Biped Cartoon Retrieval Using LBG-Algorithm Based State Vector Quantization

Transcription

1 Bed Cartoon Retreval Usng LBG-Algorthm Based State Vector Quantzaton Srraa Padee Deartment of Comuter Engneerng Facult of Engneerng Chulalongorn Unverst Pzzanu Kanongchaos Deartment of Comuter Engneerng Facult of Engneerng Chulalongorn Unverst ABSTRACT Effcenc of cartoon moton retreval deends on ndexng method. Keword based ndexng methods for restorng cartoon moton s smle, but sometmes the rocess of addressng ndex to the desred moton s not trval. Although the methods based on clusterng cls of motons or eframes can be used for retreval automatcall, the comlext of tme and relablt deend on sze of the database. Ths research rooses a method for bed cartoon moton retreval usng state vectors of eframes as the moton ndexes. The state vectors derved from the nut moton s quantzed b our enhanced LBG Algorthm to comute the roer number of ndexes for the set of nut eframes. The results show that not onl the recson and recall of the cartoon moton retreval s ncreased accuratel but the rocess for restorng and retreval s also erformed automatcall. Kewords Comuter Anmaton, Bed Cartoon, Vector Quantzaton, State Vector, LBG Algorthm. INTRODUCTION Comuter games and anmaton ndustr at resent s growng ncreasngl. Each anmated move or comuter game has a lot of moton nformaton whch s exensve for constructon and mantenance. In addton, creatng a new anmated move or game needs a lot of tme and resources, so the reuse of anmaton comonents s needed for decreasng the cost and tme. Storng cartoon motons n a database s an mortant method for reusng cartoon moton. If the storng method of cartoon moton databases s not effcent enough, t wll affect the retreval of cartoon motons. A method for restorng motons usng moton ndex [Keo04a] have roosed a novel technque to seed u smlart search under unform scalng, based on boundng enveloes for ndexng human motons. Lu et al. [Lu05a] Permsson to mae dgtal or hard coes of all or art of ths wor for ersonal or classroom use s granted wthout fee rovded that coes are not made or dstrbuted for roft or commercal advantage and that coes bear ths notce and the full ctaton on the frst age. To co otherwse, or reublsh, to ost on servers or to redstrbute to lsts, requres ror secfc ermsson and/or a fee. Corght UNION Agenc Scence Press, Plzen, Czech Reublc. demonstrate a data-drven aroach for reresentng, comressng, and ndexng humanmoton based on ecewse-lnear comonents obtaned usng K-means clusterng. Forbes and Fume [For05a] resented a search algorthm to use wth samled moton data. The also develoed a reresentaton for moton data ntroducng a meanngful dstance metrc for nut oses. The methods have been aled to the searchng human moton n human moton database for moton sntheszng. Edmunds et al. [Edu05a] demonstrate a method of generatng long sequences of moton b erformng varous smlart-based ons on a database of catured moton sequences, whle Basu et al. [Bas05a] have roosed how to fnd smlar frames to cluster them. For matchng motons, quer b examle and cluster grah s used to fnd stored comonents havng same sgnfcant DOFs. These methods for storng cartoon motons have some advantage of ablt to store the cartoon moton automatcall and radl, but ther tme comlext are stll not good enough for large database, whle ther relabltes of the retreval motons deend on the sze of the database. Ths research rooses a method for bed cartoon moton retreval usng state vectors of eframes as ndces. The state vectors derved from the nut moton s quantzed b our enhanced LBG

2 Algorthm to comute the roer number of ndexes for the set of nut e frame. Most algorthms for fndng the reresentaton of a vector set roerl s based on Lnde Buzo Gra (LBG Algorthm [Ln80b, Non05a] and the ar-wse nearest neghbor (PNN Algorthm [Ar03a] but ther effcenc s lmted b the user defned number of codewords whch s the ower of two. Imroer sze of the codeboo causes the denst roblem such as the set of vector shown n Fgure, whle the roer number of codewords gves more sutable denst n set of vector as shown n Fgure 2. algorthm was ndeed more comutatonall effcent than the PNN algorthm. The rest of ths aer s organzed as follows. In Secton 2, we descrbe the rncle of Vector Quantzaton and roosed how to enhance the LBG algorthm for fndng number of codewords automatcall n Secton 3. State vectors are used to reresent cartoon motons n Secton 4. Fnall, Secton 5 shows an exerment of the restorng and retreval cartoon moton. 2. VECTOR QUANTIZATION The Vector Quantzaton algorthm s to select reresentatves of vectors from vector sace R nto a set of vectors. Each s a codeword, whle set of codewords s a codeboo. Each codeword belongs to a nearest neghbor area called Vorono regon defned as follow; (a V = { x R : x x, for all } For examle, two dmensonal vectors n Fgure 3 are n ther belongng regons. Each grou of vectors was reresented b ther codeword. A codeword must be a vector n the same regon as ts neghborng vectors. (b Fgure. Problem of codeboo havng mroer number of codewords: (a Code boo of two words and three words reresentng hgh denst vector set (b Code boo sze of two words and three words reresentng vector set havng lower denst Codeword Vector Fgure 3. An examle of vector quantzaton Fgure2. Codeboo has a number of codewords corresondng to denst of vector. Shanbehzadeh and Ogunbona [Sha97a] comared the comutatonal comlext of the ar-wse nearest neghbor (PNN and Lnde Buzo Gra (LBG. The showed that for a ractcal codeboo sze and tranng vector sequence, the LBG The obectve of vector quantzaton s to reresent a grou of vectors X wth a codeboo Y.When a vector x X s aroxmated b a codeword, an error usuall occurs because x. Mean Square Error can be comuted from the sum of dstorton error of ever grou dvded b total number of codeword. Effcenc of vector quantzaton s comared to the dstorton error.

3 Calculaton for dstance of x from starts from defnng a dstance d as: d : D D R Vector quantzaton error can be comuted usng a functon ( x functon ( x q( x d, whch equals to d,. In ths research, the dstance functon for fndng error s the Eucldean dstance; ( x d( x, = ( = Therefore the error functon s Mean Square Error (MSE when MSE = N N = d( x 2, q( x (2 x s the th nut vector and N s the number of d ( x, q s Eucldean dstance. codewords and ( x 2.2 LBG Algorthm LBG algorthm s a oular method among several codeboo desgn methods. The algorthm s descrbed as follows; Algorthm Fndng quantzed reresentaton wth LBG algorthm Pre-condton: N s number of codeword, T s threshold dstance Post-condton: All vectors are quantzed and reresented b randoml choose nut vector For all number of codeword do If d ( x d( x, x s subset of else x s subset of end f end for Calculate dstorton Whle ( D D D T rev curr curr > Fnd centrod for new codeword If d ( x d( x, x s subset of end f end whle Fnal codeboo else x s subset of At the begnnng, a vector n set X wll be selected as an ntal codeboo b randomzaton and ts Vorono regon s defned. B comutng the Eucldean dstance between each vector and the ntal codeboo, each vector neghborng to the codeword wll be quantzed to the same regon. Then, the dfference between MSE n resent and revous teraton s comuted to fnd the stablt of the codeboo. If stable condton s acceted, the algorthm s termnated. If not, the algorthm wll teratvel calculate the cancrods vector of each regon. The centrod s treated as a new codeboo for the ntal of next teraton. 3. ENHANCEMENT OF LBG ALGORITHM We develo an enhanced LBG algorthm and use t to fnd number of reresentatve vectors for each cluster automatcall. In ths research, the accetance threshold and accetance mean square error s user-defned. Whle comarng MSE from each teraton n the algorthm to the re-defned threshold and re-defned MSE that we can nsert a new codeword to the codeboo. If both values are less than the re-defned value, the outut result s the current codeboo. If the MSE s greater than the re-defned value but the MSE rato less than threshold, then another codeword s nserted randoml and the LBG algorthm starts agan. The enhanced algorthm s shown below and dslaed as a dagram n Fgure 6. Algorthm 2 Enhanced LBG algorthm Pre-condton: S s MSE, T s threshold, M = Post-condton: All vectors are quantzed and reresented b randoml choose nut vector For all number of codeword do If d ( x d( x, x s subset of

4 x s subset of end f end for Calculate dstorton Whle ( D D D T rev curr curr > Fnd centrod for new codeword M = M + If d ( x d( x, x s subset of else x s subset of end f Calculate dstorton end whle whle ( D curr S Fnd quantze reresent b randoml choose nut vector M = M + If d ( x d( x, x s subset of else x s subset of end f Calculate dstorton end whle Fnal codeboo 4. MOTION REPRESENTATION In ths Secton, we wll descrbe how to store cartoon moton nto a database. Frst we reresent cartoon motons extracted from eframes as state vectors whch s a set of arameter secfng angular values for each ont of the artculated cartoon character bod at s a gven tme t. The dmenson of the state vector s defned corresondng to the degrees of freedom (DOF of the cartoon bod. For examle n Fgure 5, the movng arm havng three onts have two DOFs, one DOF and one DOF resectvel, so each state vector of the arm eframe n Fgure 5 has fve dmensons or fve elements. In our examle wll show storng the moton of an arm whch has 3 onts. We use state vectors to reresent eframes of cartoon and use vector quantzaton b usng enhance LBG algorthm as n fgure 4. Fnal codeboo End S = m = m+ start MSE = 4 Threshold = 0.2 N= Random ntalzaton New artton calculaton { x X: d( x, d( x,, =,2,3, K N, }, =,2,3, KN D m MSE Dstorton calculaton D D rev < threshold Random curr D curr New codeboo calculaton ( x, = N C =,..., n m = m+ Fgure 4. Procedure of enhanced LBG Movng arm has 0 eframes whch have state vectors as follows: q ((0, 20, 20, 30, q2 ((0, 20, 20, 35 q3 ((0, 20, 25, 35, q4 ((0, 20, 25, 35 q5 ((5, 25, 25, 30, q6 ((5, 25, 30, 30 2 DOF DOF DOF Fgure 5. Arm whch st ont has two DOFs (can move two drectons. 2 nd and 3 rd ont have DOF (can move one drecton.

5 q7 ((5, 25, 30, 25, q8 ((20, 35, 30, 25 q9 ((20, 35, 35, 20, q0 ((20, 35, 35, 5 These state vectors are then reresented as a codeboo usng enhance LBG vector quantzaton algorthm. B reeatng ths algorthm 3 tmes, the result of the codeboo s shown n table. Result s otmal codewords for state vector of our moton as n fgure 8 whch θ show state vector whch s reresent frst ont whch has two DOFs, θ 2 show state vector whch reresent second ont whch has one DOF and θ 3 show state vector whch reresent thrd ont whch has one DOF. 5. EXPERIMENTAL RESULTS In ths research, we set the threshold mentoned n Secton 3 to 0.2 and MSE to 4 accordng to our statstcal exermental results. When we got state vectors, we got one ntal codeword b random. Defne each vector to be same grou wth the nearest codeword: the nearest dstance between codeword and state vector was calculated b Eucldean dstance. Calculate Mean Square Error from dstorton. Frst, we stored seletal cartoon moton data that was fle format MDL whch MDL was Aron Tutorals frst 3D seletal anmaton format modfed b Ronn André Reerstad. The 3D Model format called MDL s actuall a converted Mlshae 3D ASCII format. You are able to load, mort or create our own 3D models and anmatons wth the oular Mlshae 3D edtor and exort as Mlshae 3D ASCII (*.txt fles. Seletal cartoon moton data were stored n seletal cartoon moton database. Those are the bed cartoon motonเ as worng, runnng, umng, and cng and are stored nto database n state vector form and number that s secfed n cartoon through our rogram. Then we classf nformaton nto cluster and fnd reresentaton of each cluster. We exlan and show table that store all cartoon moton n fgure 6. In the rocess, Informaton of bed cartoon n state vector format and also cartoon moton fle and ndex of cartoon (use sequence of number to reresent nut cartoon moton b order s stored nto anmaton table n database b our rogram. Then we brng quer cartoon moton to calculate ts state vector whch s characterstc of cartoon moton n that tme. State vector attrbute defne moton of each cartoon. Number of state vector s not equal n each cartoon deend on number of eframes of cartoon moton. State vector also s stored n anmaton table. So ths table uses the attrbute Fle_anmaton to reresent cartoon moton, Number_anmaton reresent cartoon ndex and State vector reresent state vector. When we get state vector of each cartoon moton, we brng ts to fnd reresentaton of state vectors seres n each moton b usng vector quantzaton whch reresent out state vector b Reresentaton table. Fgure 6. Show E-R model show relaton of database that conssts of entt Anmaton whch has Prmar e s Number_anmaton and entt Reresentaton whch rmar e s Number_anmaton and Reresentaton. Reresentaton of each moton dfferent deends on number of eframes n each cartoon moton. Ths number of eframes s flexble b number of moton.relaton of each table can be exlaned b E-R Model n fgure 7 whch relaton of entt Anmaton and entt Reresentaton s :. In fndng reresentaton of state vector of moton to store nto database and : N n gettng ale quer moton to show and entt Reresentaton entt has relaton : N wth tself n fndng reresentaton that ale as quer moton. The retreval of bed cartoon moton s tested b usng state vector nstead of eframe of cartoon. Then usng vector quantzaton b LBG algorthm. We tested b storng 30 motons nto database.

6 Database had several bed cartoon motons whch were snthetc data. In retreval of cartoon motons, we retreve from moton of cartoon whch s stored 30 examles. We get moton nformaton from desred cartoon. In ths case we use walng to search moton nformaton whch s the same or ale as moton nformaton n database as n fgure 7. B quantzng vector of quer cartoon, the result s a codeboo, and then we brng t to comare wth each codeboo n database. We comare the dfferent dstance of each codeboo n database wth the moton we need, usng Eucldean dstance. We show these values n table and these values must not exceed 5.We show result of desred moton n fgure 8. The moton retrevals The dstance of each codeboo. Moton 2.4 Moton Moton Moton Moton 5.30 Table. Show value of the dfferent dstance of each codeboo n database wth the moton we need. Then we comare outut wth nut. We calculated the recall that was number of tems retreved and relevant and total relevant n moton database rato and calculated the recson that was number of tems retreved and relevant and total retreve rato. We reeated ths 00 tme and consder the entre of the recson and recall whch results are satsfactor. 6. CONCLUSION In ths aer we have roosed a method for bed cartoon moton retreval usng state vectors of eframes as ndexes. Inut moton gve state vector s quantzed b enhanced LBG Algorthm, develoed b our, to calculate ndexes for set of nut e frame. Because of the moton of cartoons whch have dfference the number of eframes, are stored n database. If we defne the number of codewords are constant, the result of codewords are calculated s not flexble to number of frame. The result s the retreval of cartoon moton that s more accuratel and automatcall. In the future wors, we wll tr to seed u the comutaton of the state vector and the codeboos Fgure 7. Show rocedure of the retreval. If we use sortng technques and searchng technques to sort and search the moton of cartoon, the resonse tme to fnd the result of the retrevals would be decrease. We comare the resonse tme of the retreval that use our method, between dfferences searchng techncal as Rtree search algorthm and FastScan algorthm. The accurac of retreval b our method, deend on searchng technques b usng same database. If the szes of database are ncrease, the result could var. Moton Moton 2 Moton 3 Moton 4 Moton 5 Fgure 8. Show examle outut of walng moton. 7. REFERNCES [Ar03a] O. Aran, Davd A., F. James and F. O'Bren. Moton Snthess from Annotatons. ACM Transactons on Grahcs, , [Bas05a] S. Basu, S. Shanbhag and S. chandran. Search and Transtonng for Moton Catured Sequences. Proceedngs of the ACM smosum on Vrtual realt software and technolog VRST '05, , 2005.

7 [Edu05a] T. Edumunds, S. Muthurshnan, S. Sadhuhan and S. Sueda. MoDB: Database Sstem for Sntheszng Human Moton. Proceedngs of the 2st Internatonal Conference on Data Engneerng (ICDE'05,. 3 32, [For05a] K. Forbes and E. Fume. An Effcent Search Algorthm for Moton Data Usng Weghted PCA. Proceedngs of the 2005 ACM SIGGRAPH / Eurograhcs smosum on Comuter anmaton, , [Keo04a] E. J. Keogh, T. Palanas, V. B. Zordan, D. Gunoulos, and M. Cardle. Indexng large human-moton databases. In VLDB, , [Lu05a]G. Lu, J. Zhang, W. Wang, and L. McMllan. A Sstem for Snalzng and Indexng Human-Moton Databases. In SIGMOD 05: Proceedngs of the 2005 ACM SIGMOD nternatonal conference on Management of data, , [Ln80b] Y. Lnde, A. Buzo and R. Gra. An Algorthm for Vecter Quantzer Desgn. IEEE Transactons on [legac, re - 988], Vol. 28, , 980. [Non05a] A. Nongnuch, A. Surarers. An Algorthm for Vector Quantzaton Usng Denst Estmaton. Master s thess, Facult of Engneerng, Chulalongorn Unverst, [Pat0a] G. Patanè. Unsuervsed Learnng on Tradton and Dstrbuted Sstems. Master s thess, Unverst of Palemo, 200. [Sha97a] J. Shanbehzadeh and P. O. Ogunbona. On the Comutatonal Comlext of the LBG and PNN Algorthms. IEEE Transactons on Image rocessng, Vol. 6, No. 4, , 997. [Gra84a] R. Gra. Vector Quantzaton, IEEE ASSP Magazne,. 4-29, 984.