# Optimization CBIR using K-Means Clustering for Image Database

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2 Juli Rejito et al, / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 3 (), 0, work, clustering process consist of three phase, namely, to make minimum and maximum PSNR value calculation, and the PNSR range from each image record, the second phase is to make cluster initialization, and finally is cluster formatting. II. OBJECTIVE QUALITY MEASUREMENT For objective estimate of the scaling algorithm s quality is used the main approach in digital image processing, based on computing MSE and PSNR. MSE represents the average square error (difference) in the intensities and of a given color of the corresponding pixels from the both images and it is dimensionless quantity. Because of its simplicity, it is the most common method of objectively measuring image quality given a reference image ) If the cluster centers have changed, repeat ), 3) steps until the cluster centers do not change. As a result, clustering criterion function can be converged Cj is the clustering center of cluster Sj. IV. PROPOSED WORK A clustering design refers to a clustering algorithm by using both minimum and maximum PSNR values as a basis of forming clusters, as shown in fig. where Let M and N are dimensions of the images and are the to images to be compared. PSNR represents the square of the ratio between the maximum of the signal (the maximal possible value of color s intensity and the mean square error (difference) in the intensities and color of the corresponding pixels from the both images and is measured in decibels (db) The estimate can be done by computing MSE and PSNR for every single color (Red, Green, Blue), as well as totally for the three of them. III. K-MEANS ALGORITHM It is assumed that there were n clustered objects to get a sample set, that is,. By using K-means algorithm, n sample objects are grouped into K clusters to ensure the similarities among samples in the same cluster and the differences among samples in different clusters. Specific procedure is as follows: ) Randomly select K objects as initial cluster centers as following: Fig. Clustering Algorithm A. Calculation of the minimum and maximum PSNR values The record image ( ) can be calculated its PSNR values by comparing it with the basic image ( ) with condition that such two images have same pixel sizes. If those two compared pixel sizes vary, thus it must be made formerly a resizing process on either images and therefore the two images to be compared may have a same pixel sizes. The commonly used objective measure are (MSE Red), (MSE Green), (MSE Blue),, and, which are calculated as ) According to the minimum distance principle, that is, each sample object is assigned to one of K clusters 3) Take the average values of objects of each cluster as new clustering centers, average values can be get by n j is the number of objects in the cluster j In this work, images are stored in an image table with blogfield attribute utilization and they have similar size, 5x5 pixels in bits image in depth. The used basic image as key images for mapping media that will result in the PSNR value also have similar sizes and depth. 790

3 Juli Rejito et al, / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 3 (), 0, Algorithm : Calculation of and Input : Blobfield from Table_Citra and Basic. Output : PSNR_Citra Table. I := Set initial Basic. Select Id, BlobField from Table_Citra 3. While not Table_Citra.EOF do begin. ID := Table_Citra.ID 5. I := Table_Citra.Blobfield 6. ComputePSNR(I, I ) 7. Insert Into PNSR_Citra (Id, PSNR_Min, PSNR_Max) values (ID,, ). Next Record 9. End Algorithm : Compute PSNR. procedure Compute(Img,Img : Tbitmap). var R,G,B,R,G,B, i,j,pjg,lbr : integer MSEx : array[..3] of real col,col : TColor MSEMin, MSEMax,, : real 3. begin. MSEx[] := 0.0;MSEx[] := 0.0;MSEx[3] := pjg := Img.Bitmap.Width; lbr := Img.Bitmap.height 6. for i := 0 to (pjg-) do begin 7. for j := 0 to (lbr-) do begin. col := Img.Bitmap.Canvas.Pixels[i,j] 9. R := getrvalue(col) 0. G := getgvalue(col). B := getbvalue(col). col := Img.Bitmap.Canvas.Pixels[i,j] 3. R := getrvalue(col). G := getgvalue(col) 5. B := getbvalue(col) 6. MSEx[] := MSEx[]+((R-R)*(R-R)) 7. MSEx[] := MSEx[]+((G-G)*(G-G)). MSEx[3] := MSEx[3]+((B-B)*(B-B)) 9. end; 0. end;. MSEx[] := MSEx[]/(pjg*lbr). MSEx[] := MSEx[]/(pjg*lbr) 3. MSEx[3] := MSEx[3]/(pjg*lbr). MSEMin := ; MSEMax := for i := to 3 do begin 6. if MSEMin>MSEx[i] then MSEMin := MSEx[i] 7. if MSEMax<MSEx[i] then MSEMax := MSEx[i]. end 9. := 0.0 * log0((55.0*55.0)/msemax) 30. := 0.0 * log0((55.0*55.0)/msemin) 3. End B. The Cluster Initialization The cluster formatting phase was begun with an early initialization in individual clusters before it is made grouping for those records into their respective clusters. An early initialization for each clusters may be formatted by its PSNR_Min values produced in first algorithm in PSNR Table_Citra table, and then it would be treated as basis for record sequence. Furthermore, it is specified distance between clusters by counting total records and divided with total clusters and it is finalized by determining every taken cluster up from successive records in accordance with changes in distance. This early initialization algorithm is written as follow: Algorithm 3 : Set Initial Centroids Input : k // Numbered of clusters Select, from PSNR_Citra Output : Centroid. k := Set Input Cluster Count. Centroid := array[..k,..] of real 3. Select id, PSNR_Min, PSNR_Max from PSNR_Citra Order By PSNR_Min. xdistance := RecordCount DIV k 5. For i:= to k do Begin 6. RecID := PSNR_Citra.Id 7. Update PSNR_Citra set Cluster= i where ID=RecID. PSNR_Citra.moveby(xDistance) 9. End C. Cluster Formatting After an early initialization is made for individual cluster, so this centroid would be used as starting center point for each clusters, so that every records will be given adjustment in their respective cluster position by counting formerly distance of image record to nearest cluster by using this Euclidean s distance formula : where Dj is the Distance is Minimum Centroid j-th cluster is Maximum Centroid j-th cluster A distance, D j calculation is performed by counting total quadrate from differences in minimum PSNR values with the j-th minimum clustering center added by maximum PSNR value with the j-th maximum clustering center. Its product would then be made into quadrate and it will produce required distance. The nearest distance one to intended cluster is also given a recalculation for obtaining value from such clustering center. This process will be repeated again on initial record from such image database up to clustering center will not perceive a change anymore. Algorithm : Cluster Formatting Input : a set of record and number of cluster Output : K-Centroid and members of each cluster. Set Initial Centroids (Algorithm ). Selesai := true 3. While Selesai do begin 79

4 Juli Rejito et al, / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 3 (), 0, end Xquery := select Cluster, avg(pnsrmin) as Xmin, avg() as Xmax From PSNR_Citra group by Cluster While not Xquery.EOF() do begin Centroid(Xquery.Cluster,):=Xquery.XMin Centroid(Xquery.Cluster,):=Xquery.XMax Xquery.next End PSNR_Citra.first While not PSNR_Citra.EOF do begin IDPSNR := PSNR_Citra.Id ClusCurrent := PSNR_Citra.Cluster ClusPosition := ; XPSNR := centroid(,) for j:= to k do begin Compute Dj If Dj < XPSNR then ClusPosition := j End Update PSNR_Citra set Cluster=ClusPosition where PSNR_Citra.Id=IDPSNR If ClusPosition<>ClusCurrent then Selesai := true else Selesai := false PSNR_Citra.next end V. IMPLEMENTATION AND EXPERIMENTAL RESULTS This algorithm implementation is made by using,000 files of the JPEG-typical images in 5x5 pixel sizes with bits in depth and it is stored as an image record in image table by using a blob field-type attribute. The image record in such Record is furthermore known as process from those three above algorithms, and then it would be developed clusters in various testing groups. Table I shows product of minimum and maximum PSNR values for 0 initial records as sample of records from,000 records after it was made a mapping on basic images. TABLE I SAMPLE OF RECORDS RecordID RecordID ().jpg jpg ().jpg jpg _0.jpg jpg jpg jpg jpg jpg The implementation of the clustering was applied in several cluster groups, namely, clusters, clusters, and clusters, and the amounts of iteration of each cluster and the values of minimum Centroid and maximum Centroid for each cluster were shown in Table II. TABLE II CLUSTERING OF,000 IMAGE DATABASE RECORDS IN,, AND CLUSTERS Cluster group Number of cluster Cluster Centers Record Count Table III shows in detail the results of testing process by using image query and that of image query with cluster by using,000 records stored in an image database. The testing was conducted 0 times by using different searching base images. From the testing of query, a average time of ms (millisecond) was obtained, whereas from the testing of image query by using cluster for each cluster a average time of 9.6 ms, 3.07 ms, and 76.0 ms for,, and clusters, respectively, were obtained. TABLE III THE RESULTS OF ACCESS TIME TESTING OF,000 IMAGE DATABASE RECORDS BY USING IMAGE QUERY AND IMAGE QUERY WITH CLUSTER Query with Cluster (IQC) Run Test Query (IQ) Cluster Cluster Cluster Minimum Average Maximum

5 Juli Rejito et al, / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 3 (), 0, TABLE IV THE RESULTS OF ACCESS TIME RATIO IMAGE QUERY AND IMAGE QUERY WITH CLUSTER Run Test Ratio of Access Time IQ : IQC Cluster Cluster Cluster Minimum Average Maximum A comparison of the access times of image query and image query with cluster showed that the greater the size of formed cluster, the higher the speed of needed access time. The ratio of average time access of image query to image query with cluster for clusters was.7 or, in the other words, there was an increase of access time by.7 when the access used clusters as compared to that of image query. For and clusters there occurred an increase of access time by averagely 5.9 times and 9.3 times, respectively. VI. CONCLUSION. The image database record clustering used in this research was conducted based on the computation of minimum and maximum PSNR values of each image database record by using basic image.. The results of 0 times of testing on image query in image database by using records that was taken randomly by an amount of,000 showed that the average access time was ms. The results of testing by using image query with cluster for,, and clusters were 9.6 ms, 3.07 ms, and 76.0 ms, respectively. 3. The ratio of the access time of image query to image query with cluster by using,, and clusters showed significant increases in access time, that is, 3 times, 5 times, and 9 times for,, and clusters, respectively. REFERENCES [] Remco, C.V., Mirela, T., Content-based image retrieval systems: a survey. Tech. Report, Department of Computing Science, Utrecht University, 000. [] Long, F., Zhang, H., and Feng, D., Fundamentals of content-based image retrieval. In Feng, D., Siu, W. C., and Zhang, H. J., (eds.), Multimedia Information Retrieval and Management Technological Fundamentals and Applications. Springer, 00. [3] Han, J., Kamber M., Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, nd Edn., New Delhi, ISBN: , 006. [] Iyengar G., Lippman A. Clustering s Using Relative Entropy for Efficient Retrieval. Proc. Workshop on Very Low bitrate Video Coding, Urbana, IL. 99. [5] K aster T., Wendt V., G. Sagerer. Comparing Clustering Methods for Database Categorization in Retrieval. Proc. DAGM 003, Pattern Recognition, 5th DAGM Symposium, Vol. 7 of Lecture Notes in Computer Science, pp. 35, Magdeburg, Germany, 003. [6] Saux B. L., Boujemaa N. Unsupervised Robust Clustering for Database Categorization. Proc. International Conference on Pattern Recognition, Vol., pp , 00. [7] Berkhin P. Survey of Clustering Data Mining Techniques. Technical report, Accrue Software, San Jose, CA, 00 [] Jain, A.K., Dubes R.C., Algorithms for Clustering Data. Prentice Hall Inc., Englewood Cliffs, New Jersey, ISBN: X, pp: 30,9. [9] Jain A. K., Murty M. N., Flynn P. J. Data Clustering: A Review. ACM Computing Surveys, Vol. 3, No. 3, pp. 6 33, 999. [0] Linde Y., Buzo A., Gray R.. An Algorithm for Vector Quantization Design. Proc. IEEE Transaction Communications,Vol.,pp. 95, 90. [] Netravali A.N., Haskell B.G., Digital Pictures: Representation, Compression, and Standards, (nd Ed), Plenum Press, New York, NY., 995. [] Rabbani M., Jones P.W., Digital Compression Techniques, Vol TT7, SPIE Optical Engineering Press, Bellvue, Washington,99 793

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