AN EFFICIENT SKELETON-FREE MESH DEFORMATION METHOD WITH MOTION CAPTURE DATA

Transcription

1 AN EFFICIENT SKELETON-FREE ESH DEFORATION ETHOD WITH OTION CAPTURE DATA H.Y. Wu, Qng Yang, Chunhong PAN Naonal Laboaoy of Paen Recognon Insue of Auoaon,Chnese Acadey of Scences Auoaon Buldng,No.95 Zhongguancun Eas Road,Bejng,00080,P.R.Chna Eal: Keywods: huan oon anaon, Laplacan esh edng, skeleon-fee esh defoaon, oon capue daa. Absac We pesen an effcen skeleon-fee esh defoaon ehod wh oon capue daa. Wh hs echnque, he use can decly de 3D ual chaaces whou buldng skeleon sucues fo oon capue daa. Fuheoe, he copuaon coplexy of ou ehod s elae o he nube of eo-eflece akes, as he akes jus see as he consans of ou soluon syse n he unfo leas squaes sense. The fnal esuls ae obaned by opzng a quadac funconal, whch can be effcenly nzed by solng a spase lnea syse. Inoducon oon capue s a popula pocess o geneae d chaace anaon used fo eneanen, fl ndusy, copue gang, and ohe applcaons. oon capue syses ae anly of hee knds, opcal, agnec, and exoskeleon-based ones, whch all now hae he ably o pefo eal-e capue of he ypcal huan oon. The senso nfoaon fo a pefoe s always ansfoed no an aculaed, heachcal gd-body objec. any sknnng echnques ae wdely appled o odel and anae hese aculaed fgues. Aong he, skelealsubspace defoaon (SSD) s he os popula skeleonden defoaon echnque fo s splcy and plausbly. SSD [4] defne he poson of he suface geoey as a funcon of an undelyng skeleal sucue o a oe absac syse of conol paaees. Veex locaons ae weghed aeages of pons n seeal coodnae faes. The an dawbacks of SSD ae ha he defoaon s esced o he ndcaed subspace and does no pe dec anpulaon. Pose space defoaon (PSD) [] genealzes and poes upon he coon skeleon-den defoaon echnques. Ths defoaon appoach unfoly epesens seeal ypes of defoaon as he appngs fo a pose space o dsplaceens n he objec local coodnae faes. Insead of song he dsplaceen felds fo each key pose and hen nepolang beween he a une, as n PSD, EgenSkn [0] uses pncpal coponen analyss (PCA) o consuc an eo-opal egendsplaceen bass fo eoy effcency. Howee, s always cubesoe o consuc he skeleon sucue fo los of ake pons. oeoe, he nube of akes ofen changes n dffeen scenes, so does he skeleon sucue geneaed fo hose akes. Recenly, soe skeleon-fee appoaches ae used fo esh defoaon and oon ackng [6]. Allen e al. [2] deonsaed a odel fng appoach wh spase akes only. Ths ehod s based on a daase conssng of 250 scans of dffeen huans n he sae pose. Cha e al. [5] noduced an appoach o pefoance anaon ha eployed a sall se of eo-eflece akes suppleened by a daabase of pe-ecoded huan oon. SCAPE [3] s also a daa-den ehod fo buldng a huan shape odel ha spans aaon n boh subjec shape and pose. In analogy o adonal skeleon-based nese kneacs fo posng skeleons, Sune e al. [8] pesened esh-based nese kneacs, called ESHIK. ESHIK algoh leans he space of eanngful shapes fo exaple eshes and hen geneaes new shapes ha espec he defoaons exhbed by he exaples, whle sasfyng eex consans posed by he use. Kayeoy [9] noduced a aan of pyad coodnaes fo boneless oon econsucon. Howee, he econsucon of he Caesan coodnaes fo he pyad coodnaes s a non-lnea opzaon and heefoe s e consung. To poe e pefoance, Kayeoy ncopoaed a ulesoluon sucue no he econsucon pocedue. In hs pape, we pesen an effcen skeleon-fee esh defoaon ehod wh ocap daa. In conas o sandad ehods fo oon econsucon, ou echnque does no eque any addonal global knowledge of he odel sucue such as skeleon. oeoe, he akes ae aached on he suface of he pefoes body, no n he body. So he oon capue daa canno acually epesen he deal skeleon posons ha ae locaed n he cenal lne of he body. Ou dea becoes ealzable hough he ecen end o cas esh odellng pobles as dscee Laplace o Posson odels [,2,7,20,2]. Whn hs faewok, he pose of he 3D odel s eded whle peseng he geoec deals of he suface as uch as possble. Hee, we dsceze he

2 Laplace opeao usng coangen weghs nsead of unfo weghs fo fne appoxaon quales. Ou echnque s puely esh-based and need no exa daase. In addon, he ocap akes jus see as he defoaon consans, so he copuaon coplexy of ou ehod s ndependen of he nube of akes. 2 Noaon and Algoh 2. Laplacan Dffeenal Coodnaes wh Coangen Weghs Le = ( GP, ) be a 2-anfold angula esh. G = ( V, E, F) s a gaph whee V denoes he se of eces, E denoes he se of edges and F denoes he se of faces; and P s he geoey assocaed wh each eex n V. The Laplacan dffeenal coodnaes [,2,7] ae epesened by he dffeence beween and he aeage of s neghbos: ( x) ( y) ( z) δ = ( δ, δ, δ ) = j () d j N() whee N() = { j (, j) E} ae he edge neghbos, d = N( ) s he alence of a eex,.e. he nube of edges whch eanae fo hs eex. Hee, we dsceze he Laplace opeao usng coangen weghs [5]. These geoey-dependen weghs lead o δ wh noal coponens only, unlke he unfo Laplace weghs whch also hae angenal coponens. δ = w j j wj (, j) E (, j) E (2) w = coθ + co γ (3) j j j j Ewj=, and θ j, j whee (, ) oppose of edge e. j 2.2 Skeleon-Fee Huan oon Anaon γ denoe he wo angles In he followng paagaphs, we dscuss how o de a 3D esh odel wh ake pon daa n fou seps. ) Gen a esh odel (see Fgue 2a) and ocap daa (see Fgue 2c), n he fs sep, he use fsly bulds a coespondence beween he akes n he ocap daa and he counepa eces on he esh (see Fgue 2b). These feaue akes wee ypcally placed on he subjec a anhopoec landaks, such as he shouldes, elbows and wss. The coespondence podes he posons fo a subse of he odel s eces fo each fae n he oon sequence. Tha s, we use akes posons as he spaal consans of ou soluon syse. 2) Then n he second sep, we need o oban an nal esul wh soe esh edng echnque, such as ulesoluon appoaches [4,8,23], Laplacan edng [,2,7,22], Posson edng [20,2], pyad coodnaes fo ophng and defoaon [6], o lnea oaon-naan coodnaes fo eshes [3]. Hee we adop Laplacan esh edng ehod fo s splcy and effcency. Dffeen o [7], he Laplace opeao s dscezed usng coangen weghs nsead of unfo weghs fo bee quales. Noe ha n he case of he oeall defoaon of huan oon, nehe he use need specfy he desed egon of nees (ROI), no need adjus he ansfoaon of he handle fae o he ansfoaon of he handle poson, such as n [3,2]. In hs sep, we use akes posons as he spaal consans wh elae lage weghs, so he specfed eces of he defoed esh wll ach exacly wh he coesponden ake pons. Ou goal s o fnd he posons fo he eanng eces n a anne ha bes pesees he shape of he ognal odel. We sole fo he econsuced geoey V = {,..., n } by nzng: n 2 2 ( ) = δ ξ( ) + (4) = = EV Q w u whee δ s he coangen Laplacan coodnae of eex ; ξ ( ) s he coangen Laplacan coodnae of eex. U = { u,..., u } s he se of eces whose spaal w 0 locaons ae akes posons, and he wegh > can be used o weak he poance of he posonal consans. Q s he unknown ansfoaon ax ha lnealy depends on he unknown eces V. The fs e of E ndcaes he deals of he shape afe ansfoaon should be peseed. The second e specfes he spaal consans. Each ansfoaon Q should ake he ognal -ng of eex o he newly econsuced one: 2 Q = ag n Q (5) j j Q j {} N() Fuheoe, he Q s consaned o be anslaon, oaon and unfo scale only,.e., Q canno conan shea coponen. Then, a locally lneazed epesenaon of Q s gen below: s h3 h2 x h3 s h y Q = (6) h2 h s z Fo a oe dealed dscusson of he expessons fo Q see he appendx of [7]. Noe ha afacs ay appea n he nal defoed esh (see Fgue 2d) because of he ncoec coespondences of eces/akes, lage defoaons, o exaggeaed oeens. So n he followng

3 seps, we should adjus he nal esul ha aleady has capued he oeall pose nfoaon. 3) In he hd phase, we wll oban a oay esh (see Fgue 2e) pepaed fo he fnal defoed esh fnal (see Fgue 2f). Each angle n he oay esh s conguen o each coesponden angle n he ognal esh. On he ohe hand, each angle n he oay esh s fed no each coesponden angle n he nal defoed esh. Each oay angle {, 2, 3} n s obaned by nzng he followng funconal: 3 2 E{, 2, 3} = (7) = subjec o: = j (, j) {(,2),(2,3),(3,)} whee he angle j 2 3 he angle 2 3 {,, } s sla (unfo scalng) o {,, }(Fgue ): c c = s c =, 2, 3 ( c s he cenod of he angle, s c s unfo scale faco.) 3 3 c Fgue : geneang he oay angle. 3 Noe ha alhough he aboe funcon s a non-lnea opzaon poble, he eae pocess s sll ey fas because only ncludes en fee aables (he x/y/z coponens of hee eces {, 2, 3} and he scale faco s c ) fo each angle. We use a sequenal quadac pogang (SQP) ehod o sole hs non-lnea consaned opzaon. In hs ehod, he funcon soles a quadac pogang (QP) subpoble a each eaon. Fo a oe dealed dscusson of soluon ehods, we sugges a ex on he subjec such as Fleche [7] ) Hang obaned he needae esh, we now eaange he angles n o geneae he fnal esul fnal. In he fnal sep we anslae he needae angles whle sasfyng he Laplacan dffeenal consans as n Equaon 4. Thus he fnal esh fnal s obaned by nzng he followng funconal: n 2 2 f = = E ( V ) = Qδ ξ( ) + w u T 2 + w ( ) (8) k kj k kj k= (, j) {(,2),(2,3),(3,)} In ode o ensue anslaon opeaon, he hd e of nzes he dsplaceen dffeence beween he hee E f eces of each angle n fnal and he hee eces of each coesponden angle n. In hs sep, we specfy he w wh elaely sall wegh fo bee effec. The quadac opzaon foulaon (8) can be nzed by solng a spase lnea syse. Seng he gaden of he objece funcon o zeo ges he noal equaons: T T AAx= Ab (9) The copuaon s nuecally effcen wh a spase LU sole [9]. We fsly copue he facozaon of he noal equaons and hen fnd he soluon by backsubsuon. 3 Resuls The oon daa ae obaned wh ou oon capue syse, and foaed no TRC pon foa fle. The saple ae of ou ocap syse s up o 00Hz. Ths hgh saplng ae s adsable when fas oons, such as spos oons, ae capued. Then he oon capue daa ae npu no 3D skeleon-fee defoaon anaon poga. Soe esuls ae shown n Fgue 2. In hs case, a walk ans oon capue daa wh 2 ake pons ae used o de a woens 3D odel. We do no consuc he skeleon fo he oon capue daa. If he use esablshes he ncoec coespondences beween he ake pons and he eshs eces, o he segen lengh popoons ae ey dffeen, unnaual esul wll appea (see Fgue 2d). Howee, snce hs nal esul has conaned enough pose nfoaon, we can sll ge he sasfacoy fnal esul (Fgue 2f) usng ou ehod. Fgue 2g shows a oon sequence. We only need adjus he paaees fo he fs fae. Then hese paaees can be successfully appled o he ohe faes whou he uses any exa labou.

4 4 Conclusons In hs pape, we pesen an effcen skeleon-fee esh defoaon ehod wh oon capue daa. Ou appoach s nuecally effcen, as he soluon o he opzaon poble can be obaned by fas solng a spase lnea syse. Fo exaple, 5.5K eces eque 0.6 seconds fo facozaon and 0.03 seconds fo back-subsuon on an Inel P4/3.0 GHz. Expeenal esuls show ha ou ehod s effece enough fo coon applcaons. Acknowledgeens We would lke o hank Kun Zeng and Ja Pan fo he aluable adce and asssance. The wok descbed n hs pape was suppoed n pa by gans fo 863 Naonal Hgh Technology Plan of Chna (Pojec No. 2005AA430). Refeences []. Alexa. Dffeenal coodnaes fo local esh ophng and defoaon, The Vsual Copue, 9, 2, pp. 05-4, (2003). [2] B. Allen, B. Culess, Z. Popoć. The space of huan body shapes: econsucon and paaeezaon fo ange scans, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs, 22, 3, pp , (2003). [3] D. Anguelo, P. Snasan, D. Kolle, S. Thun, J. Rodges, J. Das. SCAPE: shape copleon and anaon of people, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs, 24, 3, pp , (2005). [4]. Bosch, L. Kobbel. An nue faewok fo eal-e fee fo odelng, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs 23, 3, pp , (2004). [5] J. Cha, J. K. Hodgns. Pefoance anaon fo low-densonal conol sgnals, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs, 24, 3, pp , (2005). [6] J. Deusche, A. Blake, I. Red. Aculaed Body oon Capue by Annealed Pacle Fleng, CVPR, pp , (2000). [7] R. Fleche. Paccal ehods of Opzaon, John Wley and Sons, (987). [8] L. Kobbel, S. Capagna, J. Vosaz, H.-P. Sedel. Ineace ul-resoluon odelng on Abay eshes, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs, pp. 05-4, (998). [9] V. Kaeoy, A. Sheffe. Boneless oon econsucon, Techncal skech a SIGGRAPH, (2005). [0] P.G. Ky, D.L. Jaes, D.K. Pa. Egen-Skn: Real e lage defoaon chaace sknnng n hadwae, Poceedngs of AC SIGGRAPH/ Euogaphcs Syposu on Copue Anaon, pp , (2002). [] J.P. Lews,. Codne, N. Fong. Pose space defoaons: A unfed appoach o shape nepolaon and skeleon-den defoaon, Poceedngs of SIGGRAPH, pp , (2000). [2] Y. Lpan, O. Sokne, D. Cohen-O, D. Len, C. Rössl, H.-P. Sedel. Dffeenal coodnaes fo neace esh edng, Shape odelng Inenaonal (SI), pp. 8-90, (2004). [3] Y. Lpan, O. Sokne, D. Len, D. Cohen-O. Lnea oaon-naan coodnaes fo eshes, Poceedngs of SIGGRAPH, pp , (2005). [4] N. agnena-thalann, R. Lapeèe, D. Thalann. Jon dependen local defoaons fo hand anaon and objec gaspng, Gaphcs Ineface, pp , (988). [5]. eye,. Desbun, P. Schöde, A.H. Ba. Dscee dffeenal-geoey opeaos fo angulaed 2-anfolds, Vsualzaon and aheacs, III, pp , (2003). [6] A. Sheffe, V. Kaeoy. Pyad coodnaes fo ophng and defoaon, 3DPVT, pp , (2004). [7] O. Sokne, Y. Lpan, D. Cohen-O,. Alexa, C. Rössl, H.-P. Sedel. Laplacan suface edng, Poceedngs of he Euogaphcs/AC SIGGRAPH syposu on Geoey pocessng, pp , (2004). [8] R. W. Sune,. Zwcke, C. Gosan, J. Popoć. esh-based nese kneacs, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs, 24, 3, pp , (2005). [9] S. Toledo. Taucs: A lbay of spase lnea soles, eson 2.2, Tel A Unesy, Aalable onlne a hp:// (2003). [20] D. Xu, H. Zhang, Q. Wang, H. Bao. Posson shape nepolaon, Ac Syposu on Sold and Physcal odelng, pp , (2005). [2] Y. Yu, K. Zhou, D. Xu, X. Sh, H. Bao, B. Guo, H.-Y. Shu. esh edng wh posson-based gaden feld anpulaon, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs 23, 3, , (2004). [22] K. Zhou, J. Huang, J. Snyde, X. Lu, H. Bao, B. Guo, H.-Y. Shu. Lage esh defoaon usng he oluec gaph laplacan, Poceedngs of AC SIGGRAPH / AC Tansacons on Gaphcs 24, 3, , (2005). [23] D. Zon, P. Schöde, W. Sweldens. Ineace ulesoluon esh edng, SIGGRAPH, pp , (997).

5 (a) (b) (c) (d) (e) (f) (g) Fgue 2: Skeleon-fee esh defoaon syse. (a) Ognal odel. (b) Tweny-one ake pons ae aached on he esh. (c) oon capue daa. (d) Unnaual esul nduced by ncoec coespondences. (e) The needae esh s obaned by exacng he gd coponens fo (a) o (d). (f) Fnal esul. (g) oon sequence.