Fuzzy C Mean Thresholding based Level Set for Automated Segmentation of Skin Lesions

doi:10.4236/jsip.2013.43B012

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Journal of Signal and Information Processing, 2013, 4, 66-71

doi:10.4236 /jsip.2013.43B012 Published Online August 2013 (http://www.scirp.org/journal/jsip)

Fuzzy C Mean Thresholding based Level Set for

Automated Segmentation of Skin Lesions

Ammara Masood, Adel Ali Al-Jumaily

Scho ol of Electrical, Mechanical and Mechatronic Engineer ing, Universi ty of Techn ology, Sydney, Austral ia.

Email: ammara.masoo [email protected]. edu.au, Adel.Al-[email protected]

Received April, 2013.

ABSTRACT

Accurate se gmentation is an importa nt and challe nging task in any comp uter vision s ystem. It also plays a vital role in

computerized analysis of skin lesion images. This paper presents a new segmentation method that combines the advan-

tages of fuzzy C mean algorithm, thresholding and level set method. 3-class Fuzzy C mean thresholding is applied to

initialize level set automatically and also for estimating controlling parameters for level set evolution. Parameters for

performance evaluation are presented and segmentation results are compared with some other state-of-the-art segmenta-

tion methods. Increased true detection rate and reduced false positive and false negative errors confirm the effectiveness

of proposed method for skin cancer detection.

Keywords: Skin Cancer; Segmentation; Diagnosis; Fuzzy; T hresholding; Level Se ts

1. Introduction

The incidence of skin cancer is rapidly increasing

thro ugh-out the world [1]. An estimated 76,250 new cas-

es of invasive melanoma were diagnosed in the US in

2012, with an estimated 9,180 resulting in death [2].

Australia has one of the highest rates of skin cancer in

the world. Over 1890 Australians die from skin cancer

each year [3]. Melanoma is capable of deep invasion.

The most dangerous characteristic of melanoma is that it

can spread widely over the body via the lymphatic ves-

sels and blood vessels. Thus, early diagnosis of mela-

noma is a key factor for prognosis of the disease.

Analysis of skin lesion images taken using dermo-

scopic imaging technique [4] is a commonly used me-

thod for diagnosis of skin cancer but, this method re-

quires great deal of experience [5]. Due to the lack of

reproducibility and subjectivity of human interpretation,

the development of computerized image analysis tech-

niques is of paramount importance. Segmentation is one

of the most important and difficult task in computerized

image analysis process. The accuracy of the subsequent

steps highly depends on the success of image segmenta-

tion technique.

Segmentation o f ski n lesi ons is d iffic ult because of the

great variety of lesion shapes, sizes, and colors along

with different types and textures of human skin. Other

difficulties that make it a challenging task include, low

contrast between the lesion and the surrounding skin,

smooth transitio n between the lesion and the skin, reflec-

tions d ue to wrong i llu mina tio n and art ifacts suc h as s ki n

texture, air bubbles and hair.

Image segmentation algorithms available in literature

can be broadly classified into two categories: 1) discon-

tinuity based segmentatio n 2) Similar ity based seg menta-

tion, which c a n further be classified into thresholding [6],

clustering [7], and region based approach [8]. Compara-

tive analysis of these approaches in the area of skin le-

sion segmentation can be found in literature [9-11].

Active contour is a popular approach used to estimate

boundaries in medical images. Two types of algorithms

lie under this category: 1) parametric active contours [12]

which adapt a deformable curve until it fits the object

boundary. 2) Geometric active contours based on level

set theory. Some of the active contour models need user

interventio n for initialization. Thus auto matic approaches

like gradient vector flow algorithm [13, 14] based on

anisotropic diffusion [15] and robust algorithms like

adaptive snakes and shape probability association model

[16] are ta king important plac e in liter a ture.

Level set (LS) methods, as one of the automatic proc-

ess approach have shown effective results for medical

image segmentation. However, intensive computational

requirements and regulation of controlling parameters

make it a complex and time consuming method. To

overcome such shortcomings, fuzzy clustering has been

used to facilitate the LS segmentation for automatic

segmentation of ultrasound, computed tomography and

Fuzzy C Mean Thresholding based Level Set for Automated Segmentation of Skin Lesions

magnetic resonance imaging [17-19]. Fuzzy C mean

(FCM) based thresholding [20] and LS algorithm are

different computational models that have been applied

individuall y for segme ntation of der moscopic images [21,

22]. Similarly, some work is done on using clustering for

initial segmentation followed by further edge preserving

and refining steps for border tracing of skin lesions [23].

We analyzed the advantages and limitations of these

methods for skin lesion segmentation. The observations

showed that FCM works well for making rough cluster-

ing of pixels which can further be used to get better

threshold values for image segmentation. In addition to

this, if the thresholded image is used as initial estimate

for level set evolution, it can result in more accurate

segmentation as compared to standard level set method

[24,25] and region based active contours [26,27]. We,

hereby presented a technique, based on combining these

methods to achieve higher accuracy in segmentation of

skin lesion images .

This paper introduces 3-class FCM based thresholding

to be used for ini tializi n g the LS evolu tion a nd re gulati ng

the controlling parameters. Performance evaluation is

done by comparing the diagnosis results of this method

with three other segmentation methods i.e. FCM cluster-

ing [28], region based active contours [26, 29] and adap-

tive thresholding [11]. Results show that the proposed

approach performs reasonably well for the segmentation

of ski n lesion i mages. The pap er is or ganized as follows:

Section 2 provides details of the proposed segmentation

method. Section 3 discusses experimental results and

Section 4 provides performance evaluation. Concluding

remarks ar e given in Sect ion 5.

2. Methodology

This section describes our technique for segmentation of

skin cancer images. The main parts of our proposed al-

gorithm are:

2.1. Image Pre-Processing

For skin lesion images there are certain extraneous arti-

facts such as skin texture, air bubbles, dermoscopic gel,

presence of ruler markings and hair that make border de-

tection a bit difficult. In order to reduce the effect of these

artifacts on segmentation results, the images need to be

pre-processed with a smoothing filter. We found that the

best segmentation results were obtained using median

filter with 7x7 mask to smooth the images before seg-

mentation. Thus, the first step of the overall process is to

get a filtered image.

2.2. Fuzzy C-Mean Thresholding

FCM clustering is used to partition N objects into C

classes. In our method, N is equal to the number of pixels

in the image i.e. N=Nx x Ny and C=3 for 3-class FCM

clustering. The FCM algorithm uses iterative optimization

of an objective function based on a weighted similarity

measure between the pixels in the image and each of the

c-clus ter cen ters . A local extre mism of the objecti ve func-

tion indicates an op timal clustering o f the input d ata. The

objective function that is minimized is given by (1)

(1)

where and &

where . ‖*‖ is a norm expressing the simi-

larity between any measured data value and the cluster

centre; m∈ [1, ∞] is a weighting exponent and can be any

real number greater than 1.

Calculations suggest that best choice of m is in the in-

terval [1.5, 2.5], so m=2 is used here as it is widely ac-

cepted as a good choice of fuzzification parameter. The

fuzzy c-partition of given data set is the fuzzy partition

matrix U= [ with i =1 , 2 …. C a nd j =1, 2, 3…N , where

indicate the degree of membership of jth pixel to ith

cluster. The membership functions are subject to satisfy

the following conditions.

for j=1,2,3,….N ; for i=

1,2….C;

The aim of FCM algorith m is to find an optimal fuzz y

c-partition by evolving the fuzzy partition matrix U=

[ iteratively and computing the cluster centres. In

order to achieve this, the algorithm tries to minimize the

objective function Q (1) b y iteratively updating the clus-

ter centres and the membership functions using the fol-

lowing equations.

(2)

(3)

After performing FCM clustering, finally each pixel is

assigned to the cluster for which its membership value is

maximum. Based on the intensity distribution obtained

using histogram of the image, the threshold value is

calculated by taking mean of maximum of cluster 1 and

minimum of cluster 2 or maximum of cluster 2 and

minimum of cluster 3. This method of threshold selection

takes into acco unt the intensity distrib ution i n the ima ge.

This choice helps in obtaining opti mum threshold values

for different images obtained under different conditions.

The overall FCM thresholding algorithm is presented in

Figure 1. The output of this stage is a binary image (Bi)

which has been used in the followed steps.

2.3. Fuzzy C-mean Thresholding based Level Set

Segmentation

Segmentation of images by means of active contours is a

well-established approach. Active contours [12] are used

Fuzzy C Mean Thresholding based Level Set for Automated Segmentation of Skin Lesions

to detect objects in a given image using techniques of

curve evolution. The basic idea is to evolve a curve, sub-

ject to constraints from a given image, for detecting ob-

jects in that image.

Figure 1. Algorith m for FCM thresholding.

In pr o b lems o f curve evo l uti o n, le ve l set methods have

been extensively used. LS methods are established on

dynamic implicit interfaces and partial differential equa-

tions (PDEs). In traditional LS formulation [25], the

contours denoted by C, are represented by the zero level

set C(t)= {(x,y)| (t,x,y)=0)of a level set function

(t, x,y). T he evolving eq uation of the level set functio n

can b e written in the following general form (4)

(4)

which is called levels set equation. The function F is the

speed function that represents the comprehensive forces,

including the internal force from the interface geometry

and the external force from image gradient or/and artifi-

cial mome ntums .

In order to stop the level set e volutio n near the opti ma l

solution, the advancing force has to be regularized by an

edge indication function g. The edge indication function

used here is given by (5)

(5)

where is the filtered image. T raditional LS method is

computationall y intens ive and has certain limi tations like

need of re-initialization of level set function to signed

distance function for stable curve evolution [26]. There-

fore, in this paper fast leve l set for mulation has been used

which was proposed by Li. et al. [24]. This method is

computatio nally more efficient and can be implemented

by using simple finite difference scheme. In order to

segment the skin lesion image the overall iterative proc-

ess for levels se t e volution is given by (6).

(6)

where is the term

for attracting towards the variational boundary and

is the penalty term that forces to

approach the genuine signed distance function automati-

cally.

This fast level set formulation proposed in [24] pro-

vides a benefit of flexible initialization where roughly

obtained region from thresholding can be used to con-

struct initial level set function. Taking advantage of this

facility binary image (Bi) obtained from FCM threshold-

ing algorithm, discussed in the previous section is used

here for automatic initializatio n of the level set fu nction.

The initial level se t function is given as [18] .

(7)

where is the regulator for dirac function [25] defined

as follows:

(8)

Controlling parameters are also adaptively determined

fro m the bina ry i mage (Bi) fo r re gular izi ng the LS evo lu-

tion process automatically. The weighting coefficient

of penalty term is taken as the ratio of area of on

pixels in the binary image (Bi) to its perimeter pixels.

The time step is take n a s 0 .2 / so that ( remains

s maller than 0.25 which is necessary to ensure stable

evolution as found in [24]. is the coefficient of con-

tour length for smoothness regulation and its value is

taken here as 0.1/. The val ue of can be increased for

accelerating the evolution process but it leads to

smoother contours. Thus, care must be taken especially

for skin lesion images, where over smoothened images

may lose significant details about boundary of lesion,

which is an important feature for correct diagnosis. The

balloon force which determines the advancing direction

Fuzzy C Mean Thresholding based Level Set for Automated Segmentation of Skin Lesions

and speed of the evolvi ng curve is given as ( 9)

(9)

where is the modulating argument which i s t aken her e

as 0.5 through experimental analysis. Fig ure 2 shows a

systematic diagram of the proposed method. Each block

represents different steps of the algorithm.

Figure 2. Flowchart of proposed algorithm.

3. Experimental Results

Segmentation results obtained using the proposed algo-

rithm, FCM clustering, Adaptive Thresholding (AT) and

Region based Active Contours (RBACs) are presented in

Figures 3-7 for some of the skin lesion images. While

presenting results, we tried to present images having dif-

ferent common problems of dermoscopic images which

can badly affect the segmentation process. Figure 3

shows an image of dysphasic nevi ha ving poor illumina-

tion and uneven boundary of lesion. Fig ure 4 represents

melanoma lesio n with uneven border and hair on it. Fig-

ure 5 is melanoma lesion with smooth transaction be-

tween lesion and skin. Figure 6 is a melanoma lesion

present on a skin with spots and redness effect. Figure 7

is a benign lesion surrounded by a lot of hair.

FCM clustering and AT provide rough segmentation

but cannot track the boundary exactly. Region based ac-

tive contours provided results comparable to proposed

method in some cases but this method cannot track the

border in the presence of many hair (see Figure 7(f)) or

spotty skin (see Figure 6(f)). Similarly, it missed the

exact boundary in the case where there is a smooth

transaction between lesion and skin (see Figure 5(f)).

Figure 3. Se g menta ti o n res ul t s of dy s pla s ti c ne vi ( a) or ig i nal