Image Segmentation Using Two Weighted Variable Fuzzy K Means
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Image Segmentation Using Two Weighted Variable Fuzzy K Means

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Image segmentation is the first step in image analysis and pattern recognition. Image segmentation is the process of dividing an image into different regions such that each region is homogeneous.......

Image segmentation is the first step in image analysis and pattern recognition. Image segmentation is the process of dividing an image into different regions such that each region is homogeneous. The accurate and effective algorithm for segmenting image is very useful in many fields, especially in medical image. This paper presents a new approach for image segmentation by applying k-means algorithm with two level variable weighting. In image segmentation, clustering algorithms are very popular as they are intuitive and are also easy to implement. The K-means and Fuzzy k-means clustering algorithm is one of the most widely used algorithms in the literature, and many authors successfully compare their new proposal with the results achieved by the k-Means and Fuzzy k-Means. This paper proposes a new clustering algorithm called TW-fuzzy k-means, an automated two-level variable weighting clustering algorithm for segmenting object. In this algorithm, a variable weight is also assigned to each variable on the current partition of data. This could be applied on general images and/or specific images (i.e., medical and microscopic images). The proposed TW-Fuzzy k-means algorithm in terms of providing a better segmentation performance for various type of images. Based on the results obtained, the proposed algorithm gives better visual quality as compared to several other clustering methods.

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  • 1. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 270Image Segmentation Using Two WeightedVariable Fuzzy K MeansS. Suganya Rose MargaretCMS College of Science and Commerce CMS College of Science and CommerceCoimbatore, Tamil Nadu, India Coimbatore, Tamil Nadu, IndiaAbstract: Image segmentation is the first step in image analysis and pattern recognition. Image segmentationis the process of dividing an image into different regions such that each region is homogeneous. The accurateand effective algorithm for segmenting image is very useful in many fields, especially in medical image. Thispaper presents a new approach for image segmentation by applying k-means algorithm with two levelvariable weighting. In image segmentation, clustering algorithms are very popular as they are intuitive andare also easy to implement. The K-means and Fuzzy k-means clustering algorithm is one of the most widelyused algorithms in the literature, and many authors successfully compare their new proposal with the resultsachieved by the k-Means and Fuzzy k-Means. This paper proposes a new clustering algorithm called TW-fuzzy k-means, an automated two-level variable weighting clustering algorithm for segmenting object. In thisalgorithm, a variable weight is also assigned to each variable on the current partition of data. This could beapplied on general images and/or specific images (i.e., medical and microscopic images). The proposed TW-Fuzzy k-means algorithm in terms of providing a better segmentation performance for various type ofimages. Based on the results obtained, the proposed algorithm gives better visual quality as compared toseveral other clustering methods.Keyword —Fuzzy-K-means Clustering (FKM), image segmentation, W-k-Means, variable weighting1. INTRODUCTIONImage segmentation techniques play animportant role in image recognition system. Ithelps in refining our study of images. One partbeing edge and line detection techniques highlightsthe boundaries and the outlines of the image bysuppressing the background information. They areused to study adjacent regions by separating themfrom the boundaryClustering is a process of grouping a set ofobjects into classes of similar characteristics. It hasbeen extensively used in many areas, including inthe statistics [1], [2], machine learning [3], patternrecognition [4], data mining [5], and imageprocessing [6]. In digital image processing,segmentation is essential for image description andclassification. The algorithms are normally basedon similarity and particularity, which can bedivided into different categories; thresholdingtemplate matching [7], region growing [8], edgedetection [9], and clustering [10]. Clusteringalgorithm has been applied as a digital imagesegmentation technique in various fields. Recently,the application of clustering algorithms has beenfurther applied to the medical field, specifically inthe biomedical image analysis wherein images areproduced by medical imaging devices. The mostwidely used and studied is the K-means (KM)clustering. KM is an exclusive clusteringalgorithm, (i.e., data which belongs to a definitecluster could not be included in another cluster).There are several clustering algorithms proposed toovercome the aforementioned weaknesses. FuzzyK-means (FKM), an overlapping clustering thatemploys yet another fuzzy concept, allows eachdata to belong to two or more clusters at different
  • 2. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 271degrees of memberships. In the FKM, there is noclear, significant boundary between the elements ifthey do, or do not belong to a certain class. In2010, [11] successfully proposed a modifiedversion of K-means clustering, namely, adaptiveFuzzy k -Means (AFKM) clustering. The studyproved that AFKM possesses a great ability inovercoming common problems in clustering, suchas dead centers and centre redundancy. In thispaper, we introduce a new version of clusteringalgorithm called two weighted variable - Fuzzy-K-means (TWvFKM) clustering algorithm. In thisalgorithm to build a cluster-based classificationmodel automatically. In the TWv-Fuzzy k-meansalgorithm, to distinguish the impacts of differentviews and different variables in clustering, theweights of views and individual variables areintroduced to the distance function. The viewweights are computed from the entire variables,whereas the weights of variables in a view arecomputed from the subset of the data that onlyincludes the variables in the view. Therefore, theview data, while the variable weights in a viewonly reflect the importance of variables in theview. We present an optimization model for theTWv-Fuzzy-k-means algorithm and introduce theformulae, derived from the model, for computingboth view weights and variable weights. K-meansalgorithm as an extension to the standard -meansclustering process with two additional steps tocompute view weights and variable weights in eachiteration. TW-k-means can automatically computeboth view weights and individual variable weights.Moreover, it is a fast clustering algorithm whichhas the same computation complexity as k-meansand FKM. We compared TWv-Fuzzy-k-means(TWvFKM) with various clustering algorithms (K-means, FKM, and AFKM) and the results haveshown that the TWv-Fuzzy-k-means algorithmsignificantly out performed the other algorithmsThis paper is organized as follow:Section II give details of the Image SegmentationSection III describes in detail the proposedTWvFKM clustering algorithm. Section IIIpresents the data used and also discusses the typeof analyses applied to test the capability of theproposed algorithm. Section IV presents thesegmentation results obtained by the proposedalgorithm. In addition, a comparison ofperformance comparison with several selectedconventional clustering algorithms is alsopresented. The comparison is done based on bothqualitative and quantitative analyses. Finally,Section V concludes the work focused on of thispaper2. IMAGE SEGMENTATIONImage Segmentation is the process ofdividing a digital image into constituent regions orobjects [12]. The purpose of segmentation is tosimplify the representation of an image into thatwhich is easier to analyze. Image segmentation istypically used to locate objects and boundaries inimages. Segmentation algorithms are based on thetwo basic properties of an image intensity values:discontinuity and similarity. The first step in imageanalysis is segment the image.Segmentation subdivides an image into itsconstituent parts or objects. The level to which thissubdivision is carried depends on the problembeing viewed. Some time need to segment theobject from the background to read the imagecorrectly and identify the content of the image forthis reason there are two techniques ofsegmentation, discontinuity detection techniqueand Similarity detection technique. In the firsttechnique, one approach is to partition an imagebased on abrupt changes in gray-level image. Thesecond technique is based on the threshold andregion growing.2.1 Image Segmentation byClusteringClustering is a classification technique.Given a vector of N measurements describing eachpixel or group of pixels (i.e., region) in an image, asimilarity of the measurement vectors and thereforetheir clustering in the N-dimensional measurementspace implies similarity of the corresponding pixelsor pixel groups. Therefore, clustering inmeasurement space may be an indicator ofsimilarity of image regions, and may be used forsegmentation purposes.The vector of measurements describessome useful image feature and thus is also knownas a feature vector. Similarity between imageregions or pixels implies clustering (small
  • 3. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 272separation distances) in the feature space.Clustering methods were some of the earliest datasegmentation techniques to be developed.Figure 1. ClusteringSimilar data points grouped together intoclusters.Most popular clustering algorithms suffer from twomajor drawbacks First, the number of clusters ispredefined, which makes theminadequate for batch processing of hugeimage databases Secondly, the clusters are represented bytheir centroid and built using a Euclideandistance therefore inducing generally anhyperspheric cluster shape, which makesthem unable to capture the real structureof the data. This is especially true in the case of colorclustering where clusters are arbitrarilyshaped3. PROPOSED ALGORITHM3.1 Fuzzy –K- Mean ofClustering AlgorithmTWvFKM is a clustering algorithm,which partitions a data set into clusters accordingto some defined distance measure. Images areconsidered as one of the most important medium ofconveying information. Understanding images andextracting the information from them such that theinformation can be used for other tasks is animportant aspect of Machine learning. One of thefirst steps in direction of understanding images isto segment them and find out different objects inthem. To do this, we look at the algorithm namelyTWvFKM clustering. It has been assumed thatthe number of segments in the image isknown and hence can be passed to thealgorithm.Proposed algorithm namely TWv-Fuzzy-k-means clustering algorithm that canautomatically compute variable weights in the k-means clustering process. TWV-Fuzzy-k-meansextends the standard k-means algorithm with oneadditional step to compute variable weights at eachiteration of the clustering process. The variableweight is inversely proportional to the sum of thewithin-cluster variances of the variable. As such,noise variables can be identified and their affectionof the cluster result is significantly reduced. ThisTWvFKM weights both views and individualvariables and is an extension to W-k-means.Domeniconi et al. [15] have proposed the LocallyAdaptive Clustering (LAC) algorithm whichassigns a weight to each variable in each cluster.TWvF-K- Mean algorithm is one of themost important clustering algorithms, the firstsamples are divided into two or more clusters. Inthis fuzzy algorithm the number of clusters hasbeen already specified. In FWv-Fuzzy- K Mean ofclustering algorithm the main function is:∑ ∑ ∑ ∑ | |In formula 1: m is a real number whichis bigger than 1. In most of the cases, m=2. If m=1,the non-fuzzy c-mean of main clustering functionis obtained. In above formula Xkis the kthsample,and Viis the center of it he cluster and n is thenumber of samples. Uikshows the dependency ofIthsample in kthcluster. | | is determined thesimilarity of sample(distance) from the center of
  • 4. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 273cluster and can use every function that shows thesimilarity of sample or the center of cluster.Steps of k-fuzzy mean algorithm [13]: For the first clusters initial value for k, m,and U should be estimated. The center of clusters should be calculated bysecond formula. The dependence matrix should be calculatedby in second step.If ||Ul+1−Ul|| ≤ ε the algorithm is finished, visaversa go to second step.3.2 The TW-Fuzzy-k-means ClusteringAlgorithm4. EXEPERIMENT RESULTSThe experiments on the medical imageshave been carried out in MATLAB v7.10 TWv-Fuzzy - K-means segmentation is a clusteringbased segmentation algorithm. In clustering basedsegmentation changing in the distance metric willchange the output. Euclidean distance is the defaultdistance used in the algorithm, replacing it with thecosine distance gives better segmented areas in themedical images. In the Figure 2 we can see theoriginal medical images. Figure 3 shows the clusterindex images by the applying variable weight is 7in Figure 2. Now compare it with Figure 4, whichare cluster index images by applying variableweighting is 10. We can see that segmentation ofareas is good in Figure 5 than in other figures. TheFigure 5 has variable weighting in 15. The Figure 6is another resulted image an applying weight is 20.Comparing those images the Figure 5 is better thananother. It has variable weighted is 15. Now weanalyze various images to apple TWv-Fuzzy-k-means with weight 15, the table1 has resultedimages. Table 1 shows various image analysisresults.Figure 2. The Original Medical ImageInput: The number of clusters k and twopositive real parameters,Output: Optimal values of U, Z, V and Wrandomly choose K cluster centres Z0:For t=1 to T do𝑤𝑡 ← 1/𝑇For all j  Gt do𝒗 𝒋𝟎← 𝟏/|𝑮𝒕|⬚End forEnd forr  0RepeatUpdate Ur +1Update Zr +1Update Vr +1Update Wr +1r r+1until: the objective function obtained its localminimum value;
  • 5. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 274Figure 3: medical image has weighed is 7Figure 4: medical image has weighed is 10Figure 5: medical image has weighed is 15Figure 6: medical image has weighed is 20
  • 6. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 275Table 1: Analyzing multiple images with algorithm TWv-Fuzzy-k-means with weight 15Image name Original Resulted image Weighted at 15LENABoatBridgeDiatomsDot blot
  • 7. International Journal of Computer Applications Technology and ResearchVolume 2– Issue 3, 270 - 276, 2013www.ijcat.com 2765. CONCLUSIONThis paper presents a new clustering algorithmnamed the Two Weighted variable Fuzzy-K-Meansalgorithm for segmentation purposes. TWv-Fuzzy-k-meanscan compute weights for views and individual variablessimultaneously in the clustering process. With the weightseffect of low-quality views and noise variables can bereduced. Therefore, TWv-Fuzzy-k-means can obtain betterclustering results than individual variable weightingclustering algorithms from multi-view data. We discussedthe difference of the weights between TWv-Fuzzy-k-means. For medium values weighted of Fuzzy k-meansalgorithms give good results. For larger and smaller valuesof Weight, the segmentation is very coarse; many clustersappear in the images at discrete places. The conclusion ofthis paper sees the proposed algorithm outperforming theconventional FCM, AFKM and MKM algorithms bysuccessfully producing better segmented images. Theproposed TWvFKM also successfully preserves importantfeatures on digital images. Thus, it is recommendable forthis algorithm to be applied in the post image processing inconsumer electronic products such as the digital camerafor general applications and the CCD camera which isextensively used with the microscope in capturingmicroscopic images, especially in segmenting medicalimages.6. REFERENCES[1]. D. Auber, and M. Delest, “A clustering algorithmfor huge trees,” Advances in Applied Mathematics,vol. 31, no. 1 pp. 46-60 2003.[2]. S. Mahani, A. E. Carlsson, and R. Wessel, “Motionrepulsion arises from stimulus statistics whenanalyzed with a clustering algorithm,” BiologicalCybernetics, vol. 92, no. 4, pp. 288-291, 2005.[3]. T. Abeel, Y. V. d. Peer, and Y. Saeys, “Java-ML: Amachine learning library,” Journal of MachineLearning Research, vol. 10, pp. 931-934, 2009.[4]. M. J. Rattigan, M. Maier, and D. Jensen. “Graphclustering with network structure indices,” inProceedings of the 24th International Conference onMachine Learning. 2007. Corvallis, OR.[5]. H. Wang, W. Wang, J. Yang, and P. S. Yu,“Clustering by pattern similarity in large data sets,”in Proceedings of the 2002 ACM SIGMODInternational Conference on Management of data.2002, Madison, Wisconsin[6]. S. K. Singh, K. Shishir, G. S. Tomar, K. Ravi, andG. K. A. Santhalia,“Modified framework of aclustering algorithm for imageprocessingapplications,” in First Asia InternationalConference on Modelling & Simulation, AMS 07,2007.[7]. S. K. Warfield, K. Michael, F. A. Jolesz, and K.Ron, “Adaptive, template moderated, spatiallyvarying statistical classification,” Medical ImageAnalysis, vol. 4, no. 1, pp. 43-55, 2000.[8]. N. A. Mat-Isa, M. Y. Mashor, and N. H. Othman,“Automatic seed based region growing for papsmear image segmentation,” in Kuala LumpurInternational Conference on BiomedicalEngineering. 2002. Kuala Lumpur, Malaysia.[9]. J. K. Paik, Y. C. Park, and S. W. Park, “An edgedetection approach to digital image stabilizationbased on tri-state adaptive linear neurons,” IEEETransactions on Consumer Electronics, vol. 37, no. 3,pp. 521-530, 1991[10]. X. Yang, Z. Weidong, C. Yufei, and F. Xin., “Imagesegmentation with a fuzzy clustering algorithm basedon Ant-Tree,” Signal Processing, vol. 88, no. 10, pp.2453-2462, 2008.[11]. S. N. Sulaiman and N. A. M. Isa:, “Adaptive Fuzzy-K-means Clustering Algorithm for ImageSegmentation,” IEEE Transactions on ConsumerElectronics, Vol. 56, No. 4, November 2010[12]. N.Senthilkumaram, R.Rajesh “Edge detectiontechniques for image segmentation-A survey of softcomputing approach”, International journal of recenttrends in engineering , vol.1, No.2, May 2009,pp.250-254[13]. Farhad Soleimanian Gharehchopogh, Neda Jabbari,Zeinab Ghaffari Azar ,” Evaluation of Fuzzy K-Means And K-Means Clustering Algorithms InIntrusion Detection Systems”, International JournalOf Scientific & Technology Research Volume 1,Issue 11, December 2012[14]. Vance Faber,‖Clustring and the Continuous K-meansAlgorithm‖, Los Almas since Number22, pp: 138-144,1994.[15]. C. Domeniconi, D. Gunopulos, S. Ma, B. Yan, M. Al-Razgan, and D. Papadopoulos. Locally adaptivemetrics for clustering high dimensional data. DataMining and Knowledge Discovery, 14(1):63–97,2007.