A Clustering Based Approach to Efficient Image Retrieval

Transcription

1 A Clusterng Base Aroah to Effent Image Retreval Ruofe Zhang, Zhongfe (Mark Zhang Deartment of Comuter ene Thomas J. Watson hool of Engneerng an Ale ene tate Unversty of New York at Bnghamton, Bnghamton, NY 390 E-mals: {rzhang, Abstrat Ths aer aresses the ssue of effetve an effent ontent base mage retreval by resentng a novel nexng an retreval methoology that ntegrates olor, texture, an shae nformaton for the nexng an retreval, an ales these features n regons obtane through unsuervse segmentaton, as oose to alyng them to the whole mage oman. In orer to aress the tyal olor feature nauray roblem n the lterature, fuzzy log s ale to the tratonal olor hstogram to solve for the roblem to a ertan egree. The smlarty s efne through a balane ombnaton between global an regonal smlarty measures nororatng all the features. In orer to further mrove the retreval effeny, a seonary lusterng tehnque s eveloe an emloye to sgnfantly save query roessng tme wthout omromsng the retreval reson. An mlemente rototye system has emonstrate a romsng retreval erformane for a test atabase ontanng 000 general-urose olor mages, as omare wth ts eer systems n the lterature.. Introuton Content-base mage retreval (CBIR onerns automat or sem-automat retreval of mage ata from an magery atabase base on semant smlarty between the magery ontent. The semant smlarty s tyally efne through a set of magery features. These features are extrate from shae, texture, or olor roertes efne n the magery oman. The relevane between a query mage an mages n the atabase s ranke aorng to the smlarty measure omute from the features. Due to ts we alaton otental, CBIR researh has reeve ntensve attenton over the last few years. In ths aer we resent a novel aroah to aressng the general-urose CBIR roblem. Ths aroah ntegrates semants-ntensve lusterng-base segmentaton wth fuzzy olor hstogram as well as texture an shae features to nex magery ata, an onsequently, s alle FUZZYCLUB. A omutatonally effent stane metr s roose n FUZZYCLUB to reue the query roessng tme. The resonse tme s further mrove by mosng a seonary lusterng tehnque to aheve the hgh salablty n the ase of very large mage atabases. The aer s organze as follows. We begn wth a bref revew of the relate work. Then we ntroue to the unsuervse segmentaton tehnque emloye n FUZZYCLUB, whh s followe by the eveloment of all the nexng features efne n FUZZYCLUB, wth a fous on the fuzzy olor hstogram. The stane metr an the overall smlarty ssues between two mages are subsequently susse, followe by the ntrouton to the seonary lusterng tehnque n the regon feature vetor sae to mrove retreval effeny. Fnally, the retreval erformane of FUZZYCLUB s evaluate wth a omarson wth ts two eer systems n the lterature, an the aer s onlue.. Relate Work an gnfane A broa range of researh efforts an ommeral routs [,,3] s reorte to aress the general-urose CBIR roblem. Almost all of the aroahes roose are base on nexng magery n a feature sae. Tyal features are olor, texture, shae, regon, an aearane [4,6,7,9-6]. The most oularly use features are olor hstogram an ts varants. They are use n systems suh as IBM QBIC [7] an Berkeley Chabot [8]. Color hstogram s omutatonally effent, an generally nsenstve to small hanges n amera oston. However, a olor hstogram roves only a very oarse haraterzaton of an mage, resultng a very oarse nexng; mages wth smlar hstograms may have ramatally fferent semants. The oarseness of the olor hstogram aroah s ue to the total loss of satal nformaton of xels n mages. To retan the satal

2 nformaton of a olor hstogram, many researh efforts are mae n the lterature. Pass an Zabh [4] esrbe a slt hstogram alle olor oherene vetor (CCV. Eah of ts bukets ontans xels havng a gven olor an two lasses base on the xels satal oherene. The feature s also extene by suessve refnement, wth bukets of a CCV further subve base on atonal features. Huang et al [0] roose olor orrelograms to ntegrate olor an satal nformaton. Gven n nter-xel stanes, a orrelogram s efne as a set of (k ( k n matresγ, where an element γ, s the robablty that a xel wth olor s at a stane k away from a xel wth olor. Rao et al [] generalze the olor satal strbuton by omutng the olor hstogram wth sef geometr relatonshs between xels of eah olor hstogram buket. Cnque et al [] roose another olor hstogram refnement metho, alle atal- Chromat Hstogram, n whh the average oston of eah olor hstogram an ts stanar evaton are reore to a the satal nformaton nto the tratonal hstogram. All of the refnement efforts fale to reflet the fuzzy nature of the olor features nherently exhbte n the olor hstogram tself. Ravela an Manmatha [3] roose an aearane base mage nexng tehnque usng Gaussan ervatve flters at several sales to omute low orer D fferental nvarants as nexng features. Reently, regon base features are eveloe to aress the artal mathng aablty for robust CBIR. A regon-base retreval system segments mages nto regons (obets, an retreves mages base on the smlarty between regons. Tyal regon base CBIR systems nlue Berkeley Blobworl[5], UCB Netra[6], Columba VsualEEK[9], an tanfor IRM[6], of whh [9,5,6] are the lass regon base CBIR systems whh requre sgnfant user nteraton n efnng or seletng regon features, reventng from a frenly nterfae to users, eseally to non-rofessonal users. Another roblem n the lass regon base CBIR systems s that they fous too muh on the regon-base smlarty as oose to the smlarty wth a balane fous between regons an global mages. Wang et al [6] roose an ntegrate regonal mathng sheme for CBIR, whh allows for mathng a regon n one mage aganst several regons from another mage. As a result, the smlarty between two mages s efne as the weghe sum of the stanes n a feature sae between all regons from fferent mages. Comare wth the lass regon-base CBIR systems, ths sheme ereases the mat of naurate regon segmentaton by smoothng over the nauray n stane. Nevertheless, the olor reresentaton of eah regon s smlst suh that muh of the rh olor nformaton n a regon s lost, as t fals to exltly exress the nauray of the olor feature exhbte by the fuzzy nature n the feature extraton an human ereton of olor. When we esgn FUZZYCLUB, we kee the followng three rnles n mn. Frst, we nten to aly attern reognton tehnques to onnet low level features to hgh level semants. Consequently, FUZZYCLUB s also regon-base methoology, as oose to nexng mages n the whole mage oman. eon, we nten to aress the olor nauray ssue tyally exstng n olor base mage retreval n the lterature. Wth ths onseraton, we aly fuzzy log to the system. Thr, we nten to mrove the query roessng tme to avo the tyal lnear searh roblem n the lterature; ths rves us to evelo the seonary lusterng tehnque urrently emloye n FUZZYCLUB. As a result, omarng wth the exstng tehnques an systems, FUZZYCLUB exhbts the followng stntve avantages: ( t solves for the olor nauray roblem tyally exstng n olor base CBIR systems to a ertan egree ( t evelos a balane sheme n smlarty measure between regonal an global mathng n orer to ature as muh semant nformaton as ossble wthout sarfng the effeny ( t re-organzes mage atabases to further mrove retreval effeny wthout omromsng retreval effetveness. The novelty of FUZZYCLUB s ts mrovement of the exstng tehnques an ts nororaton an ombnaton of these tehnques together n a sngle system. 3. Image egmentaton The very frst ste of FUZZYCLUB s to segment an mage nto fferent regons base on olor an satal varaton features usng a mofe verson of the k-means algorthm [7] ue to ts unsuervse learnng nature suh that we an aatvely uates the number of regons as an teratve roess to aommoate the fat that the number of regons n an mage s unknown before the segmentaton. Image nexng s then taken base on the olor, texture, an shae features n eah regon, as well as the global, overall ombnaton of the regonal features. To segment an mage nto regons, FUZZYCLUB frst arttons an mage nto 4 by 4 bloks to omromse between texture granularty an omutaton tme. To aly the k-means algorthm, a feature vetor onsstng of sx features from eah blok s efne as follows. Three of the features are the average olor omonents n a 4 by 4 blok. The LAB olor sae s use ue to ts esre roerty of the eretual olor fferene roortonal to the numeral fferene n the LAB sae. These features are enote as { C, C, C3}. The other three features are use to ature the texture nformaton of the mage, reresente by the energy n the

3 hgh frequeny bans of the Haar wavelet transform [8],.e., the square roots of the seon orer moments of wavelet oeffents n hgh frequeny bans. To obtan these moments, a Haar wavelet transform s ale to the L omonent of the mage. After a one-level wavelet transform, a 4 by 4 blok s eomose nto four frequeny bans; eah ban ontans * oeffents. Wthout loss of generalty, suose the oeffents n the HL ban are { C k, l, Ck, l+, Ck +, l, Ck +, l+ }. Then the texture feature of ths blok n the HL ban s omute as: / f = ( k +, l+ ( 4 = 0 = 0 The other two features are omute smlarly n the LH an HH bans. These three features of the blok are enote as { T, T, T3}. They an be use to sern texture by showng varatons n fferent retons. After obtanng the feature vetors for all the bloks, we erform the normalzaton on both olor an texture features to whten them suh that the effets of fferent feature ranges are elmnate. Consequently the k-means algorthm [7] s use to luster the feature vetors nto several lasses wth every lass n the feature sae orresonng to one satal regon n the mage sae. ne lusterng s erforme n the feature sae, bloks n eah luster o not neessarly form a onnete regon n the mage. Ths way, we reserve the natural lusterng of obets n general-urose mages. The k-means algorthm oes not sefy how many lusters to hoose. We aatvely selet the number of lusters C by graually nreasng C untl a sto onstrant s satsfe. The average number of lusters for all mages n the atabase vares n aorane wth the austment of the sto onstrant. In the k-means algorthm we use a olor-texture weghte L stane metr as 3 = 6 + wt ( t t = 4 w ( ( to esrbe the stane between bloks. In our mlemente rototye system of FUZZYCLUB, we set w = 0.65 an w t = After the segmentaton, FUZZYCLUB s reay for mage nexng. In other wors, mage nexng s base on the features efne n the regons obtane from the mage segmentaton. 4. Regon-Base Features Wthn eah regon, we efne three tyes of features: olor, texture, an shae, along wth the onventonal geometr nformaton as the feature vetor for mage nexng. 4. Color Features Color s the most oularly use tye of features n mage nexng. On the other han, ue to ts nherent nature of nauray n esrton of the same semant ontent by fferent the olor quantzaton an/or by the unertanty of human ereton, t s mortant to ature ths nauray when efne the features. We aly fuzzy log [][5] to the tratonal olor hstogram to hel ature ths unertanty n olor nexng. We assume that any olor s a fuzzy set [0]. That means we wll assoate any olor to a fuzzy funton, µ : µ [0,] an for any olor of the olor unverse, µ ( s the resemblane egree of the olor to the olor. The fuzzy moel we efne shoul follow the roerty that the resemblane egree ereases as the nter-olor stane nreases. The natural hoe, aorng to the tyal soft omutng lterature [0], s to mose a smooth eay of the resemblane funton when the nter-olor stane nreases. ne the LAB olor sae s of the equvalene between the eretual nterolor stane an the atual Eulean stane between the olor sae oornates, we efne a Gaussan oerator to be the fuzzy resemblane funton: (, µ ( = ex{ } (3 πσ σ where s the Eulean stane between olor an n LAB sae, an σ s the average stane between olor an efne as B B σ = (, B( B (4 = k = + where B s the number of bukets n the olor hstogram. Ths fuzzy olor moel enables to enlarge the nfluene of a gven olor to ts neghborng olors, aorng to the unertanty rnle an the eretual smlarty. Ths means that eah tme a olor s foun n the mage, t wll nfluene all the quantze olors aorng to ther resemblane to the olor. Numerally, ths s exresse as: h ( = h ( µ ( (5 µ where µ s the olor unverse n the mage an h ( s the normalze, tratonal olor hstogram. Ths fuzzy hstogram oeraton n fat s the lnear onvoluton between the tratonal olor hstogram an the fuzzy olor moel. Ths onvoluton exresses the hstogram smoothng, rove that the olor moel s nee a

4 smoothng, low-ass flterng kernel. The use of Gaussan funton as the olor moel hels generate suh a smooth hstogram, whh subsequently hels reue the quantzaton errors []. In the mlementaton of the rototye system of FUZZYCLUB, the LAB olor sae s quantze nto 96 bukets by usng unform quantzaton (L by 6, A by 4, B by 4. Then Eq. 5 s ale to obtan the fuzzy hstogram for eah regon. µ ( for eah buket n the hstogram s re-omute base on Eqs. 3 an 4, an s mlemente as a looku table to reue the onlne omutaton. 4. Texture Features The texture features are efne as the entro vetor of all the three-omonents Haar wavelet moment vetors efne n eton 3 for eah bloks of a regon. 4.3 hae Features The shae features are efne as a vetor ontanng three omonents for the normalze nerta [9] of orer to 3 of a regon, resetvely. For a regon H n - mensonal Eulean sae R (.e., an mage sae, the normalze nerta of orer s [( x xˆ ( x, y:( x, y H l ( H, + / [ V ( H ] + ( y yˆ ] / = (6 where V(H s the number of xels n the regon H, an ( x ˆ, yˆ s the entro of H. The mnmum normalze nerta s aheve by sheres. Denote the th orer normalze nerta of sheres as L. The followng features are use to esrbe the shae of a regon: = l( H, / L, = l( H, / L, 3 = l( H,3 / L3 (7 Now the nexng vetor of a regon onssts of the three fuzzy olor features, the three texture feature omonents, an the three shae feature omonents efne n Eq. 7. In aton, the loaton of the regon, reresente as the entro oornates of the regon, an the area of the regon, reresente as the total number of xels, are also ature as art of the nexng feature vetor, resultng n a omlete feature vetor for eah regon. 5. Regon Mathng an Image mlarty To omute the stane between two regons, we aly L stane metr to fuzzy olor hstogram, texture vetor, an shae vetor, resetvely. For the fuzzy hstogram, we efne the stane metr as: B [( h ( hq ( ] q = C = B (8 where B s the number of bukets n the hstogram, an h ( an h q ( are the fuzzy hstograms for regon an q, resetvely. mlarly, L stane metr s ale to the texture vetor an the shae vetor, resetvely: q = T T (9 where T, T q q = (0 are the texture feature vetor an the shae feature vetor for regon, resetvely, an T q, q q are for regon q, resetvely. To measure the stane between two regons, we searate the ontrbuton from the olor an texture features from that from the shae features, as the former s onsere more relable n mage nexng than the latter. Consequently, gven two regons an q, the nter-regon stane on olor an texture s efne as q q C T D q = + ( The ntra-regon stane (.e., the evaton for regon on olor an texture s efne as N ] / D = [ Z Z ( N = where N s the number of bloks n regon, Z s the olor-texture vetor of blok n regon efne n eton 3, an Z s the entro vetor n regon of all the olor-texture vetors for all the bloks n ths regon. Conetually, the overall stane between two regons shoul nrease when the nter-regon stane nreases an when the ntra-regon stane ereases. Hene, we efne the overall stane between two regons an q as follows: D q q DIT q = w + ( w (3 D + Dqq where w s a weght. In the rototye system of FUZZYCLUB, we set w as 0.7. ne all omonents are normalze, ths overall stane between two regons s also normalze. The searaton between the ontrbuton from the olor an texture features an that from the shae features allows us to aust the weghts for these fferent ontrbutons. The favor to the former n weght n the rototye system reflets our belef that the former s more

5 relable than the latter, whh s verfe by the exermental results. Gven the efnton of the stane between two regons, we are reay to omute the global smlarty between two mages. uose we have M regons n mage an N regons n mage, the followng algorthm omutes the global smlarty between mage an mage : te : omute the stane between one regon n mage an all regons n mage. For eah regon n mage, the stane between ths regon an mage s efne as: R Im age = Mn( DIT, (4 where enumerates eah regons n mage. Ths efnton atures the mnmum stane between a regon an all the regons n an mage, whh maxmzes the otental smlarty between the regon an the mage. te : smlarly, the stane between a regon n mage an mage s efne as R Im age = Mn( DIT, (5 where enumerates eah regons n mage. te 3: now we have M+N stanes. We efne the stane between two mages ( an as follows: M N R Im age + = w w R Im age = Dst Image(, = (6 where w s the weght for regon n mage, an w s the weght for regon n mage. ne we thnk a regon wth a larger area lays a more sgnfant role n ontrbutng to the overall smlarty value between two mages than a regon wth a smaller area, we efne N w =, where N s the number of bloks n regon N an N s the total number of bloks n mage, an efne w smlarly for mage. Ths efnton of the overall smlarty between two mages ature by the overall stane between the mages s a balane sheme n smlarty measure between regonal an global mathng. As omare wth many exstng smlarty measures n the lterature, ths efnton strves to nororate as muh semant nformaton as ossble an at the same tme also aheves a omutatonal effeny. Gven ths efnton, for eah query mage q, t s straghtforwar to omute Dst Image( q, the retreval. for every mage n the atabase n The tme of mage retreval eens n a large egree on the number of mages n the atabase n almost all CBIR systems. Many exstng systems attemt to omare the query mage wth every target mages n the atabase to fn the to mathng mages, resultng n an essentally lnear searh, whh s rohbtve when the atabase s large. We beleve that t s not neessary to onut a whole atabase omarson. In fat, t s ossble to exlot a ror nformaton regarng the organzaton of the mages n the atabase n the feature sae before a query s ose, suh that when a query s reeve, only a art of the atabase nees to be searhe whle a large orton of the atabase may be elmnate n the searh. Ths ertanly saves sgnfant query roessng tme wthout omromsng the retreval reson. To aheve ths goal, n FUZZYCLUB we a a reretreval sreenng hase to the feature sae after a atabase s nexe by alyng a seonary k-means algorthm to the stane DITq n the regon feature vetor sae to luster all the regons n the atabase nto lasses. The hlosohy s that regons wth smlar {olor, texture, shae} features shoul be groue together n the same lass. Ths seonary lusterng s erforme offlne, an eah regon s nexng ata along wth ts assoate lass ID s reore n the nex fles. Consequently, n the rototye mlementaton of FUZZYCLUB, the mage atabase s nexe n terms of a three level tree struture, one for the regon level, one for the lass level, an one for the mage level. Assumng an mage atabase s nexe base on the features efne n etons 4 an 5, an s organze base on the seonary lusterng, gven a query mage, FUZZYCLUB roesses the query as follows: te : Perform the query mage segmentaton to obtan all the regons, say we have regons Q, [0, N ] n the query mage. te : Comute the stanes between eah regon Q an all lass entros n the atabase to etermne whh lass Q belongs to by the mnmum-stane-wn rnle. Assume that regon Q belongs to lass C, [0, K ]. te 3: Retreve all the regons n the atabase whh belongs to the lass C, [0, K ]. These regons omrse a regon set T. The mages ontanng any regons n the set T s subsequently retreve from the nex struture. These mages omrse an mage set I 6. eonary Clusterng an Image Retreval

6 te 4: Comare the query mage wth the mages n the mage set I. The stane Dst Im age s use for eah ar an the to-least-stane mages are returne n the retreval. It s shown theoretally an exermentally that FUZZYCLUB saves query roessng tme sgnfantly wthout omromsng the retreval reson by avong searhng the whole atabase. 7. Exermental Evaluatons We have mlemente FUZZYCLUB as a rototye system n a latform of Pentum III 800 MHZ CPU wth 56M memory, an have evaluate ths rototye system n a general-urose mage atabase ontanng 000 mages from COREL. These mages are manually ve nto 0 well-efne grous suh as eole, nature senery, bulng, an vehles. No re-restrtons suh as fferent amera moels or lghtng ontons are sefe n the mage atabase for ths evaluaton. These mages are all n JPEG format The whole nexng tme, nlung runnng the seonary lusterng after nexng eah mage, for the 000 mage atabase takes mnutes, orresonng to about seons er mage. The average query tme for returnng to 0 mages er query s less than seon. To evaluate the retreval effetveness of FUZZYCLUB, we ranomly selet 4 query mages wth fferent semants, namely flower, nosaur, vehle, an Afran eole. For eah query, we examne the reson of the retreval base on the relevane of the mage semants. The semant relevane s etermne by manual truthng the query mage an eah of the retreve mages n the retreval. The four query retrevals are shown n Fgure. (a Flower query; 0 mathes out of the to. (b Dnosaur query; mathes out of the to. ( Vehle query; 8 mathes out of the to. ( Afran eole query; 6 mathes out of the to. Fgure. Retreval results of the four queres evaluate; the to-left orner mage s the query, an the rankng goes rghtwar an ownwar. To erform a more quanttatve evaluaton, we omare the erformane of FUZZYCLUB wth those of IRM [6] an the Geometr Hstogram []. For eah grou mages n the 000 atabase mages, we ranomly selet 30 mages as queres to eah of the three systems, resetvely. The average resons for eah grous base on the returne to mages are reore. ne the number of relevant mages n the atabase for eah query mage s the same, the reall values are not omute as they are roortonal to the reson values n ths ase. The reson omarson among these three systems s shown n Fgure. Fgure 3 shows the average resonrealls of FUZZYCLUB taken over 00 queres ranomly selete over all the ten grous.

7 Average reson/reall for eah grou FUZZYCLUB IRM Geometr Hstogram In orer to evaluate the query roessng see, we omare the query roessng tme of FUZZYCLUB wth that of IRM [6]. Fgure 4 shows the average resonse tme of the two systems to return to mages for 30 queres n eah of the 0 grous. Average Preson/reall Grou ID Fgure. Average reson/reall omarson between FUZZYCLUB, IRM, an Geometr Hstogram systems. These evaluaton results learly show that the erformane of FUZZYCLUB s sgnfantly better than those of Geometr Hstogram [] beause Geometr Hstogram aroah only fouses on the olor features, whh s not exltly semant-relate for many mages. An even for the olor features t oes not ature the nherent nauray of olor features n semant ontent reresentaton. The evaluaton results also show that FUZZYCLUB noteably outerforms IRM [6] system n most grous. Ths s n art ue to the more etale olor reresentaton an alaton of fuzzy log n the feature mathng n FUZZYCLUB. Average Preson Average Preson-Realls for FUZZYCLUB Reall FUZZYCLUB Fgure 3. Average reson-reall of FUZZYCLUB over ranomly selete 00 queres. Average Resonse Tme (s Average Resosne Tme Comarson Between FUZZYCLUB an IRM Grou ID FUZZYCLUB IRM Fgure 4. Comarson of the query roessng tme between FUZZYCLUB an IRM. From Fgure 4, the average resonse tme reuton of FUZZYCLUB to IRM [6] s 9.56%. Wth the sze of the atabase nreases, the retreval effeny of FUZZYCLUB nreases roortonally. Ths s ue to the seonary lusterng tehnque emloye n FUZZYCLUB. 8. Conluson A novel mage nexng an retreval methoology, alle FUZZYCLUB, s resente n ths aer. FUZZYCLUB ntegrates olor, texture, an shae nformaton along wth the onventonal geometr nformaton together as an nexng vetor, an ales the nexng vetor to regons as oose to a whole mage. Consequently, the overall mage smlarty s eveloe through regonal smlarty base on all the feature omonents. In orer to aress the olor feature nauray roblem, FUZZYCLUB ales fuzzy log to olor hstograms. In orer to mrove the query roessng tme, FUZZYCLUB nororates a seonary lusterng tehnque to re-organze the atabase to sgnfantly save the searh tme. Exermental evaluaton base on a 000 COREL olor mage atabase shows that FUZZYCLUB romsngly outerforms the eer mage retreval systems from the lterature. As omare wth the exstng tehnques an systems, FUZZYCLUB exhbts the followng stntve avantages: ( t solves for the olor nauray roblem tyally exstng n olor

8 base CBIR systems to a ertan egree ( t evelos a balane sheme n smlarty measure between regonal an global mathng n orer to ature as muh semant nformaton as ossble wthout sarfng the effeny ( t re-organzes mage atabases to further mrove retreval effeny wthout omromsng retreval effetveness. The novelty of FUZZYCLUB s ts mrovement of the exstng tehnques an ts nororaton an ombnaton of these tehnques together n a sngle system. Referene [] M. De Marso, L. Cnque, an. Leval, Inexng toral ouments by ther ontent: a survey of urrent tehnques, Image an Vson Comutng, 997, [] Arnlo W. M. meulers, Marel Worrng et al, Content- Base Image Retreval at the En of the Early Years, IEEE Trans. On PAMI, Vol., No., De [3] Y. Al Aslanogan, an Clement T. Yu, Tehnques an ystems for Image an Veo Retreval, IEEE Trans. on Knowlege an Data Engneerng, Vol., No., Jan [4] Greg Pass, an Ramn Zabh, Hstogram Refnement for Content-Base Image, Proeengs of the IEEE Worksho on Alatons of Comuter Vson, arasota, Flora, De [5] Constantn Vertan, an Nozha Bouemaa, Embeng Fuzzy Log n Content Base Image Regreval, Proeengs of the 9th Internatonal Meetng of the North Amera Fuzzy Informaton Proessng oety, Atlanta, Jul [6] James Z. Wang, Ja L an Go Weerhol, IMPLIty: emants-enstve Integrate Mathng for Pture Lbrares, IEEE Trans. On PAMI, Vol. 3, No.9, e. 00. [7] M. Flkner et al, Query by Image an Veo ontent: The QBIC system, IEEE Comuter, Vol. 8, No. 9, e. 995, [8] Vrgna Ogle, an Mhael tonebraker, Chabot: Retreval from a relatonal atabase of mages, IEEE Comuter, Vol. 8, No. 9, e. 995, [9] John R. mth, an hh-fu Chang, VsualEEk: a fully automate ontent-base mage query system, ACM Multmea 96, No., Nov [0] Jng Huang, Rav Kumar et al, Image Inexng Usng Color Correlograms, Proeengs of the IEEE Conf. Comuter Vson an Pattern Reognton, Puerto Ro, Jun [] Abng Rao, Rohn K. rhar, an Zhongfe Zhang, Geometr Hstogram: A Dstrbuton of Geometr Confguraton of Color ubsets, Internet Imagng, Proeengs of PIE, Vol. 3964, an Jose, Jan. 000, [] L. Cnque, G. Coa et al, Color-base Image Retreval usng atal-hromat hstograms, Image an Vson Comutng, Vol. 9, 00, [3]. Ravela, an R. Manmatha, Retrevng Image by Aearane, Proeengs of the Internatonal Conf. on Comuter Vson (ICCV, Bombay, Ina, Jan [4] H. Wang, F. Guo, an D.D. Feng, A gnature for Contentbase Image Retreval Usng Geometral Transform, ACM Multmea 98, 998 [5] C. Carson, M. Thomas,. Belonge, et al, Blobworl: A ystem for Regon-Base Image Inexng an Retreval, Proeengs of the thr nternatonal onf. on Vsual Informaton ystem, Amsteram, Netherlans, Jun. 999, [6] W.Y. Ma, an B. Manunath, NaTra: A Toolbox for Navgatng Large Image Databases, Proeengs of the IEEE Internatonal Conf. on Image Proessng, anta Barbara, Ot. 997, [7] J.A. Hartgan, an M.A. Wong, Algorthm A36: A k- means Clusterng Algorthm, Ale tatsts, Vol. 8, 979, [8] I. Daubehes, Ten Letures on Wavelets, Catal Cty Press, 99. [9] A.Gersho, Asymtotally Otmum Blok Quantzaton, IEEE Trans. On Informaton Theory, Vol. 5, No. 4, Ar. 979, [0] Zheru Ch, Hong Yan an Tuan Pham, Fuzzy Algorthms: Wth Alatons to Image Proessng an Pattern Reognton, Worl entf, 996. [] J.Kautsky, N.K.Nhols, an D.L.B.Ju, moothe hstogram mofaton for mage roessng, CVGIP: Image Unerstanng, Vol. 6, No.3, Jun. 984, [] ankar K. Pal, Ashsh Ghosh, an Malay K. Kunu, oft Comutng for Image Proessng, Physa-Verlag, 000.