C-Means clustering method is

introduced in this research work.

2 BACKGROUND STUDY

Fuzzy C-Means (FCM), a method of clustering

technique which maps each data point to two or more

clusters and showcases very good results in many

applications in the field of medicine, engineering,

economics, psychology and many other disciplines

(Ben-Dor et., 1999).

Consider

12

= { , ,...... ,...... }

in

X

xx x x

e the

n data

points and

12

= { , ,...... ,...... }

jc

Vvv v v

be the set of c

cluster centers. The objective of FCM is to partition

the data points into

c group such that the data points

present in the same group have similar characteristics

when compared to the data points present in the other

groups by reducing the objective function as shown

in equation 1.

2

=1 =1

=

nc

m

ijji

ji

J

uxv

(1)

where

m

refers to fuzzifier value,

i

v

refers to

th

i

cluster center,

[0,1]

ij

u

is the membership of the

data point

j

x

to the

th

i

cluster center and

.

is the

distance measure used to compute the distance

between data point

)(

j

x

and cluster center

)(

i

v

.

Fuzzy C-Means is an iterative algorithm which

updates the membership

)(

ij

u

and cluster centers

using following equations.

1

1

=1

1

=

ij

m

c

ji

k

jk

u

xv

xv

(2)

=1

=1

=

n

m

ij j

j

i

n

m

ij

j

ux

v

u

(3)

The Fuzzy C-Means process starts by randomly

picking the

c

number of data points as initial cluster

centers. Furthermore, the membership value is

computed based on the distance of the data point

j

x

to the cluster center

i

v

using equation 2. In the

following step, the objective function value is

computed based on previously evaluated membership

values using equation 1. The cluster centers are then

updated based on the membership values of each data

points using equation 3. This iterative process is

stopped when the difference of successive iterations

objective function value is less than the user specified

stopping criterion value. Although Fuzzy C-Means is

found to be an important tool for image processing by

producing outstanding results it has its own

limitations, such as sensitivity to noise and ignorance

of neighborhood information (Bezdek, 1994). The

use of euclidian distance metric in FCM inturn

degrades the clustering results (Koza, 1994). Kernal

FCM (KFCM) an alternative method was introduced

to overcome the noise sensitivity problem in the

traditional Fuzzy C-Means (Despotović et al., 2015).

Unlike the traditional FCM which makes use of

euclidian distance metric, the kernal FCM uses kernel

distance function which minimizes the impact of

noise. However, the limitation in the Kernal FCM is

that it do not utilize the neighbourhood information.

To overcome this problem, researchers propsed a

variant of FCM known as Spatial Kernel FCM

(SKFCM) (Timmis et al., 2008; Roy et al., 2014).

This technique incorporates neighbourhood

information into objective function of FCM. To

ICPRAM 2020 - 9th International Conference on Pattern Recognition Applications and Methods

434

certain extent the above techniques overcome the

drawbacks of Fuzzy C-Means. However they still

suffer from single feature inputs and high

computational time. To address these limitations, a

Robust Spatial Kernel FCM (RSKFCM) algorithm

was proposed in (Kumar et al., 2015). Robust Spatial

Kernel FCM (RSKFCM) consists of spatial

information to the conventional FCM function.

Similar to FCM, the main aim of the RSKFCM is to

minimize the objective function shown in equation 4.

2

=1 =1

=()()

cn

m

ij j i

ij

Jwxv

(4)

Where

c is the number of clusters, n is the number

of data points,

m is a constant, which controls the

fuzziness of the resulting partition,

ij

w

is the

RSKFCM membership degree of

j

x

in

th

i

cluster.

i

v

is the i

th

cluster center,

is an implicit non

linear map which is computed as:

2

() ()=(,) (,)2(,)

j

ijjjjji

x

vKxxKvvKxv

(5)

where

K

is the inner product of kernel function

i.e.,

)()(=),( yxyxK

T

.

2

2

(, )=exp /Kxy x y

(6)

In Gaussian kernel

1=),( xxK

and

1=),( vvK

,

hence the kernel function becomes:

2

( ) ( ) = 2(1 ( , ))

j

iji

x

vKxv

(7)

Substituting equation 7 in equation 4, the objective

function becomes:

=1 =1

= 2 (1 ( , ))

cn

m

ij j i

ij

J

wKxv

(8)

RSKFCM membership function

ij

w

is the

combination of kernel membership function

ij

u

and

neighbourhood function

ij

s

and it is computed as:

=1

=

pq

ij ij

ij

c

pq

kj kj

k

us

w

us

(9)

where

p and q are parameter to control the relative

importance of kernel membership and neighbourhood

membership functions.The kernel and neighbourhood

membership functions are computed using equation

10 and 11.

1/( 1)

1/( 1)

=1

1,

=;

1,

m

ji

ij

c

m

jk

k

Kx v

u

Kx v

(10)

()

=

ij ik

kNKx

j

s

u

(11)

where

)(

jk

xN

represents a neighbourhood data

points of

j

x

. This neighbourhood function

represents the probability that data point

j

x

belongs

to

th

i

cluster.

Similar to FCM, RSKFCM also work in iterative

process by updating the membership and cluster

center values. The cluster centers are updated using

equation 12

=1

=1

(,)

=

(,)

n

m

ij j i j

j

i

n

m

ij j i

j

wKx vx

v

wKx v

(12)

This iterative of RSKFCM will stop when stopping

criteria is satisfied i.e., the difference of successive

iterations objective function value is less than the user

specified stopping criteria value. Though RSKFCM

solved the problems of single feature inputs and high

computational time, it still holds few limitations:

Firstly, incorporating neighborhood information

only to the objective function.

Secondly, the current methods assume that, all

features have equal importance. However, in real

world cases all the features may not be equally

important.

To alleviate these drawbacks, Generalized Spatial

Kernel Fuzzy C-Means (GSKFCM) is proposed in

this article.

3 PROPOSED METHOD

Generalized Spatial Kernel Fuzzy C-Means (GSK-

FCM) incorporates the weighted neighborhood

information into distance function and uses Gaussian

kernel as distance metric.

The aim of the GSK-FCM is to minimize the

objective function shown in equation 13

2

=1 =1

=2 ,

cn

m

ij new j k

ij

J

zd xv

(13)

Sclera Segmentation using Spatial Kernel Fuzzy Clustering Methods

435

where

ij

z

is the GSK-FCM membership function

and it is computed as:

1

2

1

2

=1

1

=

,

,

ij

c

m

new j i

new j k

k

z

dxv

dxv

(14)

Where

new

d

is the GSK-FCM distance function

which incorporates the neighbourhood function into

distance function and it is computed as:

22

,= ,

new j i j i ij

dxvdxvfp

(15)

where,

ij

vxd ,

2

is the Gaussian Kernel distance

function shown in equation 7 and

1

()=

ij

ij

fp

p

is the

neighborhood function.

GSK-FCM considers neighbourhood information

and computes membership value associated with each

data point as weighted sum of traditional FCM

membership value and the membership value of the

k

N

neighbour points. The neighbourhood function

)(

ij

p

is defined as

=0

=,

N

k

ij j k ik

k

p

hx x gu

(16)

Where

k

N

is the number of neighbourhood data

points,

ikik

uug =)(

is the membership function

(equation 10),

),(

kj

xxh

is the distance function

which is computed as:

1

2

2

=0

,

,=

,

N

k

jk

jk

jl

l

dxx

hx x

dxx

(17)

Substituting equation 17 in 16 the neighbourhood

function becomes:

1

2

2

=0 =0

,

=

,

NN

kk

jk

ij ik

jl

kl

dxx

pgu

dxx

(18)

Substituting equation 15 in equation 14, the

membership function

ij

z

becomes,

1

1

2

1

2

=1

,

=

,

c

m

ji ij

ij

jk jk

k

dxvfp

z

dxv fp

(19)

1

1

21

1

1

2

=1

1

1

21

1

1

2

=1 =1

,

,

=

,

,

c

m

ji

m

ij

jk

k

cc

m

ji

m

jk

jl

kl

dxv

fp

dxv

dxv

fp

dxv

(20)

where,

1

1

2

1

2

=1

,

=

,

c

m

ji

ij

jk

k

dxv

u

dxv

Then the membership function

ij

z

becomes

1

1

1

1

=1

=

m

ij ij

ij

c

m

jk jk

k

uf p

z

uf p

(21

)

Similar to FCM and RSKFCM, GSKFCM operates in

iterative process by updating membership and cluster

center value. The cluster centers are updated using

equation 22

=1

=1

,

=

,

n

m

ij j i j

j

i

n

m

ij j i

j

zKxv x

v

zKxv

(22)

GSK-FCM decides the label based on the maximum

membership value.

4 DATASET AND RESULT

ANALYSIS

This section presents the result evaluated of the

proposed GSK-FCM clustering algorithm. To

evaluate the proposed method, experimentations are

conducted using Sclera Segmentation and

Recognition Benchmarking Competition

(SSRBC2015) dataset (Das et al., 2016). Table 1

presents the characteristics of the dataset. The dataset

contains 30 individuals eye image with different cases

such as blinked eye, closed eye, blurred eye. For

every individual eye, the images are captured in

different angles like looking at the center, left, right

and up. Thus the dataset in total consists of 120 eye

images with ground truth images.

ICPRAM 2020 - 9th International Conference on Pattern Recognition Applications and Methods

436

Table 1: Characteristics of SSRBC2015 dataset.

Number of individuals 30

Number of samples per

individuals

4

Captured Angle Center,left, right and up

Image resolution 1489 X 1105

Total number of samples 120

Figure 1: Sample sclera images and ground truth of

SSRBC2015 dataset.

To test the effectiveness of the proposed model, the

performance of the GSK-FCM method is compared

with other versions of FCM and RSKFCM. To find

the optimal value of the parameters, four well known

cluster validity indices: Partition Coefficient

pc

V

,

Partition Entropy

pe

V

, Fukuyama-Sugeno function

fs

V

, Xie-Beni function

xb

V

are used as an

evaluation metrics. For all the experiments, we have

set the fuzzifier m value to 2 and stopping criteria

to 0.00001 empirically. For sclera segmentation,

cluster number

c

is set to 3 (sclera, iris and outer

region). Figure 2 and Figure 3 presents the cluster

validity results of the existing RSKFCM and

proposed GSK-FCM method for different

p

and

q

values.

Figure 2: Cluster validity indices for different p and q

values of RSKFCM on sclera segmentation (a)

pc

V

, (b)

pe

V

, (c)

xb

V

, (d)

fs

V

.

Figure 3: Cluster validity indices for different p and q

values of GSKFCM on sclera segmentation (a)

pc

V

, (b)

pe

V

, (c)

xb

V

, (d)

fs

V

.

Figure 4 and Figure 5 presents the comparison of

four cluster validity indices values of the proposed

methods for different window size on sclera

segmentation. From empirical evaluation, it is found

1=p

,

2=q

,

= 150

and window size=5 are

optimal values for sclera segmentation. Table 2 and

Table 3 shows the cluster validity indices value,

precision and recall values of the proposed methods.

Figure 4: Cluster validity indices for different window size

of the existing RSKFCM and proposed GSK-FCM methods

on sclera segmentation (a)

pc

V

, (b)

pe

V

, (c)

xb

V

, (d)

fs

V

.

Figure 5: Cluster validity indices for different kernel width

of the existing RSKFCM and proposed GSK-FCM

methods on sclera segmentation (a)

pc

V

, (b)

pe

V

, (c)

xb

V

, (d)

fs

V

.

Sclera Segmentation using Spatial Kernel Fuzzy Clustering Methods

437

Table 2: Performance comparision in terms of cluster

validity indices on sclera traits.

Method Precision Recall

FCM 65.98 65.12

KFCM 67.43 66.96

SFCM 69.72 68.79

SKFCM 72.93 73.08

RSKFCM 85.21 80.21

GSK-FCM 85.89 80.23

Table 3: Performance comparision in terms of

segmentation on sclera traits.

Method V

pc

V

pe

V

xb

[1x10

-3

] V

fs

[-1x10

6

]

FCM 0.832

0.236 74.68

350.64

KFCM 0.848

0.225 72.19

353.68

SFCM 0.866

0.220 70.68

361.31

SKFCM 0.884

0.213 67.84

365.38

RSKFCM 0.921 0.192 60.34 387.13

GSK-FCM 0.931 0.167 59.65 390.67

5 CONCLUSION

This paper presents the Generalized Spatial Kernel-

Fuzzy C Means (GSK-FCM) clustering algorithm

which is capable of segmenting sclera images. The

proposed algorithm have overcome the drawbacks of

traditional FCM method by considering

neighbourhood information and using Gaussian

kernel distance measure. The inclusion of

neighbourhood information and use of kernel

function reduces the impact of noise which in turn

increases the results. This paper work has been

applied to sclera segmentation images, where in the

segmentation plays a crucial role for

recognition/identification purpose for future

researchers who deal in authentication of users using

sclera biometric trait. From the observations of the

results and its comparison with other methods the

proposed GSK-FCM performs better than the other

methods.

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