Animated Deformations with Radial Basis Functions

Transcription

1 Anmated Defomatons wth Radal Bass Functons Jun-yong Noh Compute Scence Depatment IMSC Unesty of Southen Calfona Douglas Fdaleo Compute Scence Depatment IMSC Unesty of Southen Calfona Ulch Neumann Compute Scence Depatment IMSC Unesty of Southen Calfona ABSTRACT We pesent a noel appoach to ceatng defomatons of polygonal models usng Radal Bass Functons (RBFs) to poduce localzed eal-tme defomatons. Radal Bass Functons assume suface smoothness as a mnmal constant and anmatons poduce smooth dsplacements of affected etces n a model. Anmatons ae poduced by contollng an abtay spase set of contol ponts defned on o nea the suface of the model. The ablty to dectly manpulate a facal suface wth a small numbe of pont motons facltates an ntute method fo ceatng facal expessons fo tual enonment applcatons such as an mmese teleconfeencng system o entetanment. Smooth defomatons of the human face o othe models ae possble and llustated wth examples of a aety of expessons and mouth shapes. Categoes and Subject Descptos I.3.5 [Compute Gaphcs]: Geometc algothms, languages, and systems; I.3.7 [Compute Gaphcs]: Anmaton; Geneal Tems Algothms, Pefomance, Desgn Keywods Geomety Defomaton, Radal Bass Functons, Facal Anmaton, MPEG-4 1. INTRODUCTION Tele-mmeson s a metapho that podes dstant people wth ealstc expeences of face-to-face meetng. In a shaed tual space, eye contact and gaze gestues between confeence patcpants ae possble. Vtual objects can be manpulated and nspected wth a haptc feedback dece. 3D epesentatons of people o objects ae sensed, tansmtted, and econstucted to pode the ewng feedom necessay to ge patcpants the sense that they occupy a shaed space. Model-based epesentatons of eal and tual scenes often contan defomable sufaces such as faces, bodes, cloth, pape, etc. The tansmsson, stoage, and dynamc defomaton of these sufaces ae effcently pefomed by sensng (encodng) and syntheszng (decodng) the defomed sufaces. Fo example, a 3D model of a peson can be tansfomed and defomed to match the behao of the confeence patcpant. In addton, the ewpont at the decodng sde can be changed to an abtay poston allowng the nspecton of the peson fom dffeent angles. Hgh-leel behao encodng of the scene also leads to hgh compesson atos. Fo human faces, typcally, the 3D model s tansmtted once ntally and anmaton paametes ae sent at subsequent tme fames. In an MPEG-4 mplementaton, when a model s not poded by the encode, the decode uses the model that aleady esdes n the decode sde. Pepang peson specfc models and anmatng them eque two sets of paametes. The fst s the defnton paamete set, pmaly esponsble fo ceatng a peson specfc model, whch ncludes the specfcaton of shape, sze and textue nfomaton. The second set contans the anmaton paametes that allow a aety of facal expessons and body postues. Due to the complexty of the stuctue and behao of human faces, modelng and anmaton of the face s often consdeed sepaately fom whole body modelng and anmaton. Indeed, defomaton mechansms fo facal anmaton ae dffeent fom body anmaton contolles that manpulate jont angles of a human fgue. In ths pape, we wll concentate on defomatons equed fo facal anmaton. We deelop methods fo defomng a gen 3D model to ceate facal expessons and mouth shapes. The ceaton of peson specfc models s a sepaate sub-poblem and example appoaches can be found n [5, 6, 15, 20, 26]. We befly suey common facal anmaton technques n the followng subsecton. 1.1 Backgound Pghn et al. [20] combne 2D mophng wth 3D tansfomatons of a geometc model to poduce facal anmaton. The success of the anmaton depends on how ealstcally a collecton of facal models can be ceated wth aous expessons. It eques the selecton of a numbe of featue ponts and caeful pepaaton of

2 textue maps. Ths appoach s a good modelng technque but anmatons ae lmted to ntepolatons between pe-made models. Facal anmaton usng Fnte Element Methods (FEM) [2, 7, 8, 11, 19] fathfully econstucts facal geomety. FEM mplctly defnes ntepolaton functons between nodes based on a descpton of the physcal popetes of the mateal, typcally a stess-stan elatonshp. When extenal foces ae appled, the dsplacements of the nodes ae computed to mnmze local stesses and stans mposed onto the nodes. Layeed skn models based on mass-spng systems mmc the anatomcal stuctue and dynamcs of the human face [15]. The mesh conssts of thee-layes coespondng to skn, fatty tssue, and muscles ted to bones. Elastc spng elements connect each mesh node and each laye. Muscle foces popagate though the mesh to ceate defomatons. The computatonal cost fo such spng systems can be ey hgh. Kala et al. [13] pefom facal anmatons usng fee-fom defomaton (FFD). FFD defoms olumetc objects by manpulatng contol ponts aanged n thee-dmensonal cubc lattces. Conceptually, the face mesh s embedded n an magnay, clea, and flexble contol box contanng a 3D gd of contol ponts. As the contol box s squashed, bent, o twsted nto abtay shapes, the embedded mesh defoms accodngly. The bass fo the contol ponts s a t-aate tenso poduct Bensten polynomal. Vecto-based muscle models [27, 28] ae adapted wdely fo the compact epesentaton. A delneated defomaton feld models the acton of muscles upon skn. The muscle defnton ncludes the ecto feld decton, an ogn, and an nseton pont. The cone shaped feld extent s defned by cosne functons and fall off factos. Facal anmaton s acheed by changng the contacton paametes of the embedded muscles unde the face mesh. Ths appoach assumes that muscles ae placed unde the face mesh n coect locatons. Placng muscles n 3D space, howee, s not ntute o consstent fom model to model. Defomaton methods also nclude spng muscles [21], splne models [4], and paametc models [18]. Pefomance den facal anmaton (PDFA) [9, 10, 14] has used deo steams as an nput, geneatng anmatons that mmc the tacked subject usng the methods descbed aboe. We use Radal Bass Functons (RBF) to ceate aous expessons and the anmatons. In ou peous wok [9], we showed defomatons usng RBF n pefomance den facal anmaton (PDFA). Befly, a small numbe of tacked featue ponts detemne new postons of etces on the mesh fo eey fame. The use of RBF s guaantees smooth geometc defomaton. Ou method s smla to Guente et al. s [10] system n that 3D featue ponts ae used as a dng foce, howee RBF s allow a moe dect and compact epesentaton of anmaton paametes than an ad hoc smoothng method. Ou fome wok shaes smla lmtaton wth othes, howee, n that the mesh needs to be equpped wth pedefned featue ponts to ensue coect defomatons. We elmnate the necessty fo pe-defned featue ponts n ou cuent appoach. In addton, nstead of hang a sngle global RBF defomaton engne, we explot a numbe of small RBF defomaton elements to localze the defomatons. Ou appoach podes unque adantages oe exstng methods fo ceatng facal anmaton. Fst, most exstng appoaches eque anmaton mechansms (e.g., muscles, o FFD) explctly embedded n the facal mesh. Fo example, muscles must be placed unde the mesh [27, 28], o spng and stffness constants must be detemned n adance [2] and tuned each tme a new face mesh s ceated. In contast, ou RBF method woks on any mesh wthout modfcaton. Second, the ceaton of facal anmatons can be easly automated wth ou method. When deo data of an acto ae aalable, featue ponts tacked on the subject ae dectly appled to defom the face model to mmc hs/he expessons. The numbe and locatons of tacked featue ponts does not need to be fxed. As moe ponts ae tacked, defomaton contol and fdelty ae nceased. Ths flexblty s due to the dect defomaton capablty of the RBF system. Thd, the behao of ou defomaton method s ey pedctable. Extenal foces ae appled dectly to the facal suface by each tacked pont, and neaby nodes ae dsplaced smoothly. Snce the suface s dectly manpulated, the pocess s moe ntute than methods that ndectly affect the facal suface [13]. The geomety defomaton mechansm usng RBF s dscussed n secton 2. Automated anmaton geneaton s descbed n secton 3. Results ae shown n secton 4 followed by dscussons n secton 5 and conclusons n secton 6. A ed pont epesents ntal contol pont poston whle a blue pont epesents new poston. Geen ponts ae ancho ponts and the aea nsde the geen ponts s the egon of nfluence. The shape of the egon of nfluence s affected by the mesh egulaty. Fgue 1 Geomety Defomaton Element defned on the facal suface 2. GEOMETRY DEFORMATION Face mesh geomety s locally defomed by a geomety defomaton element (GDE). A GDE s the smallest defomaton unt defned on the suface of the face. A GDE conssts of a contol pont, the egon of nfluence aound the contol pont, ancho ponts that le n the bounday of the nfluence egon, and an undelyng RBF system (fgue 1, 4). The moable contol pont and the statonay ancho ponts detemne the dsplacement of the etces n the nfluence egon. Specfyng

3 any pont on the face ceates a GDE. A contol pont may be deed fom a 2D mage by pojectng t to the 3D mesh suface. The egon of nfluence s bound by a dstance metc that detemnes the statonay ancho ponts. The numbe of mesh etces n the nfluence egon can be lage o small. An nfluence egon of one etex educes defomaton to etex manpulaton. 2.1 Algothm Summay Ceatng a defomaton element: 1. Specfy a contol pont on the mesh and an nfluence extent to contol the defomaton aound the pont. The selected pont does not hae to concde wth any of the etces n the mesh. 2. Fo ponts selected n 2D mages, conet them to 3D ponts on the model suface by ay castng. 3. Fnd the neaest etex on the mesh to the selected 3D pont. Ths etex becomes the oot fo the seach tee of mesh edges. 4. Seach down the tee of mesh edges wth a Beadth Fst Seach, detemnng all etces wthn a specfed dstance metc. 5. Leaf nodes of the seach tee become the ancho ponts and, togethe wth the specfed contol pont, ntalze the RBF system assocated wth the GDE (fgue 4). Actuatng a defomaton element: 1. Specfy a new poston of the contol pont ethe by mouse daggng o tackng a facal featue n a deo sequence. 2. Conet the new 2D contol pont to 3D by ay castng. 3. The RBF system computes the new locatons of all etces n the nfluence egon based on the new contol pont poston and the statonay ancho ponts. Recoeed 3D pont at the ntesecton The ntesected polygon n the face mesh Sceen wth a specfed 2D contol pont Fgue 2 Computng 3D coodnates Camea cente o eye 2.2 Ray Castng Note that the fst step n ceatng and actuatng defomaton elements can be accomplshed by manual nput o automaton. In ethe case a 2D pont s dentfed (by mouse clck o featue detecton and tackng). Unless the selected pont concdes exactly wth a mesh etex, ts 3D locaton s unknown. Howee, we hae a 3D face model so we can appoxmate the 3D pont poston by ay castng. The ntesecton pont of the model wth the ay emtted fom the camea cente though the specfed 2D mage pont ges the 3D locaton on the face mesh (fgue 2). Dect specfcaton of 3D contol pont postons ae also possble to handle cases whee the contol ponts moe out of the mesh o along slhouettes. Edge based method selects lowe mouth egon whle dstance based method selects whole mouth egon statng fom the same locaton. Fgue 3 Compason between edge based seach method and dstance based seach method 2.3 Seach Methods and Dstance Metcs Once a 3D contol pont s specfed, the egon of nfluence and ancho ponts can be detemned. We consde the edges of the face mesh to be an abtay tee wth a oot located at the neaest etex to the specfed contol pont. The GDE nfluence egon and ancho ponts ae detemned by seachng down the tee usng a Beadth Fst Seach [16]. Dung taesal, etces ae tested aganst a dstance metc to see f they fall n o out of the nfluence egon. We expemented wth two dstance metcs. One s based on edge depths and the othe s based on Eucldean dstance. The edge depth metc maks all etces wthn some ntege numbe N of mesh edges as n the nfluence egon. The dstance metc computes the Eucldan dstance between taesed etces and the contol pont, and when that dstance s below theshold, the etex s maked as wthn the nfluence egon. The theshold s a eal numbe scaled to the mesh coodnate unts. The two metcs see dffeent puposes. Fo example, when openng the mouth, the nfluence egons should be sepaate n the uppe lp aea and the lowe lp aea. In ths case, an edge based metc fnds the lowe pat of the mouth mesh fo any contol pont on the lowe lp wthout affectng the uppe mouth egon (Fgue 3). In cases whee mesh densty s ey egula, fo example n the eye egons, an edge metc poduces ey egula shaped nfluence egons. The dstance metc poduces egula shaped nfluence egons egadless of mesh densty aatons. In many cases, we fnd that both metcs poduce

4 smla defomatons. Fo lage nfluence egons o ey dense meshes, the numbe of bounday ponts can become lage. In these cases we lmt the numbe of pemete ponts to 20 sampled eenly along the bounday etex set. Input output 2.4 Radal Bass Functons Insped by the ecent success of RBF appoaches n 3D model geneaton [5, 19, 26] and ts demonstated capablty n mage wapng [24] we explot RBF olume mophng to dectly de 3D geomety defomaton of face models Intepolaton/Appoxmaton wth RBF Classcal appoxmaton theoy soles the poblem of appoxmatng o ntepolatng a contnuous multaate functon f (x) by an appoxmaton functon F( x, c) wth an appopate choce of paamete set c whee x and c ae eal ectos ( x = x 1, x 2,.., x n and c = c 1, c 2,,c n). Fndng a paamete set c s often efeed to as leanng o tanng n the neual netwok sense. In the tanng stage, a goal s to fgue out c gen an appoxmaton functon F and a set of tanng examples, whch wll pode the best appoxmaton of f. Radal Bass functons ae often chosen as an appoxmaton functon F fo ts powe to deal wth egula sets of data n mult-dmensonal space n appoxmatng hgh dmensonal smooth sufaces [22]. Examples of the RBFs ae Gaussan functons h ( ) c ( ) e Contol pont Ancho Ponts Moable Ponts 2 =, mult-quadcs Featue Ponts Mappng Coeffcents Use GDE RBF Fgue 4 Relatonshps between GDE and RBF h ( ) + c 2 2 =, 2 2 and thn plate splnes h( ) = log wth a lnea tem added. Radal bass functons ae named because of the adally symmetc dstances paametes. They can be mplemented usng smple neual netwok wth one hdden laye Face Defomatons wth RBF In ths secton, we efe to a specfed GDE contol pont and ts ancho ponts as featue ponts snce the dstnctons ae meanngless to the RBF system. As depcted n fgue 4, each GDE has one RBF system fo dsplacements computatons. A RBF system defoms the facal mesh based upon the motons of all featue ponts. The mappngs between ntal postons and new postons of the featue ponts ae descbed n tems of the ecto coeffcents. We compute ths mappng at each fame. (Ths s known as tanng n the neual netwok temnology but ths s mplct and no explct tanng pocess s equed). The est of the nodes n the nfluence egon ae tansfomed based upon the coeffcents computed. The adal bass functon appoxmaton equaton s whee F( x) N h ( ) + s = 1 c h( x x ) = (1) 2 2 = fo Hady mult-quadcs. s s called a stffness constant that egulates the local o global effects of the featue ponts and s the Eucldan dstance between the featue pont and the nput pont. When computng mappng coeffcents, nput ponts ae the featue ponts themseles and when ealuatng the new postons, nput ponts ae the ponts n the nfluence egon. Pluggng the Hady bass functon nto equaton (1) esults n x taget j = F( x souce j ) = N c = 1 x souce j x s whee 1 j Numbe of featue ponts, n ou case, N. The dmenson of x s thee (.e. x, y, z coodnates of each featue pont). x souce t et x ag (2) denotes the ntal postons of the featue ponts and denotes new postons of the featue ponts. Stffness coeffcent s s detemned as suggested by Eck [3] fo softe defomaton whee featue ponts ae wdely scatteed and stonge whee closely located. souce s = x j x (3) mn j Substtuton of N featue ponts nto the equaton (2) esults n a lnea system of N equaton whose soluton s of the fom c 1 t ag et = H x (4) The soluton gen by equaton (4) assumes that thee s no spuous data. In geneal, howee, data s not nose-fee. In the pesence of nose, usng the matx H constucted wth the assumpton of pefect data may not poduce a useful esult. In ths case, Thkhono and Asenn [25] pode a ey smple soluton. We smply eplace the matx H by ( H + λi) fo equaton (4). Then equaton (4) becomes c= ( H+ λi ) whee λ s a small paamete. The magntude of λ s popotonal to the nose magntude. Notce that equaton (5) becomes dentcal to (4) by settng λ to 0 whee nose fee pefect data ae assumed. We smply set λ to be 0.01, detemned expementally. 1 y (5)

5 The lnea system of equaton (5) s easly soled by LU decomposton [23] to obtan the coeffcent set c. The LU decomposton of the matx H happens only once at the ntalzaton of the RBF system fo each GDE. Only a backsubsttuton s computed fo defomaton fames wth new t et postons of the featue ponts x ag. Thus the defomaton computaton s fast. Once the system s soled, the defomed postons fo etces n the mesh nfluence egon ae obtaned fom the computed coeffcents. We take the appoach of pefomance den facal anmaton (PDFA) to constuct expessons. In PDFA, a human acto s tacked wth a camea whle geneatng facal expessons and mouth shapes. Ths ecoded o on-lne deo steam s analyzed to extact the moton of salent facal featues. These motons then de the defomaton of the face model to poduce smla expesson anmatons. PDFA was fst ntoduced n 1990 [29] and used n aous contexts. PDFA has been used to de 2D anmaton [1, 7, 14] and 3D anmaton [9, 10]. A majo dffculty of usng PDFA to automatcally geneate 3D facal anmatons les n the ambguous elatonshp between the tacked featues and the anmaton mechansm. Gen a spase set of tacked dsplaced ponts on the face, estmatng the anmaton paametes that noke the dsplacements s an nese poblem not easly soled wth many exstng appoaches [13, 28]. Smle conssts of two GDEs Eye up conssts of two GDEs Sadness conssts of fou GDEs Fgue 5 Expessons as a collecton of Geomety Defomaton Elements (GDEs) (a) (c) a. Input deo steam (b) b. 3D model wth eyebows up c. The defomed 3D model oelad on the deo steam tanspaently to show coect algnment of eyebows. 2.5 Geneatng Expessons A geomety defomaton element s the smallest unt fo suface defomaton. One o moe defomaton elements consttute an expesson. Fo example, two defomaton elements make one smle expesson (fgue 5). In ths way, a aety of expessons ae possble by usng aous combnatons of defomaton elements. We can contol a set of defomaton elements wth a sngle paamete d whee d=0 coesponds to a neutal expesson, and d=1 coesponds to the maxmum dsplacements of all the contol ponts of the membe defomaton elements. The expesson can then be anmated smply by changng the contol paamete oe the ange of [0, 1]. Mouth shapes used fo speech synthess ae ceated and contolled smlaly. Mxtues of multple contol paametes ae also possble. 3. AUTOMATION In the peous secton, we descbed how to defne defomaton elements on the suface of the face and manually ceate and contol aous expessons. Once a galley of expessons s constucted, anmaton acoss exstng expessons can be acheed by key fame ntepolatons of expesson paamete alues. It s desable to automate o at least sem-automate the constucton of the ntal expesson database (fgue6). Fgue 6 Defomatons den by featue ponts n the deo steam In contast, ou GDEs can be contolled dectly by the featue moton ectos measued n the mages. Ths dect elatonshp between the tacked featue ponts and the GDE contol ponts s a majo adantage n smplfyng a PDFA system. The steps to automate the geneaton of facal expessons can be summazed as follows: 1. Vdeo steams ae captued contanng the subject makng aous expessons and mouth shapes. 2. Salent contol ponts ae dentfed (manually o automatcally) on the subject face(s) and tacked oe the expesse sequences. 3. The 2D tacked ponts fom the deo steams ae teated as GDE contol ponts and coneted nto 3D ponts usng ay castng. 4. The 3D contol pont motons ae nput to the GDEs whee defomatons ae poduced as depcted n secton 2.1. Fo the tackng of the featue ponts and pose estmaton of the head n the deo steams, we use exstng wok [30] adapted to sut ou puposes. Featue tackng and pose estmaton methods

6 ae lkely to poduce eoneous esults due to analyss eos and non-deal magng condtons. Ou anmaton applcaton podes an nteacte edtng nteface that allows the anmato to manually coect o oede the tackng and pose esults to achee the desed anmatons. 4. RESULTS We ceate a aety of expessons and mouth shapes by choosng dffeent tackng/contol ponts and dffeent nfluence egons and dectly manpulatng these ponts on the face. Fgue 9 shows sample expessons. Small modfcaton of the lp egon coneys a feelng of dssatsfacton (a) o decseness (b). Mong one eyebow upwad shows cleeness (c). Pullng lps and eyebows cones down ceate sadness (d). Fo a sly look, only a small numbe of etces ae dsplaced aound the lp cone and eyebow usng small nfluence zone (e, f). The same mpesson may be ceated by totally dffeent expessons. Fo nstance, facal expessons fo ange may ay fom peson to peson, o een wthn the same peson (g, h). Sample anmaton sequences fom a neutal state to full expesson (fgue 7, 8) and between two expessons ae shown (fgue 10). Wth the 3D model, nspecton fom an abtay ewpont s possble (fgue 7, 8). Fgue 11 shows models geneated wth the automated pocess. Wthout any po pepaaton, the same GDE technques ae appled to Skp s 3D model. Thee ed ponts on the eye sockets and the tp of the nose ae used fo pose estmaton whle the motons of yellow ponts ae used fo defomatons of the face. Addtonal MPEG moes ae also aalable on We use a facal mesh wth 1954 polygons. Real tme (30Hz) anmatons ae acheed wth a modeately confgued 500MHz PC. 5. DISCUSSION Radal bass functons guaantee a smooth suface defomaton fom a spase set of contol ponts. Howee, f a contol pont s moed too fa fom ts ognal poston, say outsde the nfluence egon, lage dscontnutes occu aound the ancho ponts. Because anchos ponts ae statonay at the bounday of the nfluence egon, no nfluence of the contol pont wll popagate though the ancho ponts. Such lage contol pont motons do not occu n pactce and most defomaton engnes would poduce unnatual effects unde smla condtons. By lmtng the defomaton egons we elmnate the need to pepae o alte the mesh as equed by othe methods, ncludng ou peous appoach [9]. Cuently, we assume that a specfed contol pont can only be moed wthn the egon of nfluence. As a possble adaptaton to allow the contol pont to moe beyond the nfluence egon, one can consde a dynamc tee seach to egeneate a lage egon of nfluence wth new ancho ponts. Ou method estmates the equed 3D contol ponts usng ay castng. Howee, eoneous esults can occu. We allow manual edtng of the 3D contol ponts as needed to compensate fo such eos. An ultmate soluton fo ths poblem may be to mpose constants on the facal suface such as bone stuctues. Howee, ths ntoduces lmtatons to the use of smple meshes. Any ponts on the facal suface can be used as contol ponts to defom the model. We can estct ths flexblty to use a subset o all of the featue ponts MPEG-4 defnes. Ou defomaton mechansm can be completely MPEG-4 complant and extendble f addtonal tackng data s aalable. In the mouth egons, fo example, addtonal contol data may come fom a speech steam analyss. Anmatons usng technques such as athmetc codng o DCT codng as descbed n [17] can achee data ate as low as bts/s. 6. CONCLUSION Ceatng lfelke facal anmaton s a cucal facto n deelopng an mmese tual enonment. We pesented a method fo anmatng defomatons of 3D face models. In scenes contanng faces, the analyss of facal mages can effcently encode the data needed to contol the defomatons. Ou GDE method s a noel appoach to defomng face models by dectly manpulatng featue ponts. The RBF based computaton poduces localzed smooth defomatons on the face. Ths appoach s applcable to most meshes wthout specal ntalzaton. The pocess eques mnmal and ntute human nteenton and s easly automated by the use of a featue tackng system wth deo steams. 7. ACKNOWLEDGEMENT Ths wok was suppoted by DARPA and the Annenbeg Cente at USC. Addtonal Suppot and eseach facltes ae poded by the NSF though ts ERC fundng of the Integated Meda Systems Cente. We ecognze the contbutons to ths wok fom all ou colleagues n the CGIT laboatoy. Specal thanks go to Tae-Yong Km, Bolan Jang, Suya You, and Reyes Encso. 8. REFERENCES [1] A. Abayejan, T. Stane, B. Hoowtz, A. Pentland, Vsually Contolled Gaphcs, IEEE PAMI 15(6), June 1993 [2] S. Basu, N. Ole, A. Pentland, 3D Modelng and Tackng of Human Lp Motons, ICCV, 1998, [3] M. Eck, Intepolaton Methods fo Reconstucton of 3D Sufaces fom Sequences of Plana Slces, CAD und Computegaphk, Vol. 13, No. 5, Feb. 1991, [4] P. Eset and B. God, Analyzng Facal Expessons fo Vtual Confeencng, IEEE, Compute Gaphcs and Applcatons, 1998, ol. 18, no. 5, [5] R. Encso, J. L, D. Fdaleo, T-Y. Km, J-Y.Noh, U. Neumann, Synthess of 3D Faces, Intenatonal Wokshop on Dgtal and Computatonal Vdeo, 2000 [6] M. Esche, I. Pandzc, N. Thalmann, Facal Defomatons fo MPEG-4, IEEE Compute Anmaton, 1998, [7] I. A. Essa, S. Basu, T. Daell, A. Pentland, Modelng, Tackng and Inteacte Anmaton of Faces and Heads usng Input fom Vdeo, Poceedngs of Compute Anmaton June 1996 Confeence, Genea, Swtzeland, IEEE Compute Socety Pess

7 [8] I. A. Essa, T. Daell, A. Pentland, Tackng Facal Moton, Poceedngs of the IEEE Wokshop on Non-gd and Atculate Moton, Austn, Texas, Noembe, 1994 [9] D. Fdaleo, J-Y. Noh, T. Km, R. Encso, U.Neumann, Classfcaton and Volume Mophng fo Pefomance- Den Facal Anmaton, Intenatonal Wokshop on Dgtal and Computatonal Vdeo, 2000 [10] B. Guente, C. Gmm, D. Wood, H. Mala, F. Pghn, Makng Faces, Sggaph poceedngs, 1998, [11] B. Guente, A system fo smulatng human facal expesson. In State of the At n Compute Anmaton, 1992, [12] I. R. Jackson, Conegence popetes of adal bass functons. Constucte appoxmaton, 1988, 4: [13] P. Kala, A. Mangl, N. M. Thalmann, D. Thalmann, Smulaton of Facal Muscle Actons Based on Ratonal Fee Fom Defomatons, Euogaphcs 1992, ol. 11(3) [14] I. Koufaks, B. F. Buxton, Vey low bt ate face deo compesson usng lnea combnaton of 2D face ews and pncpal components analyss, Image and Vson computng, 1999, 17, [15] Y. C. Lee, D. Tezopoulos, K. Wates. Realstc face modelng fo anmaton. Sggaph poceedngs, 1995, [16] Edwad F. Mooe. The shotest path though a maze. In Poceedngs of the Intenatonal Symposum on the Theoy of Swtchng, Haad Unesty Pess, 1959, [17] J. Ostemann, Anmaton of Synthetc Faces n MPEG-4, IEEE Compute Anmaton, 1998, [18] F. I. Pake, Paametezed models fo facal anmaton. IEEE Compute Gaphcs and Applcatons, 1982, ol. 2(9) [19] S. Pepe, J. Rosen, and D. Zeltze, Inteacte Gaphcs fo plastc sugey: A task leel analyss and mplementaton. Compute Gaphcs, Specal Issue: ACM Sggaph, 1992 Symposum on Inteacte 3D Gaphcs, [20] F. Pghn, J. Hecke, D. Lschnsk, R. Szelsk, D. H. Salesn, Syntheszng Realstc Facal Expessons fom Photogaphs, Sggaph poceedngs, 1998, [21] S. Platt, N. Badle, Anmatng facal expesson. Compute Gaphcs, 1981, ol. 15(3), [22] T. Poggo, F. Gos, A theoy of netwoks fo appoxmaton and leanng. Techncal Repot A.I. Memo No. 1140, Atfcal Intellgence Lab, MIT, Cambdge, MA, July 1989 [23] W.H. Pess, S.A. Teukolsky, W.T. Vettelng, B.P. Flanney, Numecal Recpes n C, Cambdge Unesty Pess, ISBN [24] D. Rupecht, H. Mulle, Image Wapng wth Scatteed Data Intepolaton, IEEE Compute Gaphcs and Applcatons, 1995, [25] A.N. Tkhono and V.Y. Asenn, Soluton of Ill-Posed Poblems and the egulazaton method. Soet Math. Dokl., 1963, 4: [26] F. Ulgen, A step Towad unesal facal anmaton a olume mophng, 6 th IEEE Intenatonal Wokshop on Robot and Human communcaton, 1997, [27] K. Wates, J. Fsbe, A Coodnated Muscle Model fo Speech Anmaton, Gaphcs Inteface, 1995, [28] K. Wates. A muscle model fo anmatng thee-dmensonal facal expesson. In Maueen C. Stone, edto, Compute Gaphcs (Sggaph poceedngs, 1987) ol. 21, [29] L. Wllams, Pefomance Den Facal Anmaton, Sggaph poceedngs, 1990, [30] P. Zhenyun, Suya You and Guangyou Xu, "A Fast Method fo Detecton Facal Featues Unde Vaed Poses", Chna Jounal of Image and Gaphcs, 2 (4), 1997.

8 Fgue 7 Sequence of makng A sound Fgue 8 Sequence of makng angy face

9 (a) (b) (c) (d) (e) (f) (g) (h) Fgue 9 Sample expessons ceated by one o moe GDEs Fgue 10 Tanstons between two expessons Fgue 11 Automated anmatons wth nput deo steam