A New ISODATA Image Segmentation Algorithm Based on Intuitionistic Fuzzy

Yinlong WANG1, a, Kecheng LIN 1,a, Hongmei YU2,b, Qianjin LI 1,c,

Zhixiang LI 1,a and Xiwu WANG 1,a

1The Fifth Department of Ordnance Engineering College, Shijiazhuang, China

2Wuhan Ordnance N.C.O Academy of PLA，Wuhan，China

areturnsjz@sina.com,byhm2203@126.com, clqj2001358@sohu.com

Keywords: Image Segmentation, ISODATA Algorithm, Intuitionistic Fuzzy

Abstract. ISODATA algorithm is capable of splitting and merging categories automatically.

However, this kind of hard clustering fails to take into consideration the characteristics of image itself

and human visual features. So its effect is generally not as good as that of fuzzy clustering algorithm.

For most fuzzy recognition methods, if they are to be applied, the number of categories must be set

beforehand. Besides, there is inherent defect in traditional Fuzzy algorithms. By contrast,

intuitionistic fuzzy is a kind of improvement to make up the deficiencies of traditional fuzzy theory.

Based on the advantages of ISODATA algorithm and intuitionistic fuzzy, with those critical

functions which are related to membership and non-membership functions used as the measurement

for clustering, this thesis is to propose a kind of ISODATA algorithm that is based on intuitionistic

fuzzy, and to introduce membership function that has been improved for practical purposes. This kind

of function takes region as the sample to be classified. Finally, this thesis is to verify the effectiveness

of the proposed algorithm by applying it to Image Segmentation.

Introduction

In recent years, more and more attention has been paid to Fuzzy Clustering, because compared with

direct hard clustering algorithm, Fuzzy Clustering can retain more original image information, and it

is more accord with human recognition cognitivec habits[1]. But for most fuzzy recognition methods,

if they are to be applied, the number of categories must be set beforehand. In the case of unknown

number of categories, more often than not, the desired classification effects cannot be achieved.

ISODATA（ iterative self-organizing data analysis technique） algorithm[2] is capable of splitting

and merging categories automatically and thus gets reasonable clustering. There is inherent defect in

the traditional Fuzzy Theory. And Intuitionistic Fuzzy is a kind of effective extension based on the

traditional theory. First of all, based on the advantages of Intuitionistic Fuzzy and ISODATA

algorithm, this thesis analyzes pixel distribution from the angle of region rather than individual pixel

in the light of space coherence. Then this thesis proposes a new membership and puts forward

ISODATA clustering algorithm based on Intuitionistic fuzzy. Through experiments, good results

have been achieved, which exactly verify the effectiveness of the proposed algorithm[3,4].

Basic Concepts

Fuzzy Theory.The fuzzy theory extended from traditional set theory[5]. It is generally considered to

be the most feasible mathematical tool to solve problems in artificial intelligence. But the traditional

fuzzy theory has its inherent defect. For example, when an element has the same degree of

membership with a few categories, it is difficult to classify this element precisely. Comparatively

speaking, Intuitionistic {<x, µA(x), γA(x)>}Fuzzy is an effective extension from the traditional fuzzy

theory. Suppose that X is a given universe, A is an Intuitionistic Fuzzy set in the universe X, and its

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definition is. In this definition, µA(x):X→[0,1] is the membership function of X for A; γA(x):X→[0,1]is

the non-membership function of X for A, which indicates the degree that X doesn’t belong to A under

the condition of 0≤µA(x)+γA(x)≤1. For a subset A in the universe X, πA(x)=1-µA(x)- λA(x) is called

intuitionistic index of x for A, and it is the measure of the extent of hesitation of x for A. Thus

corresponding to the intuitionistic fuzzy subset A, while judging whether x belongs to A, with the

influence of membership and non-membership taken into consideration, the critical function T(p)=

αµA(x)+βπA(x)is introduced, with α β as the synthetic weighted coefficients for membership function

and intuitionistic index respectively.

ISODATA Clustering Algorithm.In C-Means Algorithm, every time the category of a sample is

adjusted, cluster centers of samples of all categories will be updated. Different from common

C-Means Algorithm, ISODATA Algorithm is a method of batch sample correction. It is after all

samples are adjusted that cluster centers of samples of all categories will be updated. ISODATA

algorithm can realize classification by adjusting categories that each sample belongs to. It is also

capable of splitting and merging categories automatically, in order to get a clustering whose number

of categories is relatively reasonable. In addition, this algorithm has a good rejection capability

against noise.

The ISODATA Algorithm procedure is as follows:

Suppose that there is a sample set{y1,y2,…yN}, and the sample number is N. Control parameters are

set as follows: K as expected clustering number,θN as a sample of minimum clustering, θS as the

parameter of standard deviation, θC as merging parameter, L as the maximum clustering that is

allowed to merge in each iteration, I as the allowed iterative number of times.standard deviation

Suppose that c is the initial clustering, and the initial cluster center is mi i=1,2,…C.

1. Set clustering analysis control parameters.

2. The initial classification.

3. According to the given requirements of control parameters, split and merge the previously

obtained clustering set, in order to get new clustering center and set.

4. Conduct interactive operations again, recalculate the overall indexes and discriminate whether

the clustering results conform to the requirements or not. Repeat this process until ideal clustering

results are obtained.

ISODATA Algorithm Based on Intuitionistic Fuzzy

Based on fuzzy theory, this thesis brings in membership function and uses the degree of membership to

replace euclidean distance in ISODATA Algorithm. As for image, the classification results are

determined by grayscale, and in most cases they present a type of symmetric bell distribution with the

category center as the symmetry center. Thus in this thesis, generalized bell function serves as

membership function for fuzzy classification. Generalized bell function is as follows:

b2

ii

ij

a

mx1

1)x(

−+

=µ

(1) mi as clustering center; a and b are usually positive numbers. Compared with membership

function, generalized bell function has a simpler form and less calculated amount, and conforms to

image distribution better.

There is a restricted condition among membership function µ (x), non-membership function λ(x) and

intuitionistic index π (x), that is µ (x)+ λ(x) +π (x)=1.

Suppose intuitionistic index is a constant, that is π (x)=d(0≤d≤1). Research shows that this

assumption is applicable in solving specific problems in most actual conditions. Thus a

non-membership function may be deduced, that is, λ(x)=1-dA-µA(x).

Specific procedure of the algorithm are as follows：

1.Use region formation algorithm to form pixel region.

2.Take region as the samples to be classified, and regard grayscale as measurement for features.

310 Sport Materials, Modelling and Simulation

Set the initial parameters for ISODATA clustering.

3. Calculate membership function, non-membership function, intuitionistic index and the critical

function.

4. Sort all samples into clustering, according the definition, i.e. if µA≤µA.

5. For any clustering (take Γj for example), if Nj<θN, then cast outΓj, and set C=C-1.

6. Update clustering center as

∑=

=N

i

ij

iij

j

vpT

vvpTm

1

2

2

)()(

)()(

(2) 7. Take T(p) as the measurement for distance, and use ISODATA clustering algorithm to split and

merge the samples formed by region formation algorithm.

8.If the program reaches its maximum number of iterative operations, the program stops;

otherwise, the program goes to Step “2”, and the interation counter adds 1.

Experimental Analysis and Contrast

Figure 1. The original image

Figure 2. The Segmentation by the fuzzy c-means clustering

Figure 3. The Segmentation by the ISODATA Algorithm Based on Intuitionistic Fuzzy

Advanced Materials Research Vol. 187 311

The 1st image shows that the algorithm proposed in this thesis is superior to c-means algorithm in

terms of segmentation details. The 2nd

image shows that regarding segmentation sharpness, it is

superior to c-means algorithm as well. The 3rd

image reveals that in the segmentation of inner edge

part, it has a relatively clear edge, because intuitionistic fuzzy is superior to the traditional fuzzy.

Besides, the proposed algorithm takes not pixel but region as samples, thus it has a relatively smaller

number of samples to classify and has got a faster speed.

References:

[1] M M Trivedi , J C Bezdek. Low level segmentation of aerial images with fuzzy clustering :IEEE

Trans on SMC Vol.16(1986),p.589.

[2] J C Dumn.A fuzzy relative of the ISODATA process and its use in detecting

compact,well-sepatated clusters:Journal of Cybernetics Vol.3(1974),p.32.

[3] R I Cannon , J Dave , J C Bezdek. Efficient implementation of the fuzzy c-means clustering

algorithms :IEEE Trans on PAMI Vol.8(1986) ,p.248.

[4] Atanassov K. Intuituinistic fuzzy sets:Fuzzy Sets and Systems Vol.20(1986),p. 87.

[5] Atanassov K. More on intuitionistic fuzzy sets:Fuzzy Sets and Systens Vol.33(1989),p. 37.

312 Sport Materials, Modelling and Simulation

Sport Materials, Modelling and Simulation 10.4028/www.scientific.net/AMR.187 A New ISODATA Image Segmentation Algorithm Based on Intuitionistic Fuzzy 10.4028/www.scientific.net/AMR.187.309