ARTICULATED MOTION ANALYSIS FROM MOTION CAPTURE DATA

Transcription

1 ARICULAED MOION ANALYSIS FROM MOION CAPURE DAA J. Fayad, A. Del Bue and P. M. Q. Agua 3. ABSRAC We pesent computatonal methods to extact and model dffeent onts of a genec subect, n an automatc way. he nput fo ou methods s smply a set of taectoes of 3D ponts, obtaned fom a moton captue system (MOCAP). Due to the pecewse gdty of the skeleton, these taectoes belong to dffeent subspaces (of the space of all possble taectoes). We use ths knowledge to deve computatonally smple algothms that ae able to nfe ont popetes fom the taectoes of the 3D ponts. hs model-fee appoach enables analyzng dectly specfc subects, athe than equng use-defned a po models of the skeleton. Such data-dven models ae useful n the analyss of human walk and the evaluaton of ont stess fo pathology detecton. Also, the customzed skeleton models, togethe wth physologcal muscula nfomaton, allow to accuately analyze hgh level pefomances n spots.. INRODUCION Computatonal models of human atculatons ae nowadays fundamental to pefom an accuate analyss of the mechancal moton of a human body. Applcatons of these models span vaous felds, angng fom engneeng to lfe scences, whee the analyss of human moton s cucal to accuate clncal analyss and cedble anmatons of skeleton models[]. Exstng appoaches to atculated moton analyss eque a human opeato to explctly constuct the model of the skeleton, ncludng the defnton and chaactezaton of the onts, a costly and tme-consumng task []. hs can be done by measung the dmensons of dffeent body segments and atculaton anges of moton of a human subect, whch can be toublesome. Altenatvely one can use anthopometc tables to extact statstcal measuements of those quanttes and then use scale factos to esze the model to bette ft a specfc subect. Howeve ths last appoach has the dsadvantage of scalng the model n a statstcal way and not modelng a specfc ndvdual, whch can be equed n some applcatons. In opposton, we pesent computatonal methods to extact and model dffeent onts fom a genec subect, n an ndvdualzed and sem-automatc way. he only assumpton made hee s the avalablty of an ntal segmentaton of each nea-gd pat composng the body. Such appoach has elevant elatons wth ecently developed technques n the Compute son feld [3,4,5,6] whee, gven the unpedctablty of the data extacted fom mages, unconstaned analyss s often the only vable soluton. Maste Student, Insttute fo Systems and Robotcs (ISR/IS), Av. Rovsco Pas, Lsbon, Potugal Reseache, Insttute fo Systems and Robotcs (ISR/IS), Av. Rovsco Pas, Lsbon, Potugal 3 Pofesso, Insttute fo Systems and Robotcs (ISR/IS), Av. Rovsco Pas, Lsbon, Potugal

2 Fg. Fou mages and elatve 3D nfomaton extacted fom a MOCAP system each colo coesponds to the set of ponts lyng ove the two bodes used to extact the am ont. 3. A BILINEAR FORMULAION OF SRUCURE AND MOION Ou am s to nfe the musco-skeletal popetes of a human body dectly fom the data acqued fom MOCAP system. he man dea s to fulfll the estmaton of these anatomcal popetes ndependently fom the platfom used to acque the data. Such appoach has the man featue of beng ndependent to a po models of the body. he appoach s based on the key fact that a set of ponts, lyng ove a 3D obect whch s movng n tme, shaes common popetes. Fo nstance, f the body s movng gdly, a smple otaton and tanslaton can descbe the moton of the set of 3D ponts. Smlaly, ponts lyng ove an atculated stuctue can be descbed by the 3D poston assocated to both bodes, the elatve tanslaton and otatons and the common axs of otaton gven the ont. Inteestngly, these popetes become evdent n a famewok whee the 3D obect shape and the espectve moton components ae modelled as a blnea fom such that: w = M S () whee w s a 3-vecto epesentng the 3D shape pont captued at the tme nstant. he 3x matx M epesents the moton components of the 3D obect (.e. otaton and tanslaton fo a gd shape) and the xp matx S collects a paametesaton of the 3D shape. If we collect evey 3D pont n a compact matx fom we obtan that: W M W = M = M [ S L S p ] = MS W F M F whee W s a 3FxP matx, M a 3Fx matx and S a xp matx. he scalas F and P ae, espectvely, the numbe of fames captued and the numbe of ponts belongng to the shape. Each 3 x P matx W wth = F s such that: W = [ w L wp ] he value of,.e. the dmensonalty of the blnea models, depends by the type of shape consdeed. In the followng we show a set of example fo these blnea models fo the human moton modellng scenao. 3. Rgd shapes A body movng gdly bngs the dmensonalty of the blnea models to ethe = 3

3 o = 4, dependng f we consde the otatng body wth o wthout a tanslatonal component. In the case of no tanslaton, the matces M and S take the followng fom: 3 x M = S = y z whee M s a 3x3 otaton matx and x, y and z epesent the thee coodnates of the 3D pont. hus each pont at each fame s gven by the poduct as expessed n eq. (). Gven the goupng n eq., we have that M and S ae a Fx3 and a 3xP full-ank matces espectvely. hs foces a ank constant on the measuements W (.e. ank(w) 3). Gven ths ank constant, we can compute an ntal factozaton of W by pefomng a SD gvng: SD W P = u σ v = = u σ v = U Σ whee U s a F othogonal matx, Σ a dagonal matx and a P othogonal matx. In the gd case, we have that σ 4 = 0 f no nose and measuements eos ae pesent. hus, by enfocng the sngula values afte the thd equal to zeo, we obtan a numecal ft of the measuements n the sense of the Fobenus nom. hs stage s lkely to mpove the measuements qualty snce even MOCAP systems have a cetan uncetanty ove the 3D locaton of ponts (Some systems povde also an ndcaton of ths uncetanty, thus a moe accuate denosng could be pefomed). hs ntal decomposton va SD can povde a fst affne ft of the moton and shape components M and S such that: ~ ~ M = U and S = Σ. ~ ~ Snce ths tansfomaton s vald up to an affne tansfomaton.e. W = MQQ S we seek a specfc tansfomaton Q whch enfoces the metc popetes of M (see Secton 4 fo a detaled descpton). he futhe advantage of ths pocedue s that we obtan a metc descpton of the shape S usng the complete 3D nfomaton comng fom the MOCAP system (.e. all the fames and not only a sngula fame). We avod n such way to choose a 3D shape whch eles only on a sngle nstance of the captued moton. Gven a tanslaton, the models can be smlaly defned as: x 3 t x y M = t y S = t z z whee t x, t y and t z ae the tanslatonal component and S s now expessed n homogeneous coodnates. 3. Atculated Shapes Unvesal Jont In ode to smplfy the fomulaton, we consde atculated shapes composed by pawse gd bodes. In ths case ou measuements ae gven by the 3D ponts lyng ove both pats.e. W = [W () W ]. wo types of onts ae hee consdeed: the unvesal ont and the hnge ont. When two obects ae lnked by a unvesal ont the dstance between the two centes of mass s constant (fo nstance, the head and the toso of a human body) but they have ndependent otaton components. At each fame the shapes connected by a ont satsfy the followng elaton:

4 ( ) ( ) ( ) ( ) ( ) ( ) t + R d = t + R d (3) whee t () and t ae the 3D shape centods of the two obects, R () and R the 3 3 otaton matces and d () and d the 3D dsplacement vectos of each shape fom the cental ont. he constant expessed n eq. (3) educes the dmensonalty of the model. It s then possble to efe the atculated moton to a common efeence fame egsteed on the centod of the fst obect thus smplfyng the shape matx S as: ( ) ( ) S d ( ) ( ) S = 0 S d (4) whee S s a full ank-7 matx. he moton fo a fame has to be aanged accodngly to satsfy equaton (3) gvng: ( ) ( ) M = [ R R t ]. o obtan the block dagonal stuctue as n eq. (4) fom a SD of W, we consde the two shapes egsteed to the measued taectoes centod: ( ) ~ ~ ( ) ~ ( ) ( ) S 0 W = [ W W ] = [ R R ] ( ) 0 S whch s a full-ank 6 matx. Howeve, the SD of W computes the components of = [ () ] that ae dense. he emedy s to sepaate the two obects by multplyng the ow space by a matx N such that: () () null( ) 0 [ ] = ( ) null( ) N = () () null( ) 0 null( ) whee null() etuns the left null-space of a matx. he column space U s then multpled by N n ode to etan consstency. Gven the ecoveed block stuctue, sepaate metc constants can be computed to ecove the coect stuctue and moton. 3.3 Atculated Shapes Hne Jont A hnge ont constans the elatve oentaton of the 3D obects snce both shapes have a common axs that s paallel to the axs of otaton. In ths case, the oveall ank of W dops to 6. o smplfy vsualzaton n a matx fom, we have algned the axs of otaton to the x-axs. If R () = [p p p 3 ] and R = [p p 4 p 5 ] we can wte that: ( ) ( ) ( ) ( ) x L x x L x ~ W = [ p p p p p ] y z ( ) ( ) ( ) ( ) ( ) ( ) y L yp ( ) ( ) z L zp Smlaly to the soluton poposed fo the unvesal ont, we have to compute a fst ft usng SD and then to accodngly enfoce the matx stuctue of the ow space. In ths case, we have to educe some components of the ow space of to zeo. Howeve hee we have a stong dependency on the x-axs whch does not allow to consde the shapes sepaately. hus we use a matx N constucted such that: null( N = null( () L L b ) null( ) null( y z P P P () ) ) P

5 whee b = [ ]. he column space can be then tansfomed accodngly wth N. Now a hnge ont s defned as a lne whch defne the axs of otaton and thus ts cente may be localzed anywhee on the axs. Howeve, the cente les n the null space of [p p p 3 p 4 p 5 (t t )], thus t can be extacted fom the pevous factozaton. 4. SHAPE CALIBRAION In the pevous secton we have found affne fts fo two dffeent types of onts. An upgade to a metc space s necessay n ode to compute a 3D shape that esembles the metc popetes of the bodes. Howeve, ths stage s not dectly affectng the pevous computaton of the ont poston. he upgade to metc s accomplshed by mposng that the matx M s a collecton of otaton matces at each fame. hese constants ae obtaned wth the computaton of a tansfomaton matx Q, whch can coect the matces at each fame to othogonal. he moton matx M can be gven as: ~ M ~ M = M ~ M F whee each 3 3 block M can be wtten as: m ~ M = m. (5) m3 hus, n ode to obtan the soluton fo Q, we explctly enfoce othonomalty constants n (5). hese can be expessed as a set of equatons n the fom of m dq Qm e = c de whee d, e =,, 3. he value of c de depends explctly on the gven ont. A soluton s obtaned by consdeng the poduct H = Q Q, solvng lnealy fo H usng Least-Squaes and then extactng Q wth Cholesk decomposton. he dmensonalty of Q depends by the poblem consdeed: Q 3 3 fo a sngle gd body, Q 6 6 fo a unvesal ont, Q 5 5 fo a hnge ont. 5. EXPERIMENS In ode to show the flexblty of ou appoach, we pesent esults usng two dffeent databases of 3D ponts extacted usng a ICON system. he fst set shows pont lyng ove an am pefomng unknown moton. he task hee s to obtan the locaton of the otaton axs assocated to the elbow. he 3D ponts n Fg. ae elated to mages as shown n Fg.. he only nfomaton we eque n ode to un the appoach s the assocaton of each pont to the elated segment of the 3D body (.e. a segmentaton of the pont taectoes). Fg. hee sample fames showng an am and the computed hnge ont at the elbow he second set of ponts was obtaned fom the feely avalable database of the Gaphc Lab of Canege Mellon Unvesty ( In such expement, an

6 adult s unnng n an unconstaned envonment. We wee able to extact unvesal onts at each elbow and two hnge onts fo each leg, located at the knee and ankle, as t can be seen n Fg. 3 Fg 3. hee sample fames showng an adult human unnng. wo unvesal onts (ed) and fou hnge onts (geen) ae extacted fom the full body taectoy. 6. CONCLUSIONS We have pesented a famewok fo computng the ont postons fom a set of obsevatons obtaned fom MOCAP systems. Ou analyss s not constaned by the specfc setup used fo the acquston but t accounts fo hgh degees of flexblty. As futue wok, we am to extend these methods to deal wth mssng entes n the measuements and to add consstent modellng of the muscula popetes of the body. 7. ACKNOWLEDGMENS hs wok was patally suppoted by Fundação paa a Cênca e a ecnologa (ISR/IS pluanual fundng) though the POS_Conhecmento Pogam that ncludes FEDER funds and gant PDC/EEA-ACR/70/006, MODI - 3D Models fom D Images. 8. REFERENCES [] Mündemann, L. and Coazza, S. and Andacch,.P., he evoluton of methods fo the captue of human movement leadng to makeless moton captue fo bomechancal applcatons. J. of NeuoEngneeng and Rehabltaton. ol. 3() [] Koeme, K. and Snook, S. and Meadows, S. and Seutsh, S., Egonomc models of anthopomety, human bomechancs, and opeato-equpment nteface, 988. Natonal Academy Pess. [3] omas, C. and Kanade,., Shape and moton fom mage steams unde othogaphy: a factozaton method. Intenatonal Jounal of Compute son, 99. [4] Begle, C. and Hetzmann, A. and Bemann, H., Recoveng non-gd 3D shape fom mage steams. IEEE Confeence on Compute son and Patten Recognton, 000. [5] esaden, P. and Red, I., Atculated Stuctue Fom Moton by Factozaton. IEEE Confeence on Compute son and Patten Recognton, 005. [6] Yan, J. and Pollefeys, M., A factozaton-based appoach to atculated moton ecovey. IEEE Confeence on Compute son and Patten Recognton, 005.