Neurocomputing 87 (2012) 90–98

Contents lists available at SciVerse ScienceDirect

Neurocomputing

0925-23

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/neucom

Quantum evolutionary clustering algorithm based on watershed appliedto SAR image segmentation

Yangyang Li n, Hongzhu Shi, Licheng Jiao, Ruochen Liu

Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi’an 710071, China

a r t i c l e i n f o

Article history:

Received 28 July 2010

Received in revised form

1 February 2012

Accepted 7 February 2012

Communicated by D. Taoand the quantum-inspired evolutionary algorithm is used to search the optimal clustering center, and

Available online 22 February 2012

Keywords:

Quantum evolutionary clustering algorithm

Watershed algorithm

SAR image segmentation

12/$ - see front matter & 2012 Elsevier B.V. A

016/j.neucom.2012.02.008

esponding author. Tel.: þ86 29 88202279.

ail address: yyli@xidian.edu.cn (Y. Li).

a b s t r a c t

The goal of segmentation is to partition an image into disjoint regions. In this paper, the segmentation

problem based on partition clustering is viewed as a combinatorial optimization problem. A new

algorithm called a quantum evolutionary clustering algorithm based on watershed (QWC) is proposed.

In the new algorithm, the original image is first partitioned into small pieces by watershed algorithm,

finally obtain the segmentation result. Experimental results show that the proposed method is effective

for texture image and SAR image segmentation, compared with QICW, the genetic clustering algorithm

based on watershed (W-GAC) and K-means algorithm based on watershed (W-KM).

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Clustering [1,9,6,10,21] is an important unsupervised classifi-cation technique, which is a widely used in data mining, andclassification. The existing clustering algorithms include parti-tional clustering, hierarchical clustering, density-based clustering,grid-based clustering, model-based clustering, as well as cluster-ing technology combining with fuzzy theory [17], graph theory[18], and subspace learning [4,19,20]. There is some novelclustering methods lately, such as spectral clustering [23], fastgradient clustering [25] and manifold elastic net [26].

Texture feature is the most important intrinsic attributes of animage [5]. Texture is considered to be the interpretation ofdistinction between different attribute of images. Nearly threedecades, researchers presented many segmentation algorithmsbased on texture feature, which can be divided into two cate-gories: supervised learning method and unsupervised learningmethod. But supervised learning method applied to image seg-mentation problem leads to the same target area looks differenteven in the same image, thus, not all the categorical features oftarget area can be contained. In this case, unsupervised learningmethod applied to segmentation, and so called clustering method,will be more effective. Unsupervised segmentation can be gen-erally divided into two categories: hierarchical clustering andpartition clustering. Partition clustering is a division of data intodifferent groups according to given rules.

ll rights reserved.

In this paper, the segmentation problem using partitionclustering is viewed as a combinatorial optimization problem,which is in accordance with some specific criterions that theimage dataset will be partition into different category. But theexisting optimization methods e.g., conventional genetic algo-rithms (CGAs) are often time-consuming, the convergence speedof which is slow and easy to trap in local optimal value. Forsolving above problems, a novel optimization method is intro-duced based on some concepts of quantum computing, called aquantum-inspired evolutionary algorithm (QEA) [7]. In particular,in QEA the representation is investigated to represent the indivi-duals to explore the search space with a small number ofindividuals, and to exploit the global optimal solution in thesearch space within a short span of time, respectively. But forcomplex image, based on pixel clustering methods to solve imagesegmentation, it is often time-consuming. Watershed algorithm[22,2] has the advantage of a region growing algorithm, while stillmaking use of boundaries information, as captured by thegradient surface, which is so simple and effective that it has beenwidely used image segmentation tool [8,15,14]. However, thegradient transformation is sensitive for noise, and can manifestitself as over segmentation. In the paper [13], QICW have beenproposed for segmentation. But QICW needs to set more para-meters. This paper proposes a novel algorithm for segmentationcalled a quantum evolutionary clustering algorithm based onwatershed (QWC), which aims to search for the optimum cluster-ing center quickly and effectively, locate edge position accurately,and improve the performance of image segmentation. In QWC,we use watershed algorithm to partition the original image intosmall blocks in this paper, for one thing, it can accelerate the

Y. Li et al. / Neurocomputing 87 (2012) 90–98 91

convergence speed, for another, it is a region growing algorithm,while still making use of edge information, as captured by thegradient surface. And QWC is based on the concept and principlesof quantum computing, such as the quantum bit and the super-position of states. QWC is also characterized by the representationof the individuals, the evolution mechanism, and the populationdynamics. Unlike the binary, numeric coding, the coding mannerof QWC is quantum individual coding, which can represent anystates, thus has better diversity. And the quantum mutation andcrossover operation can expedite the speed of evolution and avoidthe prematurity in the whole procedure effectively.

The rest of this paper is organized as follows. Section 2 givesthe related works about the image segmentation. In Section 3, theproposed method has been described in details. Section 4 showsthe experimental results. Finally, Section 5 represents the con-clusion of this paper.

Fig. 1. Overall structure of QWC.

2. Related works

2.1. Watershed segmentation strategy

Watershed segmentation algorithm [22] is a kind of regionextraction algorithms, which is so simple and effective that it hasbeen a widely used image segmentation tool. Watershed algo-rithm has the advantage of regional growth, namely spatiallyconsistence, with boundaries forming a closed and connected setas well as making full use of edge information captured by thegradient surface. However, the gradient transformation is sensi-tive to noise, and can manifest itself as over-segmentation. Thisproposed algorithm will make use of the over-segmentation tosupply reduced samples for the next phase of the quantumevolutionary clustering algorithm. The applied watershed seg-mentation strategy includes four steps.

Step 1: Simplify the image:The purpose of simplifying the image is to remove theinterference caused by noise and other unimportant details,as well as to smooth the image. Here the commonly used tool– Median Filter is adopted.Step 2: Compute morphological gradient image:Morphological gradient [24] image reflects the gray change inthe image. At the edge of acute gray change, the gradientvalues also change a lot and vice-versa. The definition ofmorphological gradient image is that dilating transformationsubtracting eroding transformation:

gradðf Þ ¼ ðf þsÞ�ðfYsÞ: ð1Þ

where þ represents the dilating transformation while Yeroding transformation, and s is the structuring element.Step 3: Compute the floating point activity image:

fimgðf Þ ¼ gradðf Þ � gradðf Þ=255:0: ð2Þ

Step 4: Get the initial segmentation result according to thewatershed algorithm.

2.2. Discrete wavelet transformation

The discrete wavelet transformation (DWT) is regarded as themost useful technique for frequency analysis of signals that arelocalized in time or space. It decomposes signals into basisfunctions that are extension and translations of a signal prototypewavelet function.

The discrete wavelet transformation permits the analysis of thesignal in many frequency bands or at many scales [12]. In practice,

multiresolution analysis is carried out using two channels filterbanks composed of a low-pass and a high-pass filter and each filterbank is then sampled at a half rate of the previous frequency. Thedown sampling procedure keeps the scaling parameter throughoutsuccessive wavelet transformation. Therefore, the original image isdecomposed with n layers; there will be texture features with 3nþ1dimensions {f1,f2, y, f3nþ1}, where fi is the energy of ith sub-band,which is calculated as follows:

f ¼1

MnN

XMi ¼ 1

XN

j ¼ 1

9xði,jÞ9: ð3Þ

Here, MnN is the size of sub-band, (i,j) represents the index for sub-band coefficient. In this paper, the DWT is used to decomposeimages into three layers.

3. Two-stage image segmentation approach

In this section, the proposed algorithm, quantum evolutionaryclustering algorithms based on watershed (QWC) will bedescribed in detail. First, the original image is partitioned intosmall pieces by using the watershed strategy. And then, theseprimitive regions are used to construct a graph representation ofthe image, the final segmentation is performed by the quantumevolutionary clustering algorithm.

Fig. 1 shows the overall structure of quantum evolutionaryclustering algorithm based on watershed (QWC). The overallprocedure of QWC is summarized as follows, in which Q(t), P(t)and b, respectively denote the population based on qubit at thetth generation, the population based on classical bit at the tthgeneration, and the best individual based on classical bit in the tthgeneration’s population.

Quantum evolutionary clustering algorithm based on watershed:

Step 1: Input the image, the watershed algorithm is used to getthe over segmentation result.Step 2: Compute the block feature: First, extract the waveletproperties of each pixel, and then take the mean value ofwavelet characteristics as the feature of each irregular region.Step 3: Initialize the cluster centers Q(t) and b; ai

t and bit (i¼1,

y, N) of all the qtj (j¼1, y, M) are initialized with the same

probability of 1=ffiffiffi2p

.Step 4: Observe the Q(t) by collapsing the qubit representationinto the binary representation P(t).

Table 1

The lookup table of Dy.

xi bi f(xi)Z f(bi) Dyi s(ai,bi)

aibi40 aibio0 ai¼0 bi¼0

0 0 False d 0 0 0 0

0 0 True d 0 0 0 0

0 1 False d 0 0 0 0

0 1 True d �1 þ1 71 0

1 0 False d �1 þ1 71 0

1 0 True d þ1 �1 0 71

1 1 False d þ1 �1 0 71

1 1 True d þ1 �1 0 71

1

1

10

1 α

β

α

Fig. 2. Quantum rotation gate.

Y. Li et al. / Neurocomputing 87 (2012) 90–9892

Step 5: Evaluate the fitness of each individual fk, then save thebest individual b.Step 6: Update Q(t) by using Quantum mutation (Quantumrotation gates) and then generate Qm(t).Step 7: Observe Qm(t) and generate the binary representationPm(t).Step 8: Update Pm(t) by using Quantum crossover and generate PC.Step 9: Evaluate the fitness of PC and save the best individual inPC, then perform the selection operation and generate P(tþ1).Step 10: If the stop criterion Sc is satisfied, then output thesegmentation result based on the best individual in P(tþ1)with the highest fitness value, otherwise go back to Step 4.

The major elements of QWC are presented as follows.

3.1. Representation

In this study, an individual represents a search point indecision space. Han and Kim [7] proposed a new representation,a qubit for the probabilistic representation that can represent alinear superposition of states and has a better characteristic ofpopulation diversity than other representations [11]. Therefore, itis used here. The probability amplitude of one qubit is definedwith a pair of numbers (a,b) as

ab

" #, ð4Þ

satisfying

9a92þ9b92

¼ 1, ð5Þ

where 9a92 gives the probability that the qubit will be found in the‘0’ state and 9b92 gives the probability that the qubit will be foundin the ‘1’ state. In this paper, QWC maintains a quantum popula-tion Q ðtÞ ¼ fqt

1,qt2,. . .,qt

Mg at the tth generation where M is the sizeof population, and N is the length of the qubit individual qt

i whichis defined as

qti ¼

at1 at

2 . . . atN

bt1 bt

2 . . . btN

" #, i¼ 1,2,. . .,Mð Þ ð6Þ

And in this paper, the qubit antibody qti represents cluster

centers.

3.2. The observing operation

We observe the updated qubit population Qm(t) and producebinary strings population PmðtÞ ¼ fxt

1,xt2,. . .,xt

Mg, wherext

l ðl¼ 1,2,. . .,NÞ is numeric strings of length N derived from theamplitude at

l or btl (l¼1, y, N) in Qm(t). The process is described as

follows: (a) generate a random number rA[0,1]; (b) if it is smallerthan at

i

�� ��2, the corresponding bit in xti ði¼ 1,2,. . .,NÞ takes ‘0’,

otherwise takes ‘1’.

3.3. Quantum mutation

In the quantum theory, the transform of states is fulfilled bythe quantum transformation matrix. For example, the updatingoperator can be denoted by the quantum rotation gates. Also, thebest individual in the current generation is important, i.e., thecommunication among individuals is needed to speed up theconvergence. Quantum mutation focuses on a wise guidance bythe current best individual in population. A quantum rotationgate U is

UðDyÞ ¼cosðDyÞ �sinðDyÞsinðDyÞ cosðDyÞ

" #, ð7Þ

where Dy is the rotate angle which controls the convergence ofQWC and Dy is defined as

Dyi ¼ dnsðai,biÞ, ð8Þ

where d is a coefficient which determines the speed of conver-gence. If the value of d is too small, the speed of convergence willslow down, while if the value of d is too large, divergence orpremature convergence may happen. So a dynamic regulationstrategy of rotating angle is used, which regulates the value of dbetween 0.1p and 0.005p according to the inheritance generation.The following lookup table can be used as a strategy for conver-gence. It should be indicated that it is a general way of mutationfor different problems.

In Table 1, bi and xi(i¼N) are the ith bit of the best solution b

and binary solution x, f(x) is the fitness of x, s(ai,bi) is the sign ofthe angle that controls the direction of rotation. Fig. 2 clearlyshows why it can converge to a better solution.

For example, when xi¼0, bi¼1, f(x)4 f(b). The probability ofcurrent solution xi should be larger in order to get a betterindividual, i.e., 9ai9

2 should be larger, so if (ai,bi) in the first orthird quadrant, y should rotate clockwise, otherwise rotatecounter-clockwise.

The update procedure can be described as

atþ1i

btþ1i

24

35¼UðDyt

i Þnat

i

bti

" #, ði¼ 1,2,. . .,NÞ ð9Þ

3.4. Quantum crossover

In this study, we use a quantum recombination [11] in light ofthe quantum interference as crossover, which allows moreindividuals involve in the quantum crossover.

This kind of crossover characters more individuals’ participa-tion in the operation, which aims to overcome the locality of itsclassical version and prevent the prematurity.

To summarize, the quantum mutation can guide the quantumindividuals to evolve to a better individual with a larger probability.

Y. Li et al. / Neurocomputing 87 (2012) 90–98 93

The quantum crossover is use on the classical population so as toimprove the search efficiency.

3.5. Fitness computing

The fitness value (objective function) f is calculated in Eq. (11).

JðX,U,VÞ ¼Xn

j ¼ 1

Xc

i ¼ 1

ðmijÞmd2ðxj,viÞ, ð10Þ

f ¼1

1þ J: ð11Þ

Here mij is the membership degree of xj and the ith cluster [3],d2(*) is the square of the Euclidean distance, and m is thefuzzy index.

3.6. Selection operation

Roulette selection is widely used in evolutionary algorithms.Out of exception, we choose the roulette selection operation inour algorithm. Besides that, we also take the operation of holdingthe global elite individual. Usually, the roulette selection is thestyle that the individual with high fitness value will be chosen tothe next generation with a higher probability. The operation ofholding the global elite individual avoids the best individuallosing in all the procedure. That is to say, if the fitness value ina certain generation is better than that of the best one in currentgeneration, the individual with best fitness value in currentgeneration will be replaced by the better individual of the formergeneration.

3.7. Termination criterion

To decide the appropriate termination of QWC, a propertermination condition is very important. As we all known, thenumbers of generation are normally used termination criterion inthe evolutionary algorithms. In QWC, the degrees of no assign ofimprovement can be employed as a termination criterion. Forexample, we set e¼10�5 as the stop threshold and e¼20 as thedegrees of no assign of improvement. In other words, if the

Fig. 3. (a) Original image 1. (b) Ideal image. (c) Segmentation obtained by Watershed A

rate: 0.0227). (e) Segmentation obtained by W-GAC (error rate: 0.0308) and (f) Segme

change of the best values of objective function between currentgeneration and former generation is less than e, it will be calledthe index of no assign of improvement for one time (e¼1),otherwise e¼0. If the index e¼20, that means there is noimprovement between two adjacent generations continuouslyfor 20 times, the termination criterion is satisfied.

3.8. The computational complexity

We only consider computational complexity of one generation.Assuming that the size of population is M, the length of individualis N, where N¼n1�m1� l, the number of clusters is n1, dimen-sions of feature is m1, the length of each bit is l, and then the timecomplexity of one generation for the algorithm can be calculatedas follows:

The time complexity for Quantum mutation is O(M�N); thetime complexity for Quantum crossover is O(M�N). So the worsttotal time complexity for the proposed algorithm is

OðM � NÞþOðM � NÞ: ð12Þ

According to the operational rules of the symbol O, the worsttime complexity for the proposed algorithm can be simplified as

OðM � NÞ: ð13Þ

4. Experimental study

In this section, three texture images and two SAR images areselected to verify the proposed algorithm and shown in Fig. 3–7,respectively. We will compare the segmentation results of theproposed algorithm (QWC), genetic clustering algorithm (GAC)[16] based on watershed (W-GAC) and K-means algorithm basedon watershed (W-KM).

The parameters used in QWC and QICW are set as follows: thepopulation size is 20; fuzzy index is 2.0; the index of no assign ofimprovement e¼20; and the stop threshold is 10�5.

The parameters used in GAC are set as follows: the populationsize is 20; mutation probability is 0.3; crossover probability is0.75; the index of no assign of improvement e¼20; and the stopthreshold is 10�5.

lgorithm (the number of regions: 851). (d) Segmentation obtained by QWC (error

ntation obtained by W-KM (error rate: 0.0294).

Fig. 4. (a) Original image 2. (b) Ideal image. (c) Segmentation obtained by Watershed Algorithm (the number of regions: 1114). (d) Segmentation obtained by QWC (error

rate: 0.0259). (e) Segmentation obtained by W-GAC (error rate: 0.0269) and (f) Segmentation obtained by W-KM (error rate: 0.0364).

Fig. 5. (a) Original image 3. (b) Ideal image. (c) Segmentation obtained by Watershed Algorithm (the number of regions: 2172). (d) Segmentation obtained by QWC (error

rate: 0.0908). (e) Segmentation obtained by W-GAC (error rate: 0.0949). (f) Segmentation obtained by W-KM (error rate: 0.0924).

Y. Li et al. / Neurocomputing 87 (2012) 90–9894

We evaluate the performance of texture segmentation usingthe clustering error rate, and it can be defined as

Error Rate¼ 1�1

N

Xk

i ¼ 1

XK

j ¼ 1,ia j

Correctði,jÞ: ð14Þ

Here, Correct(i,j) is the number of data points that are both in truepartitioning and in the resulting label, N is the size of data set, K isthe number of clusters.

The simulation has been carried out on a 2.0 GHz Pentium IVPC with 2 G RAM by programming with Matlab. In the followingexperiments, we performed 20 independent runs on each testproblem.

4.1. Segmentation of texture image

To ensure fair comparison, Figs. 3(c)–(e), Figs. 4(c)–(e), andFigs. 5(c)–(e) show the segmentation result with relatively stableerror rate of 20 runs where we give error rate at the figure title.From the above experiments, the performance of QWC on thetexture images is better than others in terms of regional consistencyand smoothing boundaries. As we can see from the above figuretitles, the clustering error rate of all the texture images obtained byQWC is less than that of the other comparison algorithms.

Particularly, image 3 consists of four classes, and the numberof classes is more than the two other images. Table 2 gives themean value (Mean) and the standard deviations (Std.) of the

Fig. 6. (a) Ku-SAR image in the area of Rio Grand River near Albuquerque, NM (256�256). (b) Segmentation obtained by watershed algorithm (WA) (the number of

regions: 745). (c) Segmentation obtained by QWC. (d) Segmentation obtained by W-GAC and (e) Segmentation obtained by W-KM.

Fig. 7. (a) X-SAR image, NM (256�256). (b) Segmentation obtained by watershed algorithm (WA) (the number of regions: 254). (c) Segmentation obtained by QWC.

(d) Segmentation obtained by W-GAC and (e) Segmentation obtained by W-KM.

Table 2Error rate for image 3 over 20 trials.

Algorithm Error rate

Mean Std.

W-KM 0.1601 0.0260

W-GAC 0.1301 1.0170e�005

QWC 0.0911 2.3713e�007

Y. Li et al. / Neurocomputing 87 (2012) 90–98 95

clustering error rate of image 3 for the three algorithms, respec-tively over independent 20 trials. Obviously, QWC is best of thethree algorithms in terms of robust.

4.2. Segmentation of SAR image

We performed 20 runs of each algorithm, and showed thesegmentation result with the relatively stable visual inspection.

Y. Li et al. / Neurocomputing 87 (2012) 90–9896

The image shown in Fig. 6(a) is a part of a Ku-band SAR imagewith one-meter spatial resolution in the area of Rio Grand River nearAlbuquerque, NM. This image consists of three types of land cover:water, vegetation and crop. In the segmentation results shown inFig. 6(c)–(e), the boundaries of water region can be defined correctlyby three algorithms because of the initial segmentation of WA. Inparticular, the small part of crop in water region is correctly defined.It also shows that WA has the advantage of preserving boundaries.But WA is sensitive for noise, and can manifest itself as oversegmentation. As can be seen, from Fig. 6(d) and (e), over-segmen-tation cannot be restrained in top right corner region of crop byW-GAC and W-KM. And the vegetation near the water is classifiedas the crop by W-GAC and W-KM. However, QWC gets the bestsegmentation result, as shown in Fig. 6(c). Three types of land coverare consistently identified as corresponding regions.

The last experiment is carried out on a part of an X-band SARimage for Pilotless Aircraft with five-meter spatial resolution asshown in Fig. 7(a). This image consists of four types of land cover:water, urban region, and two kinds of crops. Because of the initialsegmentation of WA the boundaries of water region can bedefined correctly by three algorithms in Fig. 7(c)–(e). However,the urban region is classified as the crop by W-KM. The over-segmentation cannot be restrained in right crop region by W-GACand W-KM. Fig. 7(c) shows the segmentation obtained by theQWC. QWC gets the best segmentation result, and four types ofland cover are consistently identified as corresponding regions.

4.3. Running time

The parameter setting is same as the mentioned before.Table 3 gives the mean value of the running time for the four

Table 3Running time for images over 20 trials.

Image Mean of running time (s)

QWC QIWC W-GAC W-KM

1 127.6249 188.6977 86.6156 0.4813

2 122.7637 187.3344 133.6651 0.4987

3 182.4566 201.9987 120.0714 0.4956

Ku-SAR 165.5889 308.7754 201.6749 0.9006

X-SAR 206.3982 301.2417 211.1694 1.3256

0 5 10 15 20 250.4

0.6

0.8

1

1.2

1.4

1.6x 10 QWC

Generations

Obj

ectiv

e Fu

nctio

n f

BestfitMeanfit

Fig. 8. The convergence of (a

algorithms, respectively over independent 20 trials. In the sameconditions, W-KM takes the least running time in the abovealgorithms. But W-KM does not belong to random search meth-ods, and W-KM is sensitive to initial value. The others algorithms-QWC, QICW and W-GAC belong to random search methods andall can overcome the above shortcoming. But QIWC takes themost running times in the above algorithms, and QWC achievesbetter performance compared with the other three algorithms.

4.4. Convergence analysis

In this section, we want to test the convergence performanceof the algorithm. For QWC and W-GAC, the main parameters areset as follows: the population size is 20; fuzzy index is 2.0; theindex of no assign of improvement e¼20; and the stop thresholdis 10�5. And in W-GAC, mutation probability is 0.3; crossoverprobability is 0.75.

Particularly, image 3 consists of four classes, and the numberof classes is more than the two other images. Fig. 8 shows thetrend of the image 3’ object function f in one run. In QWC, thebetter f value appeared in the 6th epoch and we can see QWCpresents a faster convergence.

4.5. Parameter analysis

In this section, we want to test the sensitivity of the algorithmto the parameters. For QWC, the main parameters are listed asfollows: population size and fuzzy index.

For the texture image 3, population size is changed from 10 to50, where the fixed parameters are as follows: fuzzy index¼2.0,the index of no assign of improvement e¼20; and the stopthreshold is 10�5. For each size, we performed 20 runs of thealgorithm. The results are shown in Fig. 9.

For the texture image 3, fuzzy index is changed from 1.5 to 3.5,where the fixed parameters are as follows: population size¼20,the index of no assign of improvement e¼20; and the stopthreshold is 10�5. For each size, we performed 20 runs of thealgorithm. The results are shown in Fig. 10.

Fig. 9 shows that for the texture image 3, the clustering error rateis about holding 0.09. However, considering the computational cost,choosing too large population size is not appropriate. Fig. 10 showsthat the addition of fuzzy index between 2 and 2.5 produces an

30 0 5 10 15 20 25 302

4

6

8

10

12

14x 10 W-GAC

Generations

Obj

ectiv

e Fu

nctio

n f

BestfitMeanfit

) QWC and (b) W-GAC.

10 15 20 25 30 35 40 45 500.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

0.14

population size

erro

r rat

e

QWCW-GAC

Fig. 9. The relation curve between the population size and the clustering error

rate of QWC and W-GAC.

1.5 2 2.5 3 3.50.09

0.095

0.1

0.105

0.11

0.115

0.12

fuzzy index

erro

r rat

e

QWC

Fig. 10. The relation curve between the fuzzy index and the clustering error rate

of QWC.

Y. Li et al. / Neurocomputing 87 (2012) 90–98 97

improvement in the performance of the algorithm. As a result, weoften choose fuzz inde xA[2,2.5].

Although the choice of the parameter is different for differentoptimization problems, it is sure that we can find high quality ofsolution by choosing appropriate parameters in certain scope.Parameters analysis demonstrates that QWC has stable perfor-mance and high success ratio, and is insensitive to parameters.

5. Conclusion

We developed a new algorithm, QWC, by combiningwatershed algorithm and quantum -inspired evolutionary com-puting for image segmentation. Watershed algorithm is used toperform the pre-segmentation, and quantum -inspired evolution-ary algorithm to perform clustering for the subsequent segmenta-tion. In comparison with QICW, W-KM and W-GAC which arereferred in this paper, QWC achieves better performance on thecases we have studied in terms of regional consistency and

smoothing boundaries for SAR segmentation and QWC is rela-tively robust with increasing the number of classes for the textureimages segmentation.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Nos. 60703108, 61003199 and 61001202),the Provincial Natural Science Foundation of Shaanxi of China (Nos.2011JQ8020 and 2010JQ8023), the China Postdoctoral ScienceFoundation funded project (Nos. 20090451369 and 20090461283),the China Postdoctoral Science Foundation Special funded project(Nos. 200801426 and 201104618), the Fundamental Research Fundsfor the Central Universities (Nos. K50511020014, K50511020011and K50510020011), and the Fund for Foreign Scholars in UniversityResearch and Teaching Programs (the 111 Project) (No. B07048).

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Y. Li et al. / Neurocomputing 87 (2012) 90–9898

Yangyang Li received the B.S. and M.S. degrees in

Computer Science and Technology from Xidian Uni-versity, Xi’an, China, in 2001 and 2004, respectively, and the Ph.D. degree in Pattern Recognition andIntelligent System from Xidian University, Xi’an, China,in 2007. She is currently an associate professor withKey Laboratory of Intelligent Perception and ImageUnderstanding of Ministry of Education of China atXidian University. Her current research interestsinclude quantum-inspired evolutionary computation,artificial immune systems, and data mining.

Hongzhu Shi received her master’s degree from XidianUniversity, Xi’an, China, in 2010. Her research interestsare broadly in the area of computational intelligence.

L. C. Jiao received the B.S. degree from Shanghai JiaotongUniversity, Shanghai, China, in 1982, and the M.S. andPh.D. degrees from Xi’an Jiaotong University, Xi’an,China, in 1984 and 1990, respectively. From 1990 to1991, he was a dostdoctoral Fellow in the National KeyLaboratory for Radar Signal Processing, Xidian University,Xi’an, China. Currently, he is the Dean of the ElectronicEngineering School and the Director of Key Laboratory ofIntelligent Perception and Image Understanding of Min-istry of Education of China, Xidian University. His currentresearch interests include signal and image processing,machine learning, natural computation, and intelligent

information processing.

Ruochen Liu is currently an associate professor withKey Laboratory of Intelligent Perception and ImageUnderstanding of Ministry of Education of China atXidian University, Xi’an, China. She received her Ph. D.degree from Xidian University, Xi’an, China, in 2005.Her research interests are broadly in the area ofcomputational intelligence. Her areas of special inter-est include artificial immune systems, evolutionarycomputation, data mining, and optimization.