Fuzzy -Means Intalzed by Fxed Threshold lusterng for Improvng Image Retreval NAWARA HANSIRI, SIRIPORN SUPRATID,HOM KIMPAN 3 Faculty of Informaton Technology Rangst Unversty Muang-Ake, Paholyotn Road, Patumtan, 000 THAILAND Abstract: - Fuzzy -Mean (FM) algorthm s one of the well-known unsupervsed clusterng technques. Such an algorthm can be used for unsupervsed mage clusterng. Then, mages can be ndexed n databases. The dfferent ntalzatons cause dfferent evolutons of the algorthm. Random ntalzatons may lead to mproper convergence. Ths paper proposes FM ntalzed by fxed threshold clusterng. The case study regards to retreve from the database the color JPEG mages, ndexed by color hstogram vectors. The result shows that the proposed method gves more accurate results than FM wth random ntalzaton and color hstogram clusterng do. Key-Words:-Fuzzy- Mean, olor hstogram, Image retreval, Image clusterng Introducton The growng demand for accurate access and retreval of nformaton has extended to vsual nformaton as well. The Internet and the World Wde Web are certanly part of ths evoluton. The search for mages that are smlar to a gven query example, from the pont of vew of ther content, has become a very mportant part of research. To retreve smlar mages from an mage database for a gven query mage,.e., a pattern mage, mage ndexng s utlzed [,, 3, 4]. Image ndexng became color-orented, snce most of the mages of nterests are n colors. Many of the prevous researches used the color composton of an mage [4, 5, 6]. Usng color hstogram s one way to represent or ndex an mage. The color hstogram vector s obtaned by dscretzng the mage colors and countng the number of tmes each dscrete color occurs n the mage. The man dea s to compute a color dstrbuton from the query mage and to compute t wth the same dstrbuton computed for each mage wthn the targeted database. The advantages of the hstogram are that t s nvarant for translaton and rotaton of the vewng axs. Wth ths method, the hstogram s changed very lttle when comparng the mages taken, wth lttle change of the angle of vew. The hstograms represent prmary colors, whch are red, green and blue. When the colors are extracted, they are seperated and counted nto red, green and blue hstograms. The use of color (vewed and used as a vector) was proposed as an mportant mean of retreve smlartes. One of these examples s a research [6] usng color hstogram to measure the smlarty between two mages can be defned. Fuzzy -Means (FM) [7,8] s one of the wellknown unsupervsed clusterng technques. It allows one pece of data belong to two or more clusters. The am of FM s to fnd cluster center (centrods) that mnmze dssmlarty. Its strength over the famous k-means algorthm [8] s that, gven an nput pont, t yelds the ponts membershp value n each of the clusters. The drawback of clusterng algorthms lke FM whch are based on hll clmbng heurstc, s pror knowledge of the number of clusters n the data s requred. It was ndcated n [7] that FM have sgnfcant senstvty to cluster center ntalzaton. Fxed threshold clusterng used n [9] s appled wth FM here. Such a clusterng s a segmentaton of a herarchcal technque for clusterng. A large cluster s dvded nto smaller clusters. A dstance comparson between the mean of the cluster and an mage s calculated. The result s the number of clusters and the cluster centers that are used to ntalze FM for further clusterng process. Accordng to ths paper, the algorthm of FM ntalzed by fxed threshold clusterng s proposed. The ntalzaton s relevant to the number of clusters and the cluster centers as aforementoned. The case study regards to retreve from the database the color JPEG mages ndexed by color hstogram vectors. It s notceable that after usng the proposed clusterng algorthms, all mages have some degree of membershp n each possble cluster. Then they are stored n the database for later search.
The paper s organzed as follow. Frst, the ntroducton s descrbed. In secton, the algorthm of FM ntalzed by fxed threshold clusterng for mage clusterng s shown. Secton 3 llustrates the search for mages usng a sample mage one. Secton 4 shows the experment and results. The concluson s drawn n the fnal secton. Fuzzy -Mean ntalzed by Fxed Threshold lusterng for mage clusterng Smlar to [6], a color hstogram was used to represent color compostons of an mage. Its utlzaton as the useful features array can express the characterstc of the mage. The computaton procedures of the color hstogram are shown as follows: Step : A color space of three axes (red, green, and blue) s quantzed nto n bns for each axsn as shown n fg. [7]. Then, the hstogram can be represented as an n n n array. Fg. alculaton of the color hstogram Step : The colors n the mage are mapped nto a dscrete color space (r, g, b) (r, g, b = 0,,, n-). Then, the color hstogram F(r, g, b) (r, g, b = 0,,, n-) of the colors n the target mage are obtaned. Step 3: The probablty dstrbuton P(r, g, b) (r, g, b = 0,,, n-) s defned by normalzng the color hstogram F(r, g, b) (r, g, b = 0,,, n-) as follows: P(r, g,b) = n = 0, j= 0,k = 0 F(r, g,b) F(, j,k) () When there s a need to cluster mages, color hstogram could also be of help. By utlzng the color hstograms, the smlarty between two mages can be defned as shown n step 4. Step 4: The smlarty between two mages f and f s denoted by S(f,f ) and defned as follows: S n b) r,g,b 0 ( f, f ) = mn( P ( r,g,b),p (r,g, ) () where P (r, g, b) and P (r, g, b) express the color hstograms of the mages f and f, respectvely. Further, mn (P (r, g, b), P (r, g, b)) represents the mnmum value of P (r, g, b) and P (r, g, b). olor hstogram vectors could be used for representng or ndexng the mages. After dong ths, the process of clusterng mages begns. Random ntalzaton may lead to mproper convergence regardng to FM algorthm. The algorthm requres a proper ntalzaton for good convergence. Here, fxed threshold clusterng s appled to a color hstogram vector wth an expectaton to produce a more-proper ntalzaton for FM. Such a clusterng s a segmentaton of a herarchcal technque for clusterng. A large cluster s dvded nto smaller clusters. There s a dstance comparson between the mean of the cluster and an mage. If the dstance value s lower than the threshold lmt then the mage would be labeled as a cluster name. If t s hgher than the threshold then the mage would be assgned as NoneMember and contnue seekng for a sutable cluster n the next generaton. The algorthm of fxed threshold clusterng s shown n fg.: For p= to p=n ( n = number of mage )
mage p s named as NoneMember j = 0 Loop Untl all mages are not named as NoneMember Set cluster = j For p= to p=n mage p s randomly selected as a Mean_of_ j ompute Dstance (Dst) between Mean_of_ j and mage p usng ty Block method If ( (Dst) <= threshold ) Then mage p s named as j ompute New_mean between Mean_of_ j and mage p Save mage p as a membershp of j End If End For Save j and Mean_of_ j j++ End Loop Fg. Fxed threshold clusterng Mean_of_ j refers to the center of cluster j. Such a clusterng results n a lst of center values of mage clusters and an dentfed mage cluster of each mage. Such dentfcaton leads to a recognton of the number of clusters. Then they are stored n a database. Later, Fuzzy -Means algorthm uses the cluster centers obtaned from the prevous clusterng process as an ntalzaton. The ntalzaton conssts of the number of clusters and the cluster centers. The general purpose of FM s to mnmze the objectve functon N J m = = u m mage, m < (3) j= j j Let L k = the center vector at tme t = k L k = [ j ] m = u j s the degree of membershp of mage n the cluster j U k = [u j ] k u j j= u j = =, for =,.., n (4) k = mage mage j k N u m = = j mage j N m u = j m (5) (6) The FM algorthm followng the algorthm provdng a proper ntalzaton s gven n fg.3: ε = 0.0 Intalze L 0 = U 0 = [ 0 ] k = alculate U k Loop Untl U k End Loop U = U k alculate L k k++ alculate U k [ j ] provded by fxed threshold clusterng - U k - < ε Fg.3 FM algorthm followng fxed threshold clusterng Then U s stored n a database. U could be represented by [ u j ]. Each element n U matrx ndcates the degree of membershp of the clusters for each mage. 3 Searchng Images U To search for mages n the system, a vector = [ j u ] s set to be the elements n row n U. Therefore, U represents the degree of membershp of mage for every possble cluster, j. Then, the vector of a sample mage, X = [x j ] s used to query for a set of n-condton mages from the database. The query would be smply wrtten as :
U U Select where - X ε from Where ε = 0.0. If U - X when the followng predcate s true j ( ( ).. ( j ) the database ε s true, u x + + u j + x ε ) (7) 4 Experments and results 4. Experments After, a varety of mages has been extracted n to color hstograms vectors. Usng the FM ntalzed by fxed threshold clusterng method, all mages are clustered nto sutable groups and are stored n a database. 850 color JPEG mages are used for the experments. 43 color JPEG mages are utlzed for testng the system. Each mage contans 3 smlar mages. Twelve of them are exactly the same. Only one of them s smlar but not the same as the other twelve. The mages are 8 8 pxels n sze and n many dfferent classes, such as flowers, buldngs, natural, etc. 4. Results of the Experments for Image Retreval The expermental research s concerned wth the accuracy of the mage retreval, shown n fg. 4, 5, 6, 7 as examples of the result. Fg.7 s shown as an example of a result that s not accuretely retreved from our system. The larger mage on the left s the query mage, and the mages on the rght are the mage results. The comparson among the proposed method, color hstogram usng FM wth random ntalzaton, and color hstogram s performed. It s notceable that all three algorthms proceed on the same nput data. Such nput data are color hstogram vectors produced from the same set of color JPEG mages. Table shows the comparson n percent of accurately retreved mages and the tme for extracton per 846 among the proposed method, color hstogram usng FM wth random ntalzaton, color hstogram method. 0 DSN964 4 DSN967 5 DSN963 66 DSN976 76 DSN975 34 DSN974 Fle to Retreve 40 DSN96 49 DSN96 6 DSN966 54 DSN959 68 DSN960 465 DSN956 Fg.4 Accurately retreval result n our method 74 DSN560 34 DSN559 46 DSN558 90 DSN557 9 DSN56 94 DSN556 Fle to Retreve 40 SN563 66 DSN564 7 DSN555 98 DSN554 364 DSN775 338 DSN565 Fg.5 Accurately retreval result n our method
58 DSN0368 76 DSN0366 84 DSN0367 06 DSN036 DSN0359 6 DSN0357 Fle to Retreve 9 DSN0364 00 DSN036 36 DSN0360 0 DSN0363 93 DSN0365 50 DSN0356 Fg.6 Accurately retreval result n our method 70 DSN68 7 DSN684 76 DSN679 96 DSN683 30 DSN67 36 DSN673 Fle to Retreve 38 DSN678 68 DSN676 70 DSN680 80 DSN68 86 DSN685 80 DSN677 Fg.7 Inaccurately retreval result n our method TABLE SHOW OMPARISON IN PERENT OF AURATELY RETRIEVED IMAGES AND TIME FOR EXTRATION. Method olor hstogram usng FM ntalzed by fxed threshold clusterng olor hstogram usng FM wth random ntalzaton % accurate Tme for Extract 8.307 00:03.09.8943 69.059 00:03.3.5630 olor hstogram 56.8387 00:03.09.8943 5 onclusons In ths paper, the algorthm of FM ntalzed by fxed threshold clusterng s proposed. The ntalzaton s relevant to the number of clusters and the cluster centers. The case study regards to retreve from the database the color JPEG mages ndexed by color hstogram vectors. There exsts the comparson among the proposed method, color hstogram usng FM wth random ntalzaton, color hstogram method. The same set of color hstogram vectors are used as nput data. The result shows that although the accurate percentage of the proposed method s not very hgh, but t gves more accurate results than FM wth random ntalzaton and color hstogram clusterng do. Snce the color hstogram may not be very hgh effcent color mage representaton, therefore, the future work may be fndng the very hgh effcent technque for representng color mage to dgtal nformaton. Another nterestng future work would be optmzng the FM ntalzaton.
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