Multiple-Instance Image Database Retrieval by Spatial Similarity Based on Interval Neighbor Group

Transcription

1 ultple-instance Iage atabase Retreval by Spatal Slarty Based on Interval eghbor Group John Y. Chang epartent of Coputer Scence and Engneerng, atonal Sun Yat-sen Unversty Kaohsung, Tawan Shuenn-Ren Cheng epartent of Busness Adnstraton, Cheng Shu Unversty Kaohsung, Tawan #95 YE-Ren Huang epartent of Coputer Scence and Engneerng, atonal Sun Yat-sen Unversty Kaohsung, Tawan 804 edu.tw ABSTRACT In ths paper, a ultple-nstance age retreval syste ncorporatng a general spatal slarty easure s proposed. A ultple-nstance learnng s eployed to suarze the coonalty of spatal features aong postve and negatve exaple ages. The general spatal slarty easure evaluates the degree of slarty between atchng atoc spatal relatons present n the axu coon obect set of the query and a database age based on ther nodal dstance n an Interval eghbor Group (IG). The shorter the dstance, the hgher degree of slarty, whle a longer one, a lower degree of slarty. An enseble slarty easure, derved fro the spatal relatons of all consttuent obects n the query and a database age, wll then ntegrate these atoc spatal slarty assessents and gve an overall slarty value between two ages. Therefore, ages n a database can be quanttatvely ranked accordng to the degree of enseble spatal slarty wth the query. In order to deonstrate the feasblty of the proposed approach, two sets of test for queryng an age database are perfored, naely, sngle-nstance v.s. ultple-nstance retreval by eployng the RSS-IG schee proposed and the RSS-IG schee v.s. Be-strng slarty ethod ncorporatng dentcal ultple-nstance learnng. The IG-based spatal slarty easure wth fne granularty, cobned wth the utlzaton of a ultple-nstance learnng paradg to forge a unfed query key, produces desrable retreval results that better atch user s expectaton. Categores and Subect escrptors H.3.3 [Inforaton Search and Retreval] General Ters Theory. Keywords retreval by spatal slarty (RSS), Interval eghbor Group (IG), ultple-nstance learnng, content-based age retreval (CBIR). Persson to ake dgtal or hard copes of all or part of ths work for personal or classroo use s granted wthout fee provded that copes are not ade or dstrbuted for proft or coercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc persson and/or a fee. CIVR 0, July 5-7, X an Chna Copyrght c 00 AC /0/07...$ ITROUCTIO Retreval of dgtal ages fro a database s an actve research area due to the neffcency of query processng utlzng tradtonal textual language [-3]. In content-based age retreval (CBIR) applcatons, features suffcently dscrnatve to suarze the age content are usually extracted frst to reduce the coplexty of nforaton contaned n an age. However, ages are nherently abguous snce they contan a great aount of nforaton that ustfes any dfferent facets of nterpretaton. Usng a sngle age to query a database ght adversely eploy features that do not atch user s ntenton and retreve dsslar false-postve ages, or leave slar falsenegatve ones behnd. How to autoatcally extract relable age features as a query key that eets user s antcpaton n a contentbased age retreval (CBIR) syste s an portant topc. ultple-nstance learnng procedure dentfes coon postve features and excludes negatve ones to further clarfy the user s searchng crtera. Spatal slarty for obects present n the axu coon obect set of the query and a database age are consdered. The dervaton begns wth the dscusson of slarty between two atchng atoc spatal relatons, and then extends to two sets of atoc spatal relatons. The Enseble Spatal Relaton Slarty (ESRS) reflectng the overall degree of spatal reseblance between two ages can then be deterned. The last secton deonstrates the effectveness of ths novel approach by coparng the retreval results of () sngle-nstance versus ultple-nstance learnng by applyng the sae RSS-IG paradg proposed, and () ultple-nstance retreval by eployng the RSS-IG approach and a Be-strng spatal representaton technque. ue to the dervaton of coonalty fro ultple exaple ages through ultple-nstance learnng and the fne granularty of spatal slarty easure proposed, consstent search results atchng user s expectaton are obtaned n both tests. Fnally, concludng rearks are ade.. ULTIPLE-ISTACE LEARIG The ultple nstance learnng takes a sall set of postve and negatve exaple ages, each assocated wth extracted feature clusters the user desred or unwanted [, ]. The postve concepts are then ntegrated and the negatve ones excluded to autoatcally generate a unfed query key for a CBIR syste. Each tranng exaple age corresponds to a bag contanng a pluralty of nstances. Each nstance s apped to a pont n feature space. A bag s labeled negatve f all the nstances n t are 35

2 negatve. On the other hand, a bag s labeled postve f there s at least one nstance n t that s postve. ote the nstances wthn a bag are not labeled theselves, only the bag s labeled postve or negatve. Each bag s therefore an exaple age wth abguous concepts. Fro a collecton of labeled bags, the learner tres to nduce coon concepts that wll label unseen bags correctly. The abguty between ultple feature clusters exstng wthn a sngle age s further clarfed wth the help of ultple-nstance learnng. The features extracted by gvng both postve and negatve exaple ages are then forged through ultplenstance learnng procedure to derve a unfed query key for retrevng relevant ages fro a database. 3. ERIVATIO OF THE GEERAL SIILARITY EASURE 3. Atoc Spatal Relaton and Interval eghbor Graph (IG) An age s preprocessed frst nto a sybolc pcture, coposed of nu boundng rectangles (BRs) enclosng consttuent obects, as a for of abstracton [3]. Gven two non-zero szed obects A and B that are abstracted as BRs, there are 3 possble one-densonal spatal relatons between A and B [4], as shown n Fg.. ote the assgnent of labels to obects, e.g., A and B, s known a pror. Therefore, a total of 69 spatal relatons exst for a par of two-densonal obects, as llustrated n Fg.. A spatal relaton descrbes the topologcal relaton between two obects and s consdered as the ost fundaental unt,.e., atoc spatal relaton, n an RSS syste. An atoc spatal relaton can be decoposed nto horzontal and vertcal spatal coponents by proectng onto the x- and y-axs, respectvely. Gven both the horzontal and vertcal spatal relatons, the correspondng atoc spatal relaton can also be unquely deterned. Fgure : A lstng of 3 spatal relatons between two obects. Fgure : A total of 69 possble atoc spatal relatons can be found between two BRs. In Fg. 3, the 3 spatal relatons between two obects are further arranged as an Interval eghbor Group (IG) to llustrate graphcally the relatons between varous spatal arrangeents [5]. Every spatal relaton R ( ), =,,3, n Fg. can be assocated wth one specfc node n an IG. Two nodes are neghbors, f the correspondng spatal relatons can be drectly transfored nto one another by contnuously shortenng, lengthenng or ovng operatons. An atoc spatal relaton n age, R ( ) = ( R ( ), R ( )), 3, can be x y represented by an IG node par = (, ), contanng x y two IG nodes x, y n two IGs, each assocated wth the correspondng horzontal and vertcal coponents, respectvely. Three dfferent search strateges are coonly eployed, naely, exact atch, subage and slarty retreval [6]. The goal of perforng an exact atch search as at fndng a database age dentcal to the query one [7, 8]. The age retreved and the query have exactly the sae obect set and spatal Fgure 3: The Interval eghbor Group (IG), wth nodes correspondng to 3 spatal relatons. 36

3 arrangeents. On the other hand, subage retreval ntends to fnd database ages that encopass all the obects and spatal arrangeents n the query age[9]. Subage retreval s analogous to a query fnd all ages n the database that nclude ths query age. Slarty retreval that allows dsparate obects n both the query age and a database one s the ost general knd of spatal retreval [0-4]. The purpose of slarty retreval s to fnd all database ages partally atch wth a query n ters of consttuent obects and spatal relatons. Gven a collecton of partally atched database ages, an effectve slarty easure s requred to generate a ranked retreval result accordng to the degree of spatal reseblance wth the query age. In the Be-strng schee [0], the topology of obects n an age was represented by a strng derved fro the correspondng BRs. The spatal relaton between two boundary sybols was depcted by applyng a duy obect. A duy obect was not a real obect exsted n the orgnal age, rather a vrtual obect assued. By coparng the Be-strngs of the query and a database age, the length of the longest coon subsequence (LCS) was used as the slarty ndex. An overall slarty etrc was deterned based on the average of the LCS lengths along the x- and y-axs proectons of the BRs. However, two database ages sharng the sae LCS, yet wth dfferent reanng substrngs wll not be dfferentable under ths approach. For a Retreval by Spatal Slarty (RSS) syste to be effectve, a general slarty easure wth fne granularty based on the ensebles of spatal relatons exstng n two ages s the key ssue needed to be addressed. 3. The IG odal stance and egree of Slarty between Two Atoc Spatal Relatons For every two obects n an age, there exsts an atoc spatal relaton. A set of atoc spatal relatons can be derved fro an age wth a plural nuber of obects. Before explorng the spatal slarty between two ages, the slarty easure between two atoc relatons has to be deterned frst. The degree of slarty between two atoc spatal relatons s lnked drectly to the dstance between the assocated nodes n an IG. Once all the slarty values of one-to-one atoc relatons are derved, an enseble slarty easure between two ages can then be deterned. An atoc spatal relaton R ( ) n age can be decoposed nto two coponents R ( x), R ( y ), each an orthogonal proecton along the vertcal or horzontal axs. For every spatal relaton ( ) R, there s a assocate node n an IG. Take Fg. 4 (a) as an exaple, the atoc spatal relaton fored by obects o and o n age s decoposed nto x- and y-axs coponents correspondng to IG nodes x = eet and y = overlap n two IGs, as shown n Fg. 4 (b) and (c). An IG can be represented as a tuple ( V, E ), where V s the set contanng 3 nodes assocated wth spatal relatons, and E the set of undrected edges connectng the nodes. The edge e(, ) s defned as two neghborng nodes connected by a drect lnk, where e E,, V. For a node V, ts correspondng spatal relaton s denoted as R ( ). The dstance between two nodes connected by a drect lnk s one. A path s a sequence of nodes such that fro each of ts nodes, there s an edge to the next node n the sequence. The shortest path between and s the path wth nu nuber of edges aong all paths fro to. The dstance dst (, ) s the nuber of edges traversed along the shortest path fro to. The dstance between two arbtrary IG nodes s suarzed n Table. The farthest s 6, whle the closest 0. The dstance between two IG nodes ndcates the degree of slarty between two proected - spatal relatons. eghborng nodes can be drectly transfored nto one another by a sple shortenng, lengthenng or ovng operaton, whle nodes far apart requre a cascade of the above operatons. Based on ths observaton, the forulaton of the Spatal Relaton Slarty (SRS) between two spatal relatons R ( ) and R ( ) s lnked to the dstance between the correspondng IG nodes and, as follows: dst (, ) SRS R R = 6 ( ( ), ( )). The range of SRS( R( ), R( )) s between 0 and, wth as the exact atch, 0 total rrelevance. The approach for dervng slarty easure above s Table : The shortest dstance between two nodes n an IG Before eet Overlap Fnsh urng Start Equal ~Start ~urng ~Fnsh ~Overlap ~eet ~Before Before eet Overlap Fnsh urng Start Equal ~Start ~urng ~Fnsh ~Overlap ~eet ~Before

4 extended to case by consderng the dstance frst. Assue ages and contan exactly two coon obects o and o. The atchng obect pars ( o, o ) n ages and for atoc spatal relatons R ( kl, ) and R ( ), respectvely. The x- and y-proectons of atoc spatal relatons R ( ) kl, and R ( ) are assocated wth IG node pars = ( x, y ) and = ( x, y ). The dstance, between kl, and k (b) x = eet and x = ~start can be obtaned by sung up the correspondng shortest-path dstances: kl, k l dst(, ) = dst ( x, x) + dst ( y, y ). () Followng the sae paradg, the degree of slarty between two atoc spatal relatons can be expressed as the average of slarty values along x- and y-axs: k l SRS,, ( R ( x ), R ( x )) + SRS ( R ( y ), R ( y )) kl SRS( R( ), R( )) = kl, dst (, ) =. l (c) y = overlap and y = ~overlap Take Fg. 4 (a) as an exaple. There are two coon obects o and o n ages and. An atoc spatal relaton, Fgure 4: (a) Two coon obects, o and o, are present n R ( kl, ) and R ( ), can be derved for every age. The ages and. An atoc spatal relaton can be derved for each age. The IG nodes correspondng to x- and y-axs kl, par of spatal relatons, ( R( ), R( )), fored by two proected spatal relatons of the atchng atoc pars are coon obects n two ages s called a atchng atoc par. shown n (b) and (c), respectvely. The eleents of a atchng atoc par are each assocated wth an IG node par = ( x, y ) = (eet, overlap) and 3.3 Slarty easure between Two Sets of Atoc Spatal Relatons, and Two Iages = ( x, y ) = (~start, ~overlap), as llustrated n Fg. 4 (b) (ESRS) kl, and (c). The dstance dst (, ) can be obtaned by Assue q and d obects are contaned n the query and a sung up the correspondng path dstances accordng to Eq. database age, respectvely,.e., obect s t (): sets O = { o s =,, q} and O = { o t =,, d}. These q+ d kl, dst (, ) = dst (eet, ~start) () obects can be parttoned nto three dsont sets, naely, O O, O O, and O O. The ntersecton + dst (overlap,~overlap)= 3+=5. = O O s called the axu coon obect set. Obects Therefore, the degree of spatal slarty between a atchng n the axu coon obect set can be found n both ages, atoc par n ages and can be calculated accordng to Eq. whle obects belongng to the dfference set, O (): O or kl, 5 7 SRS( R( ), R( O O )) = =. () appear only n ether age or. Every two obects n consttute an atoc spatal relaton n ages and, respectvely. These two atoc spatal relatons further for a atchng atoc par. On the other hand, due to lack of correspondence between ages and for obects n the dfference sets O O and O O, no atchng atoc uery age atabase age spatal relatons can be establshed. We wll focus on dervng the slarty easure of spatal relatons for obects belongng to the (a) axu coon obect set next. Assue the axu coon obect set contans obects coon to ages and,.e., = { o,, o }. Aong the, a total of C = ( ) / obect pars ( b o, o ), a, b, a > b, can be fored. For each of the obect pars a b ( o, o ), a atchng atoc par (, ), (, ), ( R o a b ( ), R o a b ( k l )) contanng spatal relatons n ages 38

5 and can be dentfed. The correspondng one-to-one spatal relaton slarty of the atchng atoc par can be derved by Fnally, the degree of enseble spatal reseblance between ages and can be obtaned by followng Eq. (4): followng Eq. (): 3 5 C 5 kl, a b a b dst (, ), (, ), (, ESRS(, ) ). 4 3 o o o o k l SRS( R ( ), R ( 3 C C 8 )) =. The total aount of spatal slarty contrbuted by all atchng atoc pars n can be obtaned by sung up the slarty value of ndvdual atchng par of atoc spatal relatons. SRS = SRS ( o, ), (, ), ( o b o ( ), o b k l R R ( )). (3) (a) (3) a b o, o, a, b, a> b The SRS above represents the degree of spatal slarty between atchng atoc spatal relatons consttuted by obects n the axu coon obect set of ages and. On the other hand, the enseble spatal relaton slarty (ESRS) stands for the overall reseblance between ages and by takng all possble correspondences of spatal relatons fored by consttuent obects nto consderaton. For a query wth q q obects, C atoc spatal relatons can be dentfed. Slarly, d C atoc spatal relatons for a database age wth d obects. q d Therefore, a total of C C possble correspondences of spatal relatons between ages and can be establshed. Aong the, only C atchng atoc pars of spatal relatons, fored (b) by the obects n the axu coon obect set, can successfully fnd ts correspondng counterparts. Wth the above dscusson, the enseble spatal relaton slarty (ESRS) can be forulated by noralzng SRS wth the rato of the nuber of 4 successful atchng atoc pars to the total nuber of possble (c) { o } correspondences, as follows: Fgure 5: (a) Iage s coposed of four obects and three C obects. The axu coon obect set contans three ESRS(, ) = SRS (4) (4) q d 3 C C coon obects,.e., = { o, o, o }. Three atchng atoc pars, consttuted by coon obects n, are shown n (b). (c) One dsparate obect o 4 s added to the age n (a). reans unchanged, yet the nuber of possble correspondences between atoc relatons ncreases due the ncluson of a new obect. where O = q, O = d, and = O O =. The ESRS (, ). reflects the overall degree of spatal reseblance between ages and. When the nubers of obects present n, and are all equal to, Eq. (4) degenerates nto (),.e., the degree of slarty between two atchng atoc spatal relatons. 3 4 Let s assue there are four obects { o, o, o, o } n age and three obects { o, o, o 3 } n, as shown n Fg. 5 (a). The axu coon obect set contans three coon obects, 3.e., = { o, o, o }. Fg. 5 (b) llustrates the three atchng atoc pars, consttuted by the coon obects n. The IG nodal dstance between each atchng atoc spatal relatons can be derved as follows: dst ((eet,overlap),(~start,~overlap) ) = dst(eet, ~start) + dst(overlap, ~overlap) = 3 + = 5, dst ((~fnsh,~overlap),(~overlap,overlap) ) = 4, dst ((~eet,after),(~overlap,before) ) = 7. Accordng to Eq. (3), the total aount of spatal slarty contrbuted by the atchng obect pars n s equal to SRS = ( ) + ( ) + ( ) =. 3 In the above exaple, all obects n database age are also present n query,.e., O O, and = O O = O. ext, 4 we wll add a new obect o to the current age, as shown n Fg. 5 (c). Snce 4 4 o and o are two dsparate obects, the axu coon obect set reans unchanged after the 3 ncluson of a new obect,.e., = { o, o, o }. So does the total aount of spatal slarty SRS, contrbuted by the atchng obect pars n. However, the dfference set O O ncludes a 4 new eleent o after the nserton. The nuber of atoc spatal relatons lackng correspondence ncreases due to the placeent of a dsparate obect. Ths decrease n spatal reseblance between ages and wll be reflected on the degree of ESRS as follows: ESRS 5 5 (, ) = C. 3 = C C Fro the above dscusson, next we wll prove the onotoncty property of the proposed enseble spatal relaton slarty 39

6 (ESRS). For a query age, database ages wth dfferent nuber of dsparate obects wll be dfferentable n ters of the ESRS, even sharng the sae axu coon obect set. Ths desrable fne granularty feature for the proposed slarty easure cannot be found n the aforeentoned exact atch, subage and slarty retreval search strateges [6-4]. Preposton The enseble spatal relaton slarty (ESRS) between two ages ncreases as the nuber of obects n the dfference set O O or O O decreases, and vce versa. Proof Assue q, d and obects are contaned n the query, database age and axu coon obect set, respectvely. The orgnal enseble spatal relaton slarty (ESRS) s forulated accordng to Eq. (4): C ESRS(, ) = SRS. q d C C Wthout loss of generalty, let s assue the nuber of obects n the dfference set O O s decreased by one due to reoval of an obect fro the query. enote the age after the reoval operaton as '. Snce the axu coon obect set reans ntact, the total aount of spatal slarty, SRS, contrbuted by the atchng obect pars n s unchanged. The enseble spatal relaton slarty (ESRS) can be rewrtten as: C ESRS( ', ) = SRS q d C C = C q SRS ESRS(, ). q d C C q > 4. EXPERIETAL STUY Every pcture contans two to fve BR-covered obects, each obect generated wth rando denson and postonng. In order to effectvely copare the retreval results, rotaton wth 90- degree-ncreent, rrorng, ncluson of new obect(s) and reoval of exstng obect(s) are appled on every base pcture to produce 6 ore varants. Therefore, for every age n the database, a total of seven pctures are closely correlated n ters of consttuent obects and topology, as shown n Fg. 6. (c) IG node pars P = (, ) Px Py = (after, durng) and P = (, ) Px Py = (after, durng) correspondng to the x- and y- axs proected spatal relatons of atchng atoc par between obects ( o, o ) n ages (a) and (b). ote that both atoc relatons are dentcal. Therefore, the x- and y-axs IG nodes are the sae. So does the nduced coon spatal characterstcs fro ultple-nstance learnng. 4. Sngle-Instance v.s. ultple-instance (a) Postve age P (b) Postve age P (d) IG node pars P = (, ) Px Py = (durng, ~overlap) and Fgure 6: For every database age, there are a total of seven pctures P = closely (, ) Px correlated Py = (before, n ters after) correspondng of consttuent to obects the x- and y- spatal arrangeent. axs proected spatal relatons of atchng atoc par between 40

7 3 obects ( o, o ) n ages (a) and (b). The spatal coonalty nduced s (overlap, ~eet). (b) Fgure 8: The result retreved by usng Fgure 7 (a) as a snglenstance query, and (b) ultple-nstance retreval result usng two postve ages n Fg. 7 (a) and (b). The correspondng ESRS value and age nuber n the database are also lsted. (e) IG node pars P = ( Px, Py ) = (before, ~durng) and = (, ) = (before, after) correspondng to the x- and y- P Px Py axs proected spatal relatons of atchng atoc par between 3 obects ( o, o ) n ages (a) and (b). The spatal coonalty nduced s (before, ~overlap). (a) egatve age n (f) The unfed query forged through the ultple-nstance paradg wth postve ages (a) and (b). Fgure 7: (a) and (b), Two postve ages. The IG node pars correspondng to the x- and y-axs proected spatal relatons of atchng atoc par between obects (c) ( o, o ), 3 3 (d) ( o, o ), (e) ( o, o ), and (f) the spatal coonalty nduced by eployng the dverse densty strategy. (b) IG node pars P = (, ) Px Py = (durng, ~overlap), = (, ) = (before, after), and P Px Py = (, ) = (durng, ~ durng) correspondng to the uv, u v n nx ny 3 atchng atoc par between obects ( o, o ) n ages 7 (a), 7 (b) and 8 (a). ote the coonalty nduced, after the ncluson of a negatve age, s changed fro (overlap, ~eet) n Fg. 7 (d) to (before, after). (a) 4

8 Fgure 9: (a) One negatve age. The IG nodes correspondng to (b) x- and y-axs proected spatal relatons of two postve ages and a negatve one. 4. RSS-IG Proposed v.s. Be-strng (a) (b) Fgure 0: (a) The ultple-nstance counterpart by eployng Be-strng wth two postve exaple ages and one negatve age. (b) The top 50 ages retreved and ther correspondng slarty value derved for RSS-IG and Be-strng schees. The plot shows a better dscrnablty between dfferent spatal relatons for RSS-IG. 5. COCLUSIOS The proposed RSS-IG spatal feature representaton and slarty easure evaluates the degree of slarty between atchng atoc spatal relatons present n the axu coon obect set of the query and a database age based on ther nodal dstance n an Interval eghbor Group (IG). The spatal features dentfed are further analyzed through a ultnstance learnng stage to nduce coonalty aong nuerous features exstng n ultple exaple ages. The cobnaton of a good spatal feature assessor and feature cluster locator wll generate query eetng user expectaton, produce consstent database retreval result and exclude both false-postve and falsenegatve cases. The constrants regardng color, texture, sze, orentaton, locaton, etc., can be further posed upon the feature clusters extracted and ncorporated n the slarty coparson. The slarty easure proposed can also explore the cobnaton of other global or local features to produce an even ore effectve age feature evaluaton. 6. REFERECES [] W. C. Ln, Y. C. Chang and H. H. Chen, Integratng textual and vsual nforaton for cross-language age retreval: A trans-eda dctonary approach, Inf. Process. anage., Vol. 43, o., pp , ar [] K. Barnard and. Johnson, Word sense dsabguaton wth pctures, Artf. Intell., Vol. 67, o. -, pp. 3-30,005. [3] W. R. Hersh, H. uller, J. R. Jensen, J. Yang, P.. Goran and P. Ruch, Advancng Boedcal Iage Retreval: evelopent and Analyss of a Test Collecton, J. A. ed. Inf. Assoc., Vol. 3, o. 5, pp , 006. [4] John Y. Chang and Shuenn-Ren Cheng, ultple-instance Content-Based Iage Retreval Eployng Isoetrc Ebedded Slarty easure, Pattern Recogn., Vol. 4, o., pp , Jan [5]. R. ooly, S. A. Goldan, S. S. Kwek, Real-valued ultple-nstance learnng wth queres, J. Coput. Sys. Sc., Vol. 7, o., pp. -5, 006. [6] Z. H. Zhou and. L. Zhang, Solvng ult-nstance probles wth classfer enseble based on constructve clusterng, Knowledge Inf. Syst., Vol., o., pp , 007. [7] X. Lu, S. Shekhar and S. Chawla, Obect-based rectonal uery Processng n Spatal atabases, IEEE Trans. Knowl. ata Eng., Vol. 5, o., pp , 003. [8] Ahad and W. Grosky, Indexng and retreval of ages by spatal constrants, J. Vs. Coun. Iage Repres., Vol. 4, pp. 9-30, 003. [9] J. T. Lee and H. P. Chu, Z-strng: A ew Spatal Knowledge Representaton for Iage atabases, Pattern Recogn. Lett., Vol. 4, o. 6, pp , ec [0] S.. Hseh and C. C. Hsu, Graph-based representaton for slarty retreval of sybolc ages, IEEE Trans. Knowl. ata Eng., Vol. 65, o. 3, pp , 008. [] P. Puntha and. S. Guru, An effectve and effcent exact atch retreval schee for sybolc age database systes based on spatal reasonng: A logarthc search te approach, IEEE Trans. Knowl. ata Eng., Vol. 8, o. 0, pp , 006. [] P. Puntha and. S. Guru, An Invarant Schee for Exact atch Retreval of Sybolc Iages: Trangular Spatal Relatonshp Based Approach, Pattern Recogn. Lett., Vol. 6, pp , 005. [3] Y. H. Wang, Iage ndexng and slarty retreval based on spatal relatonshp odel, Inf. Sc.: Int. J., Vol. 54, o. -, pp , 003. [4] P. W. Huang, L. P. Hsu, Y. W. Su, and P. L. Ln, Spatal Inference and Slarty Retreval of an Intellgent Iage atabase Syste Based on Obect's Spannng Representaton, J. Vs. Lang. Coput., accepted 007. [5] T. K. Shn, C. S. Wang, A. Y. Chang and C. H. Kao, Indexng and retreval schee of the age database based on color and spatal relatons, IEEE Int. Conf. ICE,