Multiobjective Genetic Clustering for Pixel Classification in Remote Sensing Imagery

1506 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 5, MAY 2007

Multiobjective Genetic Clustering for PixelClassification in Remote Sensing ImagerySanghamitra Bandyopadhyay, Senior Member, IEEE, Ujjwal Maulik, Senior Member, IEEE,

and Anirban Mukhopadhyay

Abstract—An important approach for unsupervised landcoverclassification in remote sensing images is the clustering of pixels inthe spectral domain into several fuzzy partitions. In this paper,a multiobjective optimization algorithm is utilized to tackle theproblem of fuzzy partitioning where a number of fuzzy clustervalidity indexes are simultaneously optimized. The resultant setof near-Pareto-optimal solutions contains a number of nondomi-nated solutions, which the user can judge relatively and pick upthe most promising one according to the problem requirements.Real-coded encoding of the cluster centers is used for this purpose.Results demonstrating the effectiveness of the proposed techniqueare provided for numeric remote sensing data described in termsof feature vectors. Different landcover regions in remote sensingimagery have also been classified using the proposed technique toestablish its efficiency.

Index Terms—Cluster validity measures, fuzzy clustering,genetic algorithm (GA), multiobjective optimization (MOO),Pareto-optimal, pixel classification, remote sensing imagery.

I. INTRODUCTION

R EMOTE SENSING satellite images have significant ap-plications in different areas such as climate studies, as-

sessment of forest resources, examining marine environments,etc. For remote sensing applications, classification is an im-portant task where the pixels in the images are classified intohomogeneous regions, each of which corresponds to someparticular landcover type. The problem of pixel classification isoften posed as clustering in the intensity space [1]. Clustering[2], [3] is a popular exploratory pattern classification techniquewhich partitions the input space into K regions based onsome similarity/dissimilarity metric, where the value of K mayor may not be known a priori. The main objective of anyclustering technique is to produce a K × n partition matrixU(X) of the given data set X , consisting of n patterns, X ={x1, x2, . . . , xn}. The partition matrix may be represented asU = [ukj ], k = 1, . . . ,K and j = 1, . . . , n, where ukj is themembership of pattern xj to the kth cluster. For fuzzy clusteringof the data, 0 < ukj < 1, i.e., ukj denotes the probability ofbelongingness of pattern xj to the kth cluster.

Manuscript received May 3, 2006; revised October 31, 2006.S. Bandyopadhyay is with the Machine Intelligence Unit, Indian Statistical

Institute, Kolkata 700108, India (e-mail: [email protected]).U. Maulik is with the Department of Computer Science and Engineering,

Jadavpur University, Kolkata 700032, India (e-mail: [email protected]).A. Mukhopadhyay is with the Department of Computer Science and Engi-

neering, University of Kalyani, Kalyani 741235, India (e-mail: [email protected]).

Digital Object Identifier 10.1109/TGRS.2007.892604

Remotely sensed multispectral images contain several spec-tral bands. In a satellite image, a pixel represents an area ofthe land space, which may not necessarily belong to a singlelandcover type. Hence, it is evident that a large amount ofimprecision and uncertainty can be associated with the pixelsin such images. Therefore, it is natural to apply the principlesof fuzzy set theory in the domain of pixel classification.

Recently, the application of genetic algorithms (GAs) [4]in the field of pixel classification has attracted the attentionof researchers [1], [5]. These techniques use a single clustervalidity measure as the fitness function to reflect the goodnessof an encoded clustering. However, a single cluster validitymeasure is seldom equally applicable for different kinds ofdata sets with different characteristics. Hence, it is necessaryto simultaneously optimize several validity measures that cancapture the different data characteristics. In order to achievethis, in this paper, the problem of fuzzy partitioning is posedas one of the multiobjective optimizations (MOOs) [6]–[9],where a search is performed over a number of, often conflicting,objective functions. The final solution set contains a numberof Pareto-optimal solutions, none of which can be furtherimproved on any one objective without degrading it in another.A popular elitist real-coded multiobjective GA, nondominatedsorting GA-II (NSGA-II) [6], is used to determine the appro-priate cluster centers and the corresponding partition matrix.(Note that although the NSGA-II has been used in this paper,any other multiobjective GA can be used instead; a study inthis regard is in progress). The Xie-Beni (XB) index [10] andthe fuzzy C-means (FCM) [11] measure (Jm) are used as theobjective functions.

Clustering results are reported for the remote sensing dataavailable as both set of labeled feature vectors as well asimages. Comparison with the well-known FCM algorithm [11](which directly optimizes the Jm criterion), the single-objectiveversion of the genetic clustering method that minimizes theXB index [1] and a widely used hierarchical clustering algo-rithm (average linkage) [3] are also provided. The comparativeperformance of the algorithms for the labeled remote sensingnumeric data, obtained from the satellites Systeme Probatoired’Observation de la Terre (SPOT) and Landsat, is reportedin terms of Jm and XB indexes (indicating the goodnessof the obtained clustering), and a cluster goodness index I[12]. For the image data, a comparison is provided in quali-tative terms (i.e., visually) and in quantitative terms using theindex I. An Indian Remote Sensing (IRS) satellite image ofparts of the cities of Calcutta and Mumbai and a SPOT imageof a part of the city of Calcutta have been segmented using theproposed method.

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BANDYOPADHYAY et al.: GENETIC CLUSTERING FOR PIXEL CLASSIFICATION 1507

II. MULTIOBJECTIVE GAS

In many real-world situations, there may be several ob-jectives to be optimized simultaneously in order to solve acertain problem. The MOO can be formally stated as follows[9]. Find the vector x∗ = [x∗

1, x∗2, . . . , x

∗v]T of v decision vari-

ables which optimizes the objective function vector f(x) =[f1(x), f2(x), . . . , fk(x)]T satisfying some equality and in-equality constraints. A decision vector x∗ is called Pareto-optimal if and only if there is no x that dominates x∗, i.e., thereis no x such that ∀i ∈ {1, 2, . . . , k}, fi(x) ≤ fi(x∗) and ∃i ∈{1, 2, . . . , k}, fi(x) < fi(x∗). Pareto optimality usually admitsa set of solutions called nondominated solutions.

NSGA-II [6], strength Pareto evolutionary algorithm (SPEA)[7], and SPEA2 [8] are some recently developed multiobjectiveelitist techniques. Of these, the NSGA-II has been used inthis paper for developing the proposed multiobjective fuzzyclustering technique, described in the next section.

III. PROPOSED TECHNIQUE

The proposed NSGA-II-based clustering technique is de-scribed below in detail.

A. String Representation and Population Initialization

In NSGA-II-based clustering, real-valued chromosomes rep-resenting the coordinates of the centers of the partitions areused. For K clusters, the centers encoded in a chromosome inthe initial population are randomly selected K distinct pointsfrom the data set.

B. Computing the Objectives

The XB index [10] and Jm measure [11] are taken as thetwo objectives which need to be simultaneously optimized. Forcomputing the measures, the centers z1, z2, . . . , zK encodedin a chromosome are first extracted. The membership valuesuik, i = 1, 2, . . . ,K and k = 1, 2, . . . , n are computed asfollows [11]:

uik =1

∑Kj=1

(D(zi,xk)D(zj ,xk)

) 2m−1

(1)

where D(zi, xk) is the Euclidean distance between point xk

and cluster center zi. m is the weighting coefficient. (Note thatwhile computing uik using (1), if D(zj , xk) is equal to zero forsome j, then uik is set to zero for all i = 1, . . . ,K, i = j, whileujk is set equal to one.) Subsequently, the centers encoded in achromosome are updated using the following equation [11]:

zi =∑n

k=1(uik)mxk∑nk=1(uik)m

, 1 ≤ i ≤ K (2)

and the cluster membership values are recomputed.The XB index is defined as a function of the ratio of the total

variation σ (=∑K

i=1

∑nk=1 u2

ikD2(zi, xk)) to the minimumseparation sep (= mini=j{D2(zi, zj)}) of the clusters, i.e.,

XB =σ(U,Z;X)n sep(Z)

=∑K

i=1

(∑nk=1 u2

ikD2(zi, xk))

n (mini=j {D2(zi, zj)}) . (3)

Note that when the partitioning is compact and good, σ shouldbe low while sep should be high, thereby yielding lower valuesof the XB index. The objective is therefore to minimize the XBindex for achieving a proper clustering.

The Jm measure, which needs to be minimized also, isdefined as [11]

Jm =n∑

j=1

K∑k=1

umkjD

2(xj , zk), 1 ≤ m ≤ ∞ (4)

where m is the fuzzy exponent.

C. Genetic Operators

Crowded binary tournament selection as in NSGA-II, fol-lowed by conventional crossover and mutation, is used here.The most characteristic part of the NSGA-II is its elitismoperation, where the nondominated solutions among the parentand child populations are propagated to the next generation. Fordetails on the different genetic processes, the reader may referto [6]. The near-Pareto-optimal strings of the last generationprovide the different solutions to the clustering problem.

IV. CHOICE OF OBJECTIVES

Performance of the multiobjective clustering highly dependson the choice of objectives which should be as contradictoryas possible. In this paper, the XB and Jm have been chosen asthe two objectives to be optimized. From (4), it can be notedthat Jm calculates the global cluster variance, i.e., it considersthe within cluster variance summed up over all the clusters.The lower value of Jm implies better clustering solution. On theother hand, the XB index [see (3)] is a combination of global(numerator) and local (denominator) situations. Although thenumerator of XB index [σ in (3)] is similar to Jm, the de-nominator contains an additional term (sep) representing theseparation between the two nearest clusters. Therefore, the XBindex is minimized by minimizing σ (or J2) and by maximizingsep. These two terms may not attain their best values for thesame partitioning when the data have complex and overlappingclusters. Since the remote sensing data sets typically have suchoverlapping clusters (as evident in Fig. 2), considering Jm andXB (or in effect σ and sep) will provide a set of alternatepartitionings of the data.

Fig. 1 shows, for the purpose of illustration, the final Pareto-optimal front (composed of nondominated solutions) of oneof the runs of the proposed algorithm for the numeric SPOTdata set (described in the next section) to demonstrate thecontradictory nature of Jm and XB indexes.

V. RESULTS FOR NUMERIC REMOTE SENSING DATA

Two numeric satellite image data obtained from SPOT (apart of the city of Calcutta) and Landsat are considered herefor experimenting. The numeric image data mean that somepixels from several known landcover types are extracted froman image. The landcover type serves as the class label, and theintensity values (in multiple bands) serve as the different featurevalues. Moreover, in contrast to the normal image data, in thenumeric image data, no spatial information is available as the


Fig. 1. Nondominating Pareto front for SPOT data set.

Fig. 2. Scatter plot of 932 points of SPOT image of Calcutta having sevenclasses.

pixel locations are not retained. The data sets are first describedin the following.

1) SPOT: This is a 3-D data set [5] [corresponding togreen, red, and near-infrared (NIR) bands] consisting of932 samples partitioned into seven distinct classes ofturbid water (TW), pond water (PW), concrete (Concr.),vegetation (Veg), habitation (Hab), open space (OS), androads (including bridges) (B/R). For the purpose of illus-tration, Fig. 2 shows the scatter plot of the data set fromwhere it can be seen that the clusters are highly complexand overlapping in nature.

2) Landsat: This data set has 795 samples and four bands(features) [5]: green, red, NIR, and IR. Since the featuresare highly correlated, the feature space is reduced to twoby using the principal component analysis. The data setcontains five classes, viz., Manda Granite, RomapahariGranite, Vegetation, Black Phillite, and Alluvium.

TABLE IRESULTS FOR NUMERIC SPOT DATA

TABLE IIRESULTS FOR THE LANDSAT DATA

A. Performance Measure

The clustering results have been evaluated objectively, i.e.,by measuring the goodness of the clusters. For this purpose,a validity index I [12] as well as the XB and Jm indexes, de-scribed in Section III-B, is used. The I index has been proposedrecently as a measure of indicating the goodness/validity of acluster solution. It is defined as follows:

I(K) =(

1K

× E1

EK×DK

)p

(5)

where EK =∑K

k=1

∑nj=1 ukjD(xj , zk) and DK =

maxKi,j=1{D(zi, zj)}. The different terms are defined earlier.

I index has been shown to provide a superior performancewhen compared to several other validity indexes [12]. In thispaper, we have taken p = 2. Larger value of I index impliesbetter solution. Note that for computing the index I, knowledgeabout the true partitioning of the data is not necessary.

B. Input Parameters

The parameters of the GA-based clustering (both singleobjective and multiobjective) are as follows: population size =50, number of generations = 100, crossover probability = 0.8,mutation probability = (1/length of chromosome). Results re-ported in the tables are the average values obtained over tenruns of the algorithms. The FCM is executed for a maximum of100 iterations, with m, the fuzzy exponent, equal to 2.0.

C. Results

Tables I and II present the performance of the proposedmethod for clustering the SPOT and Landsat numeric imagedata (which, as mentioned earlier, correspond to the pixel valuesof some known landcover types), respectively. The solutionproviding the best value of the I index is selected from the setof nondominated solutions. The Jm, XB, and I index values,along with the percentage of correctly classified pairs (%CP),are reported corresponding to this solution. For the purpose ofcomparison, three other clustering algorithms, viz., a single-objective genetic clustering optimizing the XB index only,FCM, and average linkage, are considered.

The single-objective genetic clustering algorithm minimizesthe XB index only. Hence, as expected, it provides the bestXB index value (Tables I and II). However, the Jm value


reported for this algorithm (as attained by the solution with thebest XB index) is quite poor. Again, since the FCM optimizesthe Jm index, it provides the best value for this index. Thecorresponding XB index value (as attained by the solution withthe best Jm value) is once again quite poor. The multiobjectivemethod is found to provide values of the XB and Jm indexesthat are only slightly poorer than the best values. Interestingly,in terms of I index, which none of the algorithms optimizesdirectly, the multiobjective method significantly outperformsthe other methods. Also, the multiobjective scheme providesbetter classification accuracy in terms of the %CP scores. Thissignifies that, in terms of the algorithm independent measureof clustering goodness (or, validity), i.e., the I index, justoptimizing the XB index (as the single-objective version does)or the Jm index (as the FCM does) is not good enough. Atradeoff solution, provided by the multiobjective scheme, thatbalances both the objectives, appears to be better. The averagelinkage method provides the poorest scores which could be dueto the highly overlapping nature of the clusters as evident inFig. 2. Thus, this section highlights the importance of utilizingthe multiple criteria and optimizing them simultaneously ratherthan using only a single optimizing objective.

VI. PIXEL CLASSIFICATION

Three image data sets used for the experiments are twoIRS satellite images of the parts of the cities of Calcutta andMumbai [1] and a SPOT satellite image of a part of the city ofCalcutta [5]. Each image is of size 512 × 512, i.e., the size ofthe data set to be clustered in all the images is 262 144. TheIRS images consist of four bands viz., blue, green, red, andNIR, whereas the SPOT image consists of green, red, and NIRbands. To show the effectiveness of the proposed multiobjectivetechnique quantitatively, the cluster goodness index I has beenexamined. The efficiency of multiobjective genetic clusteringcan also be verified visually from the clustered images andcomparing them with the available ground knowledge about thelandcover areas.

A. IRS Image of Calcutta

Fig. 3 shows the IRS Calcutta image clustered using the pro-posed multiobjective GA clustering scheme. From our groundknowledge, we know that the image has four classes [1]: TW,PW, Concr., and OS. The river Hooghly cutting across themiddle of the image has been classified as TW, whereas severalfisheries observed toward the lower right portion of the imageare correctly identified as PW. It appears from the figure that thewater class has been differentiated into TW (the river Hooghly)and PW (canal, fisheries, etc.) because they differ in theirspectral properties. Toward the lower right side of the image, atownship, Salt Lake, has come out partially as a combination ofConcr. and OS, which appears to be correct, since this particularregion is known to have several OSs. The canal bounding SaltLake from the upper portion has also been correctly classifiedas PW. Two parallel lines observed toward the upper right-handside of the image correspond to the airstrips in the Dumdumairport, and the airstrip is classified rightly as belonging to theclass Concr. The presence of some small areas of PW besidethe airstrips is correct again as these correspond to the several

Fig. 3. Clustered IRS image of Calcutta using multiobjective GA.

Fig. 4. Clustered IRS image of Calcutta using FCM.

ponds around the region. The predominance of Concr. on bothsides of the river, particularly toward the bottom of the image,i.e., the central part of the city, is also correct.

Fig. 4 shows the Calcutta image partitioned using the FCMalgorithm. From the figure, it can be noted that the riverHooghly and the city region have been incorrectly classified asbelonging to the same class. Another flaw is apparent that thewhole Salt Lake city has been put into one class. It is evidentthat although some portions like the canals, parts of airstrip,and fisheries are correctly identified, a significant amount ofconfusion lies in the FCM clustering result.

B. IRS Image of Mumbai

Fig. 5 shows the Mumbai image segmented using the pro-posed multiobjective technique. According to the availableground knowledge [1], the different clusters are labeled as,Concr., OSs (OS1 and OS2), Veg, Hab, and TWs (TW1 andTW2). As can be seen, the elongated city area is surroundedon three sides by the Arabian sea which is distinguished intotwo classes TW1 and TW2. It is evident from figure thatthe sea water has two distinct regions with different spectralproperties. Hence, the clustering result providing two partitionsfor this region is expected. Toward the bottom right of theimage, there are several islands, including the well-knownElephanta islands. The dockyard is situated on the southeastern


Fig. 5. Clustered IRS image of Mumbai using multiobjective GA.

Fig. 6. Clustered IRS image of Mumbai using FCM.

part of Mumbai, which can be seen as a set of three fingerlikestructures. Note that the classes Hab and Concr. share commonproperties. The islands, dockyard, and several road structureshave mostly been correctly identified in the image. Within theislands, as expected, there is a high proportion of OS and Veg.The southern part of the city, which is heavily industrialized,has been classified as primarily belonging to Hab and Concr.

Fig. 6 demonstrates the Mumbai image clustered using theFCM technique. As evident from the figure, the water of theArabian sea has been partitioned into three regions, rather thantwo as obtained earlier. The other regions appear to be classifiedmore or less correctly for this data.

C. SPOT Image of Calcutta

Fig. 7 shows the SPOT image of Calcutta clustered usingthe proposed multiobjective scheme. The image has sevenclasses [5]: TW, PW, Concr., Veg, Hab, OS, and B/R. The riverHooghly cuts through the image, and it is correctly classified asTW. Below the river, on the left side, two distinct patches arethe water bodies Khidirpore dockyard (on the right) and GardenReach lake (on the left). Each of the water bodies is rightlyclassified as PW. Just on the right side of those water bodies,a very thin line is noticed, starting from the river and goingtoward the bottom edge of the picture. This is a canal calledthe Talis nala, and this is also correctly placed into the TW

Fig. 7. Clustered SPOT image of Calcutta using multiobjective GA.

Fig. 8. Clustered SPOT image of Calcutta using FCM.

class. The triangular patch on the right side of Talis nala is theracecourse. There is a thin line starting from the top right handcorner of the picture and stretching toward the middle of it. Thisis the Beleghata canal (classified as TW) with a road beside it.Several roads (combination of Hab, Concr., and B/R) are foundat the right side of the picture mainly near the top and middleportions. Around the center of the image, a bridge (secondHooghly bridge) can be noticed across the river Hooghly. Thebridge was being constructed when the picture was taken.Another bridge, called Rabindra Setu, cuts the river near thetop of the image. Both the bridges are correctly identified as acombination of B/R and Concr.

It seems that in Fig. 7, there are some confusions betweenthe classes Concr and B/R and between Concr. and Hab. Theseare expected as these classes have large amount of overlap inreality. In contrast, the FCM algorithm performs poorly (Fig. 8),having a significant amount of confusion among the classesTW, PW, Veg, and Concr. For example, the Khidirpore dock-yard has come out as a combination of PW and Concr. Also,the FCM cannot distinguish between the two water classes(TW and PW). The Talis nala is also not very prominent in thiscase. Also, the FCM fails to recognize Rabindra Setu properly.

For the purpose of illustration, the segmentation results ofthe racecourse part of the image are magnified in Fig. 9 fordifferent clustering algorithms. It can be noticed that only themultiobjective method is able to identify a lighter outline withinit properly. This line corresponds to the tracks of the racecourseand belongs to the class OS.


Fig. 9. Segmented SPOT image of Calcutta (zooming the racecourse) using(a) FCM algorithm, (b) single-objective GA minimizing XB, and (c) multiob-jective GA optimizing Jm and XB.

TABLE IIII INDEX VALUES FOR CALCUTTA AND MUMBAI

IMAGES FOR DIFFERENT ALGORITHMS

Table III shows the I index values for all the images. Thevalues indicate the superiority of the multiobjective techniquewhich produces a far better value of the I index than those ofsingle-objective clustering optimizing XB and FCM algorithm.The results therefore demonstrate that the multiobjective fuzzygenetic clustering technique clearly outperforms the relatedmethods for all three images.

VII. DISCUSSION AND CONCLUSION

The problem of the fuzzy clustering has been modeled asa simultaneous optimization of two cluster validity measures,namely, XB index and the Jm. In this regard, the well-knownNSGA-II algorithm has been used. Results on numeric imagedata sets indicate that rather than considering these indexesindividually, a better clustering performance is obtained if bothof them are optimized simultaneously. In this context, the IRSsatellite images of Calcutta and Mumbai and a SPOT image ofCalcutta have been classified using the proposed technique andcompared with the single-objective GA and FCM algorithms toshow its effectiveness. Good performance of the multiobjectivegenetic clustering method for such large image data sets showsthat it may be motivating to use this algorithm in data miningapplications also.

As a scope of further research, the technique of MOO withother cluster validity indexes needs to be studied. Moreover,new ways of comparing the performance of multiobjectivesolutions have to be defined. Finally, a comparative study withother approaches of MOO should be performed. The authorsare currently working in these directions.

REFERENCES

[1] U. Maulik and S. Bandyopadhyay, “Fuzzy partitioning using a realcodedvariable-length genetic algorithm for pixel classification,” IEEE Trans.Geosci. Remote Sens., vol. 41, no. 5, pp. 1075–1081, May 2003.

[2] A. K. Jain and R. C. Dubes, Algorithms for Clustering Data. EnglewoodCliffs, NJ: Prentice-Hall, 1988.

[3] J. T. Tou and R. C. Gonzalez, Pattern Recognition Principles. Reading,MA: Addison-Wesley, 1974.

[4] D. E. Goldberg, Genetic Algorithms in Search, Optimization and MachineLearning. New York: Addison-Wesley, 1989.

[5] S. Bandyopadhyay and S. K. Pal, “Pixel classification using variablestring genetic algorithms with chromosome differentiation,” IEEE Trans.Geosci. Remote Sens., vol. 39, no. 2, pp. 303–308, Feb. 2001.

[6] K. Deb, Multi-objective Optimization Using Evolutionary Algorithms.Chichester, U.K.: Wiley, 2001.

[7] E. Zitzler and L. Thiele, “An evolutionary algorithm for multiobjectiveoptimization: The strength Pareto approach,” Swiss Federal Inst. Technol.,Zurich, Switzerland, Tech. Rep. 43, 1998.

[8] E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: Improving the strengthPareto evolutionary algorithm,” Swiss Federal Inst. Technol., Zurich,Switzerland, Tech. Rep. 103, 2001.

[9] C. A. Coello Coello, “A comprehensive survey of evolutionary-basedmultiobjective optimization techniques,” Knowl. Inf. Syst., vol. 1, no. 3,pp. 129–156, Aug. 1999.

[10] X. L. Xie and G. Beni, “A validity measure for fuzzy clustering,” IEEETrans. Pattern Anal. Mach. Intell., vol. 13, no. 8, pp. 841–847, Aug. 1991.

[11] J. C. Bezdek, Pattern Recognition With Fuzzy Objective Function Algo-rithms. New York: Plenum, 1981.

[12] U. Maulik and S. Bandyopadhyay, “Performance evaluation of some clus-tering algorithms and validity indices,” IEEE Trans. Pattern Anal. Mach.Intell., vol. 24, no. 12, pp. 1650–1654, Dec. 2002.

Sanghamitra Bandyopadhyay (M’99–SM’05) re-ceived the Ph.D. degree from the Indian StatisticalInstitute, Kolkata, in 1998.

She has worked with the Los Alamos Na-tional Laboratory, University of New South Wales,Australia, University of Texas at Arlington, Uni-versity of Maryland Baltimore County, FraunhoferInstitute AiS, Germany, and Tsinghua University,China. She is currently an Associate Professor withthe Indian Statistical Institute. She has coauthoredthree books and more than 100 papers. Her main

research interests include pattern recognition, data mining, soft computing, andbioinformatics.

Ujjwal Maulik (M’99–SM’05) received the Ph.D.degree from Jadavpur University, Kolkata, India,in 1997.

He has worked with the Center for AdaptiveSystems Application, New Mexico, University ofNew South Wales, Australia, University of Texas atArlington, University of Maryland BaltimoreCounty, and the Fraunhofer Institute AiS, Germany.He is currently a Professor with the Departmentof Computer Science and Engineering, JadavpurUniversity. He has coauthored two books and about

100 papers. His main research interests include evolutionary computing,pattern recognition, data mining, bioinformatics, and distributed systems.

Anirban Mukhopadhyay received the M.S. de-gree in computer science from Jadavpur University,Kolkata, India, in 2004. He is currently workingtoward the Ph.D. degree at the same university.

He is currently a faculty member with the Depart-ment of Computer Science and Engineering, Univer-sity of Kalyani. He has coauthored about 15 papers.His research interests include soft and evolutionarycomputing, data mining, bioinformatics, and opticalnetworks.

Mr. Mukhopadhyay is the recipient of the Uni-versity Gold Medal and Amitava Dey Memorial Gold Medal from JadavpurUniversity in 2004.

Multiobjective Genetic Clustering for Pixel Classification in Remote Sensing Imagery

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