MoCap Toolbox - A Matlab toolbox for computational analysis of movement data

This is an elec onic ep in o he o iginal a icle. This ep in may di e om he o iginal in pagina ion and ypog aphic de ail. Au ho (s): Ti le: Yea : Ve sion: Please ci e he o iginal e sion: All ma e ial supplied ia JYX is p o ec ed by copy igh and o he in ellec ual p ope y igh s, and duplica ion o sale o all o pa o any o he eposi o y collec ions is no pe mi ed, excep ha ma e ial may be duplica ed by you o you esea ch use o educa ional pu poses in elec onic o p in o m. You mus ob ain pe mission o any o he use. Elec onic o p in copies may no be o e ed, whe he o sale o o he wise o anyone who is no an au ho ised use . MoCap Toolbox - A Ma lab oolbox o compu a ional analysis o mo emen da a Bu ge , Bi gi a; Toi iainen, Pe i Bu ge , B., & Toi iainen, P. (2013). MoCap Toolbox - A Ma lab oolbox o compu a ional analysis o mo emen da a. In R. B esin (Ed.), P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, Logos Ve lag Be lin, S ockholm, Sweden (pp. 172-178). Logos Ve lag Be lin. P oceedings o he Sound and Music Compu ing Con e ences. h p://smcne wo k.o g/sys em/ iles/MOCAP%20TOOLBOX%20%E2%80%93%20A%2 0MATLAB%20TOOLBOX%20FOR%20COMPUTATIONAL%20ANALYSIS%20OF%20MOV EMENT%20DATA.pd 2013 MOCAP TOOLBOX – A MATLAB TOOLBOX FOR COMPUTATIONAL ANALYSIS OF MOVEMENT DATA Bi gi a Bu ge Pe i Toi iainen Finnish Cen e o Excellence in In e disciplina y Music Resea ch, Depa men o Music, Uni e si y o Jy äskylä, Jy äskylä, Finland [email p o ec ed] [email p o ec ed] ABSTRACT The MoCap Toolbox is a se o unc ions w i en in Ma lab o analyzing and isualizing mo ion cap u e da a. I is aimed a in es iga ing music- ela ed mo emen , bu can be bene icial o o he esea ch a eas as well. Since he oolbox code is a ailable as open sou ce, use s can eely adap he unc ions acco ding o hei needs. Use s can also make use o he addi ional unc ionali y ha Ma lab o e s, such as o he oolboxes, o u he analyze he ea u es ex ac ed wi h he MoCap Toolbox wi hin he same en i onmen . This pape desc ibes he s uc u e o he oolbox and i s da a ep esen a ions, and gi es an in- oduc ion o he use o he oolbox o esea ch and anal- ysis pu poses. The examples co e basic isualiza ion and analysis app oaches, such as gene al da a handling, c ea ing s ick- igu e images and anima ions, kinema ic and kine ic analysis, and pe o ming P incipal Compo- nen Analysis (PCA) on mo emen da a, om which a complexi y- ela ed mo emen ea u e is de i ed. 1. MOTIVATION AND OVERVIEW The MoCap Toolbox is a Ma lab1 oolbox dedica ed o he analysis and isualiza ion o mo ion cap u e (MoCap) da a. I has been de eloped o he analysis o music- ela ed mo emen , bu is po en ially use ul in o he a eas o s udies as well. I is open sou ce, dis ibu ed unde GPL license, and eely a ailable o download a : www.jyu. i/music/coe/ma e ials/mocap oolbox. The MoCap Toolbox is mainly in ended o wo king wi h eco dings made wi h an in a ed ma ke -based op- ical mo ion cap u e sys em. Such mo ion cap u e sys ems a e based on an ac i e sou ce emi ing pulses o in a ed ligh a a e y high equency, which is e lec ed by small, usually sphe ical ma ke s a ached o he acked objec (e.g., a pa icipan dancing o playing an ins u- men ). Wi h each came a cap u ing he posi ion o he e lec i e ma ke s in wo-dimensional, a ne wo k o se - e al came as can be used o ob ain posi ion da a in h ee 1 www.ma hwo ks.com 2 www.c-mo ion.com/p oduc s/ isual3d/ dimensions. Besides op ical mo ion cap u e, he MoCap Toolbox can also be used o analyzing da a cap u ed wi h o he acke echnologies, such as ine ial o mag- ne ic acke s. Howe e , some ea u es o he oolbox will be limi ed, since such acke s do no p oduce posi ion da a, bu de i a i e da a, (e.g., accele a ion). Fu he - mo e, he oolbox is op imized o he use o 3- dimensional posi ion da a, so using da a wi h six deg ees o eedom (posi ion and o a ion) migh equi e cus om- ized adjus men s o unc ions. The e a e p op ie a y (closed sou ce) so wa e solu ions a ailable o mo ion cap u e analysis and isualiza ion, such as Visual3D2 o Mo ionBuilde 3, and applica ions ha a e p ima ily used o eco ding da a (such as Qual- isys T ack Manage 4 o Vicon Nexus5). Howe e , such applica ions a e usually ei he oo limi ed in hei unc- ionali y, oo ocused on isualiza ion and/o oo es ic- i e o adap o he needs o he esea che , such as de el- oping new mo emen ea u es use ul o hei indi idual esea ch ques ions. To o e come hese issues, we imple- men ed his oolbox in Ma lab, a gene ic scien i ic com- pu ing en i onmen , and made i a ailable o o he e- sea che s o be used in a o o hei needs. The Mocap Toolbox is no he only Ma lab oolbox a ailable o mo- ion cap u e analysis; one o he oolbox wo h men ioning is he oolbox c ea ed by Cha les Ve on [1]. This oolbox is mo e limi ed han he MoCap Toolbox, bu o e s a g aphical use in e ace (GUI). Ma lab o e s p e-buil isualiza ion oppo uni ies and gi es access o a la ge ange o o he unc ionali y. Some unc ions included in he MoCap Toolbox use, o exam- ple, he Signal P ocessing Toolbox p o ided by Ma h- Wo ks, o he Fas ICA package6, a eely a ailable hi d- pa y oolbox o Independen Componen Analysis. Fu - he mo e, he use s hemsel es can make immedia e use o he addi ional unc ionali y and oolboxes p o ided by Ma lab, o example he S a is ics Toolbox, o u he analyze ea u es ex ac ed wi h he MoCap Toolbox wi h- ou he need o swi ch be ween di e en applica ions. MoCap Toolbox code is w i en using he gene ic Ma lab syn ax and is openly assessable, so use s can add and adap unc ions o hei own needs. 2 www.c-mo ion.com/p oduc s/ isual3d/ 3 www.au odesk.com/mo ionbuilde 4 www.qualisys.com/p oduc s/so wa e/q m/ 5 www. icon.com/p oduc s/nexus.h ml 6 www.cis.hu . i/p ojec s/ica/ as ica/ Copy igh : © 2013 Bu ge e al. This is an open-access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License 3.0 Unpo - ed, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. 172 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden The MoCap Toolbox suppo s a ious mo ion cap u e da a o ma s, in pa icula he .c3d7 ile o ma (which, e.g., Vicon8 o Op iT ack9 op ical mo ion cap u e sys ems can p oduce), he . s o ma and he .ma o ma , bo h p oduced by he Qualisys mo ion cap u e sys em10, and he .wii da a o ma p oduced by he WiiDa aCap u e so wa e11. The MoCap Toolbox p o ides 64 unc ions o analyz- ing and isualizing mo ion cap u e da a. The main ca e- go ies can be summa ized as da a inpu and edi unc- ions, coo dina e ans o ma ion and coo dina e sys em con e sion unc ions, kinema ic and kine ic analysis unc ions, ime-se ies analysis unc ions, isualiza ion unc ions, and p ojec ion unc ions. Fu he mo e, i uses h ee di e en da a s uc u es, he MoCap da a s uc u e, he no m da a s uc u e, and he segm da a s uc u e. To con e be ween he di e en da a ep esen a ions and enable ce ain isualiza ions, h ee di e en pa ame e s uc u es a e used, he m2jpa , he j2spa , and he anim- pa s uc u es. Bo h he da a and he pa ame e s uc u es will be discussed and explained in he nex sec ion. 2. DATA REPRESENTATIONS The MoCap Toolbox uses h ee di e en da a s uc u es, he MoCap da a s uc u e, he no m da a s uc u e, and he segm da a s uc u e. A MoCap da a s uc u e in- s ance is c ea ed when mocap da a is ead om a ile o he Ma lab wo kspace using he unc ion mc ead. A MoCap da a s uc u e con ains he 3-dimensional loca- ions o he ma ke s (in he .da a ield) as well as basic in o ma ion, including he ype o s uc u e, he ile name, numbe o ames o he eco ding, he numbe o came as used o he eco ding, he numbe o ma ke s in he da a, he ame a e, he names o he ma ke s, and he o de o ime di e en ia ion o he da a. Addi ionally, he MoCap da a s uc u e con ains ields o da a cap u ed wi h analog da a, such as EMG. Finally, he ime s amp o he eco ding and he da a ype (e.g., 3D) can be add- ed. A MoCap da a s uc u e ins ance is also c ea ed when he unc ion mcm2j is used. This unc ion ans o ms a ma ke ep esen a ion o a join ep esen a ion. These wo ep esen a ions use he same da a s uc u e, al hough hey a e concep ually di e en : he ma ke ep esen a ion e- lec s he ac ual ma ke loca ions, whe eas he join ep- esen a ion is ela ed o loca ions de i ed om ma ke loca ions. A join can consis o one ma ke , bu i can also be de i ed om mo e han one ma ke s. I can, o example, be used o calcula ing he loca ion o a body pa whe e i is impossible o a ach a ma ke . The mid- poin o a join , o ins ance, can be hen de i ed as he cen oid o ou ma ke s a ound he join . The no m da a s uc u e, c ea ed by he unc ion mcno m, is simila o he MoCap da a s uc u e, excep ha i s .da a ield has only one column pe ma ke . This column con ains he Euclidean no m o he ec o 7 www.c3d.o g 8 www. icon.com 9 www.na u alpoin .com/op i ack/ 10 www.qualisys.com 11 www.jyu. i/music/coe/ma e ials/mocap oolbox da a om which i was de i ed. I , o ins ance, mcno m is applied o eloci y da a, he esul ing no m da a s uc- u e holds he magni udes o eloci ies, o speeds, o each ma ke . The hi d da a s uc u e, he segm da a s uc u e, is no , like he o he wo, ela ed o poin s in space (ma ke s o join s), bu o segmen s o he body (see, e.g., [2]). The unc ion mcj2s pe o ms a ans o ma ion om a join ep esen a ion o a segmen ep esen a ion and p oduces as ou pu a segm da a s uc u e ins ance. Mos ields o a segm da a s uc u e a e simila o he ones o a MoCap da a s uc u e, howe e , he .da a ield is eplaced by ou o he ields. The .pa en ield con ains in o - ma ion abou he kinema ic chains o he body, i.e., how he join s a e connec ed o o m segmen s, and how seg- men s a e connec ed o each o he . The ields . oo ans and . oo o s o e he loca ion and o ien a ion o he cen e o he body, he oo . The .segm ield consis s o se e al sub ields ha s o e he o ien a ion o he body segmen s in se e al ways. The .eucl sub ield con ains o each segmen he Euclidean ec o poin ing om he p oximal o he dis al join o he segmen . The leng h o each segmen is s o ed in he . sub ield. The .qua sub ield includes he o a ion o each segmen as a qua e nion ep esen a ion (see, e.g., [3] and [4]). Finally, he .angle sub ield con ains he an- gles be ween each segmen and i s p oximal segmen . To con e be ween he di e en ep esen a ions and o enable ce ain isualiza ions, he MoCap Toolbox o e s h ee di e en pa ame e s uc u es: m2jpa , j2spa , and he animpa s uc u es. The m2jpa s uc u e is used by he unc ion mcm2j and con ains he in o ma ion needed o pe o m he ans- o ma ion om ma ke o join ep esen a ion. Besides ields holding he numbe o join s and he names o he join s, i includes a ield wi h he numbe s o he ma ke s de ining he loca ion o each join . The j2spa s uc u e is used by he unc ion mcj2s and con ains he in o ma ion needed o pe o m he ans o - ma ion om join o segmen ep esen a ion. Besides he ields con aining he segmen names and he numbe o he oo (cen e o he body) join , i includes ields wi h he numbe s o he h ee join s ha de ine he on al plane o he body and a ec o indica ing he numbe o he pa en segmen ( he segmen ha is p oximal in he kinema ic chain) o each segmen . The animpa s uc u e is used by he unc ions mcplo ame and mcanima e and con ains he in- o ma ion needed o c ea e ame (s ick igu e) plo s and anima ions. The s uc u e includes ields o he sc een size, limi s o he plo ed a ea, iewing angles, ma ke sizes, plo ing colo s, connec ion line con igu a ions and wid hs, and plo ing o ma ke and ame numbe s. Addi- ionally, he s uc u e con ains ields ela ed o c ea ing anima ions, such as he ames pe second, a subs uc u e o pe spec i e p ojec ion pa ame e s, and se ings o plo ing ma ke aces. 173 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden 3. USING THE TOOLBOX In wha ollows, we will gi e an in oduc ion o he use o he oolbox o esea ch and analysis pu poses. The MoCap Toolbox manual, p o ided wi h he down- load o he oolbox, o e s an example chap e wi h ele - en demos explaining he basic usage o he oolbox. Ad- di ionally, a demo da a se called mcdemoda a, includ- ing mo ion cap u e da a and associa ed pa ame e s uc- u es, is p o ided wi h he download. The MoCap da a s uc u es dance1 and dance2 used below a e a aila- ble in he mcdemoda a da a se . 3.1 Reading Da a and Filling Gaps Reco ded mo ion cap u e iles can be impo ed in o Ma lab using he unc ion mc ead s o ing he con en o he ile as a MoCap da a s uc u e, i.e., d = mc ead(' ile. s '); An essen ially use ul i s s ep is usually o check o missing ames in he eco ding. Taking he mocap da a s uc u e d, we can use mcmissing(d) o de ec missing ames in he eco ding. In case o missing da a, we can ill hem using linea in e pola ion wi h he unc ion mc illgaps: d = mc illgaps(d); F om his poin onwa ds, we will use he wo MoCap da a s uc u es dance1 and dance2 om he mcdemoda a. Since hey a e al eady a ailable as MoCap da a s uc u es and do no con ain missing da a, bo h impo ing and gap illing a e no equi ed anymo e. 3.2 Visualizing and Anima ing Da a A good app oach o ge an o e iew o he da a is o is- ualize and anima e da a. Using he MoCap Toolbox, mocap da a can be plo ed in di e en wo ways: as a ime se ies o as single ames. As a unc ion o ime, ma ke loca ion da a can be plo ed wi h he unc ion mcplo imese ies, e.g., mcplo imese ies(dance1,[1 20 28], 'dim',3) which plo s he hi d/ e ical dimension o ma ke s 1, 20, and 28 (le on head, igh hand, and igh oo ) (see Fig. 1). Ma ke loca ions as single ames can be plo ed using he unc ion mcplo ame (using he (x,y) p ojec ion o he ma ke s): mcplo ame(dance1,450); Figu e 1. Ma ke loca ion da a plo ed as unc ion o ime using mcplo imese ies. This call, plo ing he 450 h ame o he eco ding (see Fig 2a), uses he de aul anima ion pa ame e s uc u e. Howe e , i a cus omized animpa s uc u e is used, we can, o ins ance, se he connec ion lines be ween he ma ke s o ob ain a isualiza ion ha is easie o unde - s and and ha looks mo e human-like (see Fig. 2b): ap = mcini animpa ; ap.conn = [1 2; 2 4; 3 4; 3 1; 5 6; 9 10; 10 12; 11 12; 11 9; 8 9; 8 10; 8 5; 8 6; 5 9; 5 11; 6 10; 6 12; 7 11; 7 12; 7 5; 7 6; 5 13; 13 15; 13 16; 16 19; 15 19; 6 14; 14 17; 14 18; 17 20; 18 20; 9 21; 11 21; 10 22; 12 22; 21 23; 23 25; 23 26; 25 26; 22 24; 24 27; 24 28; 27 28]; mcplo ame(dance1,450,ap); In case use s collec ed he da a wi h a Qualisys mo ion cap u e sys em and c ea ed a bone s uc u e du ing he labeling p ocess in he Qualisys so wa e, hey can expo he so-called label lis (which con ains he ma ke con- nec ions) and use his ile o c ea e he connec ion ma ix by employing he unc ion mcc ea econnma ix. We can change he gene al colo scheme and he colo s o indi idual ma ke s, connec o lines, aces, and num- be s by adjus ing he alues o he espec i e ields o he animpa s uc u e, o example (see Fig. 2c): ap.colo s = 'w bgy'; ap.ma ke colo s = 'bmgy kk'; mcplo ame(dance1,450,ap); Figu e 2. Ma ke loca ion da a plo ed as ame using mcplo ame: a) using he de aul pa- ame e s; b) using a connec ion ma ix; c) chang- ing colo s; d) join ans o ma ion. 174 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden The unc ion mcanima e is used o c ea e anima ions: mcanima e(dance1,an); The MoCap Toolbox p oduces he single anima ion ames as .png iles. They ha e o be compiled in o a mo ie using o he so wa e, such as QuickTime P o on Mac, o Mo ieMake on Windows. Anima ions can be c ea ed as 2D p ojec ions in wo ways, ei he o hog aphic (de aul ) o pe spec i e, he la e one by including he pe spec i e p ojec ion pa ame- e : mcanima e(dance1,an,1); 3.3 Kinema ic Analysis Kinema ic a iables, such as eloci y and accele a ion, a e es ima ed using he ime-de i a i e unc ion mc imede : d1 = mc imede (dance1,1); % el. d2 = mc imede (dance2,1); d1a = mc imede (dance1,2); %acc. d2a = mc imede (dance2,2); To analyze such ime se ies, we can calcula e hei means and s anda d de ia ions using mcmean and mcs d (igno ing e en ual missing ames). Fo his sample analysis, we will ake he no m da a, ha is, he magni udes o he 3-dimensional da a o eloci y and accele a ion. To simpli y he app oach, we i s combine he da a om ma ke 1 (le on head) o he ou MoCap da a s uc u es using mcconca ena e: d a = mcconca ena e(d1 ,1,d1a,1,d2 ,1, d2a,1); d a_mean = mcmean(mcno m(d a)); d a_s d = mcs d(mcno m(d a)); The esul s (see Table 1) show ha bo h mean and s anda d de ia ion o eloci y and accele a ion o he le on head ma ke a e highe o dance2 han o dance1, so he dance in dance2 mo ed as e and a a wide ange o speeds and also used mo e and la ge di- ec ional changes. mean SD eloci y dance1 235.85 110.79 dance2 520.24 192.27 accele a ion dance1 2233.66 1326.55 dance2 3347.21 1423.19 Table 1. Means and s anda d de ia ions o eloci- y and accele a ion (magni udes) o he le on head ma ke da a o dance1 and dance2. The cumula i e dis ance a elled by a ma ke can be calcula ed wi h he unc ion mccumdis ( e u ning a no m da a s uc u e): d1dis = mccumdis (dance1); d2dis = mccumdis (dance2); We use he Ma lab unc ion ba h o plo ing ma ke s 1 (le on head), 20 ( igh inge ), and 28 ( igh oo ) (see Fig. 3): igu e, ba h([d1dis .da a(1500,[1 20 28]); d2dis .da a(1500,[1 20 28])],'b'); Figu e 3. Cumula ed dis ance a elled by ma k- e s 1, 20, and 28 o mocap da a dance1 and dance2 (labels and i le we e added sepa a ely). We can see in Figu e 3 ha he h ee ma ke s, especial- ly he igh hand ma ke , a elled mo e o dance2 han o dance1, so we can assume ha he amoun o mo emen was highe in dance2. A measu e ela ed o he amoun o mo emen is he a - ea co e ed by he mo emen , which can be calcula ed using mcbound ec . I we wan o calcula e he bound- ing ec angle o he ou hip ma ke s, we do: b 1 = mean(mean(mcbound ec (dance1,[9 10 11 12]))); b 2 = mean(mean(mcbound ec (dance2,[9 10 11 12])));12 The bounding ec angle alue o dance1 equals .1806 and o dance2, i equals .9724. Since he alue o dance2 is highe , dance2 no only had a highe amoun o mo emen , bu also used mo e space han dance1. The bounding ec angle measu e was ound o be a ele an mo emen ea u e in [5] and [6]. We can also calcula e dis ances be ween ma ke s using mcma ke dis . The s anda d de ia ion o he dis ance be ween le and igh inge , md1 = s d(mcma ke dis (dance1,19,20)); md2 = s d(mcma ke dis (dance2,19,20)); gi es us in o ma ion abou he a iabili y o he ma ke dis ance. The s anda d de ia ion o he inge ma ke dis ance o dance1 equals 49.0 and o dance2 175.65, so he inge s in dance2 exhibi ed mo e a ia- ble dis ances. Pe iodici y o mo emen can be es ima ed using he unc ion mcpe iod. I is based on au oco ela ion, and 12 mcbound ec uses window decomposi ion. The unc ion ou pu he e is a e aged ac oss he windows and he ou ma ke s. 175 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden ei he he i s o highes peak o he au oco ela ion unc- ion is aken as pe iodici y es ima ion dependen on he pa ame e inpu . Wi h d1m1 = mcge ma ke (d1a,20); d2m1 = mcge ma ke (d2a,20); [pe 1 ac1 eac1] = mcpe iod(d1m1,2, 'highes '); [pe 2 ac2 eac2] = mcpe iod(d2m1,2, 'highes '); we calcula e he pe iodici y o he accele a ion o he igh inge ma ke . mcpe iod esul ed in a pe iodici y es ima e o each dimension being [1.04, 0.53, 0.52] o dance1 and [1.04, 1.01, 1.06] o dance2. While he i s dimension is simila , he second and hi d dimen- sions a e oughly hal o dance1, sugges ing ha in his case he inge mo ed in double empo in y and z di ec- ions. A mo e accu a e pe iodici y analysis can be pe o med using windowed au oco ela ion: [pe 1 ac1 eac1] = mcwindow(@mcpe iod, d1m1,2,0.25); [pe 2 ac2 eac2] = mcwindow(@mcpe iod, d2m1,2,0.25); To allow isual inspec ion o he ime de elopmen o he pe iodici y, he enhanced au oco ela ion (eac) ma ix can be plo ed as an image (see Fig. 4). The colo s indi- ca e he egula i y o pe iodic mo emen , wi h wa m col- o s co esponding o egions o egula pe iodic mo e- men in he pe iod- ime plane: igu e, imagesc(eac1(:,:,3)), axis xy se (gca, 'XTick',0:4:46, 'XTickLabel', 0.5*(0:4:46), 'YTick',[0 30 60 90 120], 'YTickLabel',[0 0.5 1 1.5 2.0]) igu e, imagesc(eac2(:,:,3)), axis xy se (gca, 'XTick',0:4:46, 'XTickLabel', 0.5*(0:4:46), 'YTick',[0 30 60 90 120], 'YTickLabel',[0 0.5 1 1.5 2.0]) Figu e 4. Enhanced au oco ela ion unc ion o he e ical componen s o he igh inge accel- e a ion in dance1 and dance2. We can see in Figu e 4 ha he e ical componen o he igh inge accele a ion o dance1 shows qui e clea pe iodic mo emen wi h a pe iod o abou 500 millisec- onds, whe eas he pe iodici y o dance2 is weake and mo e i egula . 3.4 Kine ic Analysis The MoCap oolbox o e s he possibili y o calcula e kine ic a iables using Demps e ’s body-segmen model [7]. To make ou p esen da a compa ible wi h Demp- s e ’s model, we i s ha e o educe he amoun o ma k- e s om 28 o 20. We will accomplish his wi h a ma ke - o-join ans o ma ion, implemen ed in he unc ion mcm2j. The m2jpa pa ame e s uc u e equi ed o his ans o ma ion is c ea ed like his: m2j = mcini m2jpa ; m2j.nMa ke s = 20; m2j.ma ke Num = {[9 10 11 12],[9 11], 21,23,26,[10 12],22,24,28,[7 8 7 8 9 10 11 12],[5 6],[1 2 3 4],5,13,[15 16],19,6,14,[17 18],20}; m2j.ma ke Name = {' oo ', 'lhip', 'lknee','lankle','l oe',' hip', ' knee',' ankle',' oe','mid o so', 'neck','head','lshoulde ','lelbow', 'lw is ','l inge ',' shoulde ', ' elbow',' w is ',' inge '}; The join ' oo ', o example, is ob ained by calcu- la ing he cen oid o ma ke s 9, 10, 11, and 12. The ma ke - o-join ans o ma ion is ca ied ou as ollows: d1j = mcm2j(dance1,m2j); d2j = mcm2j(dance2,m2j); Figu e 2d isualizes ame 450 o he join ep esen a- ion o dance1. The nex s ep is o do he join - o- segmen ans o ma ion. The j2spa pa ame e s uc u e equi ed o he ans o ma ion is c ea ed like his: j2s = mcini j2spa ; j2s. oo Ma ke = 1; j2s. on alPlane = [6 2 10]; j2s.pa en = [0 1 2 3 4 1 6 7 8 1 10 11 11 13 14 15 11 17 18 19]; j2s.segmen Name = {'lhip','l high', 'lleg','l oo ',' hip',' high', ' leg',' oo ','l o so','u o so', 'neck','lshoulde ','lua m','lla m', 'lhand',' shoulde ',' ua m',' la m', ' hand'}; The join - o-segmen ans o ma ion is accomplished using he unc ion mcj2s: d1s = mcj2s(d1j,j2s); d2s = mcj2s(d2j,j2s); In o de o calcula e kine ic a iables, such as ene gy, each body pa has o be associa ed o i s pa ame e (i.e., masses and leng hs) speci ied by he Demps e model. The e o e, a a iable is c ea ed speci ying he ypes o he segmen s13: 13 Fo a lis o he segmen ypes, see he MoCap Toolbox manual. 176 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden s_ind = [0 0 8 7 6 0 8 7 6 13 12 10 11 3 2 1 11 3 2 1]; This a iable associa es each join wi h a segmen ype. Each componen indica es he ype o body segmen o which he espec i e join is a dis al join . Join s ha a e no dis al o any segmen ha e ze o alues. The pa ame e s o each body segmen can be hen ob- ained using he unc ion mcge segmpa : spa = mcge segmpa ('Demps e ',s_ind); Wi h his body-segmen ep esen a ion we can es ima e kine ic a iables o each segmen indi idually. The ime- a e age o he kine ic ene gy o he whole body, o ex- ample, can be calcula ed like his: [ ans1 o 1] = mckinene gy(d1j,d1s, spa ); [ ans2 o 2] = mckinene gy(d2j,d2s, spa ); kinEn1 = sum(mcmean( ans1)) + sum(mcmean( o 1)); kinEn2 = sum(mcmean( ans2)) + sum(mcmean( o 2)); The alue o he o e all kine ic ene gy o dance1 equals 2.21, and he alue o dance2 is 11.37, hus mo e ene gy was used in dance2, which suppo s ou a gumen a ion d awn ea lie , ha he e is mo e mo e- men in dance2 han in dance1. 3.5 P incipal Componen Analysis (PCA) P incipal componen analysis can be used o decompose mo ion cap u e da a in o componen s ha a e o hogonal o each o he . By using [pc1 p1] = mcpcap oj(d1j,1:5); [pc2 p2] = mcpcap oj(d2j,1:5); we calcula e he i s i e p inciple componen p ojec- ions o he posi ion da a (as join ep esen a ions) o d1j and d2j. p1.l and p2.l con ain he amoun o a i- ance explained by each componen . F om hese a i- ances, we can de i e, o ins ance, a measu e o mo e- men complexi y, de ined as he cumula i e sum o he p opo ion o explained a iance con ained in he i s i e PCs (see, e.g., [5] and [8]): pcap op a 1 = cumsum(p1.l(1:5)); pcap op a 2 = cumsum(p2.l(1:5)); The esul s, p esen ed in Table 2, indica e ha , in case o pcap op a 1, mos mo emen is al eady explained wi h he i s componen , and he i s i e componen s explain almos all mo emen . In case o pcap op a 2, howe e , only abou 50% o he mo emen is explained wi h he i s componen , and he i s i e componen s explain less han he i s i e componen s o pcap op a 1, so mo e componen s a e needed o ully explain he mo emen s o dance2. Such a mo emen would be cha ac e ized as complex, since a high numbe o PCs is needed o explain he mo emen su icien ly, whe eas a low p opo ion o unexplained a iance (dance1 case) implies a simple mo emen . pcap op a 1 pcap op a 2 cumsum(1) 0.79 0.48 cumsum(1:2) 0.90 0.78 cumsum(1:3) 0.95 0.85 cumsum(1:4) 0.97 0.90 cumsum(1:5) 0.98 0.93 Table 2. Cumula i e a iances o he i s i e p inciple componen s o dance1 (pcap op a 1) and dance2 (pcap op a 2). 4. CONCLUSION The MoCap Toolbox is a Ma lab oolbox dedica ed o he analysis and isualiza ion o mo ion cap u e da a. I has been de eloped o he analysis o music- ela ed mo e- men , bu is po en ially use ul in o he a eas o s udies as well. I has a ac ed esea che s’ a en ion wo king in a ious ields and has been downloaded o being used in a wide ange o di e en esea ch pu poses; music- ela ed, bu also, o ins ance, ace ecogni ion, spo s, gai , o biomechanics esea ch. I has also gained a ac- ion in a i icial in elligence esea ch, such as obo ic mo ion, human- obo in e ac ion, and machine lea ning. The MoCap Toolbox has con inuously been de eloped u he since i s i s launch in 2008 by bo h he au ho s and he use s, whose bug epo s and sugges ions o new unc ionali y has g ea ly helped o imp o e and ex end i . In he u u e e o handling will be imp o ed, o in- s ance, when w ong da a s uc u es a e used. Toolbox unc ions usually ecognize he mis ake, bu in he p e- sen e sion, some unc ions do no e u n su icien ly clea e o messages. Fu he mo e, some unc ions will be adap ed o s and- a d Ma lab con en ions, as i is al eady done in, o in- s ance, mcplo imese ies (speci ying he plo ing pa ame e s as a s ings- alue combina ion). Indi idual unc ions will be imp o ed, such as mc illgaps, ha would bene i om he implemen a- ion o mo e ad anced gap- illing me hods han linea illing, o example spline in e pola ion. Addi ionally, mo e body segmen models besides Demps e ’s model will be included, such as models p oposed in [9] o [10]. As comme cial ools (e.g., Visual3D) commonly p o- ide GUIs ins ead o ope a ing on a command-line basis, a g aphical use in e ace could also be implemen ed o he MoCapToolbox. I would make he oolbox mo e us- e - iendly – o example, connec ion ma ices o s ick igu es could be d awn in he GUI, o gap illing could be g aphically suppo ed. Acknowledgmen s This s udy was suppo ed by he Academy o Finland (p ojec 118616). 177 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden 5. REFERENCES [1] C. Ve on, T ai emen e Visualisa ion de Vonnées Ges uelles Cap ées pa Op o ak. IDMIL Repo , 2005. [2] D.G.E. Robe son, G.E. Caldwell, J. Hamill, G. Kamen, and S.N. Whi lesey, Resea ch Me hods in Biomechanics. Human Kine ics, 2004. [3] P. Kelland, In oduc ion o Qua e nions, wi h Nume ous Examples. Ra ebooksclub.com, 2012. [4] A.J. Hanson, Visualizing Qua e nions. Mo gan Kau mann Publishe s, 2005. [5] B. Bu ge , S. Saa ikallio, G. Luck, M.R. Thompson, and P. Toi iainen, “Rela ionships be ween pe cei ed emo ions in music and music-induced mo emen ,” in Music Pe cep ion 30, 2013, pp. 519-535. [6] G. Luck, S. Saa ikallio, B. Bu ge , M.R. Thompson, and P. Toi iainen, “E ec s o he Big Fi e and musical gen e on music-induced mo emen ,” in Resea ch in Pe sonali y 44, 2010, pp. 714-720. [7] W.T. Demps e , Space Requi emen s o he Sea ed Ope a o : Geome ical, Kinema ic, and Mechanical Aspec s o he Body wi h Special Re e ence o he Limbs. WADC Technical Repo 55-159, W igh - Pa e son Ai Fo ce Base, 1955. [8] S. Saa ikallio, G. Luck, B. Bu ge , M.R. Thompson, and P. Toi iainen, “Dance mo es e lec cu en a ec i e s a e illus a i e o app oach-a oidance mo i a ion,” in Psychology o Aes he ics, C ea i i y, and he A s, in p ess. [9] C.E. Clause , J.T. McCon ille, and J.W. Young, Weigh , olume and cen e o mass o segmen s o he human body. AMRL Technical Repo 69-70, W igh -Pa e son Ai Fo ce Base, 1969. [10] C.L. Vaughan, B.L. Da is, and J.C. O’Conno , Dynamics o Human Gai . Human Kine ics, 1992. 178 P oceedings o he Sound and Music Compu ing Con e ence 2013, SMC 2013, S ockholm, Sweden