Realistic 3D Face Modeling by Fusing Multiple 2D Images

Transcription

1 Realstc 3D Face Modelng by Fusng Multple D ages Changhu Wang EES Departent, Unversty of Scence and echnology of Chna, wch@ustc.edu Shucheng Yan, Hongjang Zhang, Weyng Ma Mcrosoft Research Asa, Bejng,.R. Chna scyan@ath.pku.edu.cn {hjzhang, wya}@crosoft.co Abstract n ths paper, we propose a fully autoatc and effcent algorth for realstc 3D face reconstructon by fusng ultple D face ages. Frstly, an effcent ultvew D face algnent algorth s utlzed to localze the facal ponts of the face ages; and then the ntrnsc shape and texture odels are nferred by the proposed Syncretzed Shape Model (SSM) and Syncretzed exture Model (SM), respectvely. Copared wth other related works, our proposed algorth has the followng characterstcs: the nferred shape and texture are ore realstc owng to the constrants and co-enhanceent aong the ultple ages; ) t s fully autoatc, wthout any user nteracton; and 3) the shape and pose paraeter estaton s effcent va EM approach and unt quaternon based pose representaton, and s also robust as a result of the dynac correspondence approach. he experental results show the effectveness of our proposed algorth for 3D face reconstructon. Key words: Morphable 3D Model, Realstc 3D Face Modelng, Syncretzed Shape Model, and Syncretzed exture Model.. ntroducton Modelng 3D huan faces has been a challengng ssue n coputer graphcs and coputer vson lteratures n the past decades. Snce the poneerng work of arke [, ], any algorths have been proposed for odelng the geoetry of faces [, 3, 8, 4, 6]. he D-based ethods do not consder the specfc structure of huan faces, thus result n the poor perforance on profle face ages. n the work of a et al. [7], face saples wth out-of-plane rotaton are warped nto frontal faces based on a cylnder face odel, but t requres heavy anual labelng work. Shape fro shadng [7] has been explored to extract 3D face geoetry nforaton and generate vrtual saples by rotatng the generated 3D face odels. However t requres that the face ages are precsely algned pxel-wse, whch s dffcult to be pleented n practce and even possble for practcal applcatons. he two ost popular works on 3D face odelng and analyss are the orphable 3D face odel proposed by Vetter et al. [, 3] and the artfcal 3D shape odel proposed by Zhang et al. []. he forer presented a 3D reconstructon algorth to recover the shape and texture paraeters based on a face age n arbtrary vew, and the latter developed a syste to construct textured 3D face odel fro vdeo sequence. Recently, Hu and Yan et al. [6] presented an autoatc D-to-3D ntegrated face reconstructon ethod to recover the 3D face odel based on a frontal face age and t s uch faster. However, there are stll shortcongs n these works: ) both Vetter and Zhang s works requre anual ntalzaton. Moreover, the speed of the can not satsfy the requreents of practcal face recognton systes; ) Zhang s work needs two ages close to the frontal vew and two condtoned sequences ncludng about 4 ages, whch are practcal for real applcatons; and 3) Hu and Yan s work assued fxed pose paraeters whch lted ts extenson to sde vew ages. n ths paper, we propose a fully autoatc and effcent fraework for realstc 3D face reconstructon based on ultple D face ages n arbtrary vews. t not only nherts the advantages of the above three works, but also successfully overcoes ther shortcongs. Frstly, a recently developed ult-vew face algnent algorth [9] s utlzed to autoatcally localze the feature ponts of the face ages; then the Syncretzed Shape Model s proposed to reconstruct the 3D face geoetry, n whch the pose and shape paraeters are deterned by EM algorth and the unt quaternon based pose representaton, furtherore, the correspondences between the contour ponts and ther vertex ndces n the 3D face odels are dynacally deterned; fnally, texture s obtaned by the Syncretzed exture Model whch fuses the texture nforaton of dfferent ages by the exture Confdence Functon. he rest of ths paper s organzed as follows. We gve an ntutve explanaton to the 3D face reconstructon roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

2 proble wth ultple face ages n Secton. n Secton 3, we ntroduce the SSM n detal to reconstruct the 3D geoetry of a face. SM s descrbed to obtan the 3D face texture n Secton 4. n Secton 5, we provde the experental results. Conclusons and the future work are presented n Secton 6.. roble defnton he proble dscussed n ths paper s to reconstruct the realstc personalzed 3D face odel fro ultple D face ages captured fro the sae person. An llustraton exaple s lsted n Fgure. age s derved fro the correspondences between s d and the 3D odel; then, the fnal 3D texture s obtaned by fusng these 3D texture odels, whch s based on the texture confdence functons. We ntroduce the detals of SMnsecton4. c s d... s S sd c... c sd s d f ( x, α, α )... f(, x α, α) sd f ( x, α, α )... s d Outputs: + (a) SSM (b) SM Fgure. Graphc odel of SSM and llustraton of SM 3. Syncretzed Shape Model nputs: Fgure. roble defnton Fgure llustrates that the nputs of the reconstructon proble are one/ultple D face ages n arbtrary vews; and the objectve s to autoatcally reconstruct the personalzed 3D face odel ncludng the 3D shape S and the 3D texture. n ths paper, we propose the Syncretzed Shape Model (SSM) and Syncretzed exture Model (SM) to nfer S and, respectvely, whch are deonstrated n Fgure. n SSM, let S denote the reconstructed 3D shape, and s d ( < ) represent the D shape derved fro the - th nput D age by a ult-vew face algnent algorth. c and s are the pose and shape paraeters whch need to be estated n SSM. As descrbed n secton 3, SSM presents an effcent approach n ters of EM algorth and quaternon based pose representaton to derve the shape paraeter s and pose paraeter c by consderng the constrants aong the ultple ages. n SM, td denotes the texture of the -th nput D age, denotes the fnal reconstructed 3D texture, and denotes the reconstructed 3D texture odel fro the - th D age. Frstly, the 3D texture for each nput D n ths secton, we descrbe the Syncretzed Shape Model n detal. Frst of all, a newly developed ult-vew face algnent algorth s utlzed to localze the feature ponts of the face ages, and then the D shape s d ( < ) and the correspondng Feature ont Confdence (FC) for each pont are obtaned. As followed, SSM presents the orphable pror 3D shape odel and observaton lkelhood odel, oreover, the shape and pose paraeters are estated n ters of the EM algorth and the quaternon based pose representaton. Fnally, we dscuss the dynac correspondence approach. 3.. Effcent ult-vew D face algnent Autoatc ult-vew face algnent s stll a dffcult proble. n ths work, we utlze a newly proposed ultvew D algnent algorth [9] for facal pont localzaton, n whch the texture s redefned as the un-warped grey-level edges n the orgnal age; then, a Bayesan network s desgned to descrbe the correlatons between shape and texture; fnally, EM algorth s appled to nfer the optal paraeters of the proposed exture-drven Shape Model. here are 83 feature ponts located, part of whch are adaptvely selected for 3D face reconstructon n dfferent vews and denoted by s d. Accordngly, the confdenceα Fj, naely Feature ont Confdence (FC), s derved for each pont va a rankng pror lkelhood odel. n addton, the confdence of the D shape s d roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

3 denoted as α, whch s called as age Confdence (C), s obtaned n proporton to the su of FCs for all the ponts: α = α / () j= 3.. Morphable pror 3D shape odel Fj Slar to Vetter s work [], the 3D shape of a face s 3 represented as a vector S = ( x, y, z, x,..., y, ) z, whch contans the x, y and z coordnates of the representatve vertces. We apply the probablstc extenson of tradtonal CA [5] to odel the shape varatons based on 3D faces wth about 89 vertexes. 3 S = U s+ S + ε, ε N(, σ3d3), σ3d = λ /3 =+ l () where the coluns of U are the l ost sgnfcant egenvectors, S s the average shape of saples and s s the low densonal shape paraeter. he ε denotes the sotropc nose wth σ 3d as the standard devaton whch can be estated fro the tranng saples drectly Observaton lkelhood odel he relatonshp between the 3D shape odel and D shape s d ( ) can be forulated as n Eqn. (3) by the orthogonal projecton rule: sd = ( fr) S + t + η, η N(, σd ) (3) where η denotes an sotropc observaton nose wth standard devaton σ d for the -th age; σ d s dynacally decded accordng to the change of the shape n each step; = 3 = (,) s the projecton atrx wth = and s the Kronecker productf s the scale paraeter; R= R 3 3 = R s the rotaton atrx fro { α, βγ, } of the -th projecton and t (, ) = t = t x ty s the translaton paraeter. For splcty, we denote c as the pose paraeters{ αβγ,,, f, t, t } for the -th age n the followng araeter estaton x y t s dffcult to nfer the shape paraeter s and pose paraeter c fro the gven D shape s d drectly. Here we descrbe an effcent EM algorth based on the unt quaternon based pose representaton to estate the MA paraeters fro s (,{ c} { s d}). We consder S as a hdden varable and s d as the observaton. Shape paraeter s and pose paraeter c are the MA paraeters to be estated n the EM algorth. n the E-step, let s defne the Q-functon as: Qs (,{ c}, s,{ c }) = E ln ( s,{ c} { sd}, S) { sd}, s,{ c } (4) = ln s (,{} c { s }, S) S ( { s }, s,{ c }) ds d d where { sd} denotes the set of s d,( ). Notce that the frst two arguents s, { c } M are the paraeters to be estated ang at axzng the posteror. he other two arguents s and { c } old old correspond to the paraeters of the prevous step or the ntalzatons. he second step (the M-step) of the EM algorth s to axze the expectaton defned n the E-step. hat s: * * ( s,{ c } ) = arg ax Q( s,{ c }, s,{ c } ) (5) s,{ c} E-Step. Wth sple coputaton based on Eqn () and (3), we have ln s (,{ c} { sd}, S) α = S U s S + s Λ s+ { s d ( fr) S t } + const σ3d = σd (6) ln S ( { sd}, s,{ c } ) old α (7) = S U s S + s d MS t + const σ3d = σd where const, const are constants and Λ s a dagonal atrx wth dagonal eleents as the leadng egenvalues of the shape odel. On the other hand, the condtonal probablty S ( { sd}, s,{ c } ) obeys the followng Gaussan dstrbuton: S ( { sd}, s,{ c } )~ Nµ (, Σ ) (8) where ( M = f R ) µ = S = ( σ3d + ασdm M ) σ3d ( U s + S) + ασdm ( s t ) old d (9) 3d ασ dm M = = = Σ= ( σ + ) () where S denotes the condtonal expectaton E S { sd}, s,{ c }. hen we have: SS =Σ+ S S () We can see that Σ s the nverson of a very large atrx, whch s expensve n coputaton. n fact, M has sple for wth a *3 atrx M = fr. M = (,) M () hen we can derve a uch ore sple expresson of Σ n coputaton and we only need to copute the nverson of a 3*3atrx: roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

4 Σ= ( + ) + σ3d3 ασdmm σ3d3 = (3) S and µ can also be splfed lke Σ. Due to the Eqn (6)-(), Eqn (5) can be wrtten as: * * ( s,{ c} ) = arg n α S U s S + s Λ s+ { s ( fr) S t } (4) d σ sc, 3d = d M-Step. Notce that the pose paraeters { c } are ndependent of the shape paraeter s. hus they can be optzed separately. ) Optze shape paraeter s: shape paraeter s can be easly derved by settng the dervatve of the Q- functon to zero: s =Λ( Λ+ σ 3d ) U ( S S) (5) ) Se-closed-for soluton for pose paraeter { c } usng quaternon: n ths part, we optze the pose paraeter { c } separately. hus we rewrte { c } and { sd} as c and s d,andsoon. Fro Eqn (4), we can get c = argaxq(,, s c s, c ) = argns M S (6) c σ d c = S where sd denotes the -th pont of s d,and denotes the correspondng pont n S. t s a nonlnear optzaton proble and can not be optzed drectly. radtonally, unt quaternon [4, 5] based pose representaton has been appled to solve 3D-to-3D pose paraeter varaton proble. n the followng, we ntroduce a se-closed-for algorth n ters of unt quaternon for pose estaton. A quaternon s represented as q = q + qx + qy j + qzk, and ts coplex conjugate s defned as * q = q qx qy j qzk and {} q = ( q,, ) x qy qz. A 3D pont p s represented by the purely agnary quaternon p = + px + py j + pzk and a rotaton of p s defned as * * * qpq, then f = q. q and frp= { q. pq. }. he detaled relatonshp aong rotaton atrx R, scale paraeter f and quaternon q s referred to [5]. Wth quaternon representaton, the objectve functon n Eqn (6) can be re-wrtten as: n * * d d = n E = < ( s { qs q } t) W( s { qs q } t) > (7) where 3D pont s d s extended fro s d wth z-value beng zero and W represents the drectonal constrant of the -th pont here. W = Assue that we have soe estaton of q avalable at δ the r-th teraton as q r and a new estaton q = r+ q +, r then * * * * * qr+ Sqr+ = qsq r r+ δ Sqr+ qs r δ + δ Sδ q r { } { } (8) Assue δ s sall wth respect to be approxated as * * * { qr S qr+ S qr+ qr S } = frrr S + G, then Eqn (8) can δ δ δ (9) where G can be derved fro the defnton. et (,,,,, ) v = q qx qy qz tx ty, z = s d frrrs and G = G,(,), then we have: v ( ) n n E z Gvv W z Gvv = = < ( ) ( ) > () he optal soluton can be obtaned by solvng the followng tradtonal functon: n 6 n gw j gv k k gwz j = k= = = ( j 6) () where gj s the j-thcolunofatrxg v. Gv s a lnear functon of S,soaregj and z. herefore both sdes of Eqn (), whch are quadratc functons of S at ost, can be drectly coputed out fro Eqn () Dynac correspondence strategy Hu s work [6] assued that the correspondence between the D shape ponts and the 3D face odel vertexes are known and fxed, whch s napproprate n the case wth out-of-plane rotaton. Here we assue that the correspondences for the eyes, outh, and nose ponts are fxed snce they are corner ponts wth explct seantcs; whle for the contour ponts, the correspondences are not fxed especally n the cases wth out-plane rotaton. Note that the absolute value of z coordnate of the noral drecton for the contour pont s sall; we utlze the nforaton for the selecton of contour ponts and search for ore proper ponts to replace the orgnal contour ponts after each teraton, whch results n a ore precse correspondence between the contour ponts of D age and 3D face odel vertces. Fgure 3 deonstrates one exaple on how to dynacally deterne the contour ponts n dfferent vews. 4. Syncretzed exture Model n ths secton, we descrbe the SM n detal. Frst of all, we ntroduce soe defntons n SM; then, the approach for texture extracton fro sngle nput age s roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

5 4.. exture extracton for sngle nput age Fgure 3. Dynac deternaton of the contour ponts. eft: orgnal contour ponts; Mddle: postons of the orgnal ponts after pose varaton; Rght: dynacally deterned postons of the contour ponts. descrbed; fnally, the exture Confdence Functon and Syncretzed exture Model Algorth are proposed to reconstruct 3D face texture by fusng ultple 3D face textures. 4.. Soe defntons n SM ) ose Confdence (C): t ndcates the poston n an age wth the axal confdence, naely the confdence center. t changes as pose changes. he C of the - th D age s denoted as α. n ths paper, we only consder the confdence along the x axs, thus C ndcates the x coordnate wth axal confdence, whch s valuable for texture fusng fro ultple 3D textures represented n the cylnder coordnates ages. ) exture Confdence Vector (CV): t s w- densonal vector that ndcates the texture confdence dstrbuton along x axs, where w s the wdth of the cylnder age. We denote the CV of the -th age as tcv. herefore, can be descrbed as: =.*( eh tcv), where eh = s an h-densonal vector wth all eleents equal to one and h s the heght of the cylnder age. 3) exture Confdence Functon (CF): t odels the CV wth the varable α and α.wedenotecfas f( x ). 4) Confdence Constrant (CC): n order to ake every eleent of be a weghted average of all the 3D textures, we constran that tcv [ j] and noralze tcv [ j] as: = k k = tcv [ j] =. For t, we tcv [ j] = tcv [ j]/ tcv [ j]. After the 3D face geoetry has been reconstructed, the texture of the D age t d s projected orthogonally to the 3D geoetry to generate the 3D texture.hereare soe vertces occluded n a face age for any gven vew age, and there are no correspondng texture nforaton avalable for these vertces. o solve ths proble, a rror strategy s appled to defne the texture of the nvsble vertces based on the vsble part. Moreover, we sooth the area that separates the nvsble and vsble vertces by nterpolaton ethod exture Confdence Functon As descrbed above, we ntroduced the followng functon to nfer fro { } : =.*( eh tcv) () = where tcv denotes CV. he exture Confdence Functon s used to update CV. t s desgned as a functon wth paraeter C and C,.e.: tcv[ j] = f ( j, α, α) j (3) Fro the Confdence Constrant: tcv [ j] = j (4) = we can derve the representaton of the exture Confdence Functon: f( j, α, α) =, j < w (5) = n the followng subsecton, we wll ntroduce the detals on how to desgn the exture Confdence Functon and how to optze the paraeters n the novel Syncretzed exture Model Syncretzed exture Model Algorth n our work, we deal wth the exture Confdence Functon n the dscrete condton. Moreover, the functon s related wth the pose confdence, whch ndcates the confdence center. Now, we ntroduce the detals of the Syncretzed exture Model. ) Choose confdence paraeter α s fxed for each D age, so we only need to fnd the forulaton of α. α s related wth the rotaton paraeters of a face: α, β, γ. n our experent, we roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

6 α use the lnear functon of β to approxate snce α doesn t affect α and γ can be easly justfed: α = aβ + b (6) where a and b are decded by the cylnder age sze. ) Choose exture Confdence Functon For a gven age, the exture Confdence Functon s only related to C and t s natural that the nearer x to α, the larger the functon value s. n our experents, we use the followng functon: f ( α < V / V /6): x α f( x) = { + cos[ π( x α ) / V]} / other f ( α > V / + V /6) x α f( x) = { + cos[ π( x α ) / V ]} / other else (7) x α V /4 4 x α V V f( x) = < x α < V 4 V x α Based on confdence nforaton, the unrealstc part s set wth saller functon value, whle the realstc part wth bgger functon value. When there are ultple ages, the exture Confdence Functon s also related wth the C. n all our experents, t s desgned as: f( x, α, α) = α f( x α) (8) 3) Update exture Confdence Vector We update vector tcv as n Eqn (3), then we constran the as: F[ j] = tcvk [ j] j (9) k = f F[ j ] >, tcv[ j] = tcv[ j]/ F[ j] (3) else, = j tcv [ j] = (3), j where { j = argn α j }. 4) 3D texture reconstructon Fnally, we use Eqn () to obtan the fnal 3D texture. 5. Experents We constructed a fully autoatc 3D face synthess syste based on the above proposed algorth. he nputs of the syste are ultple face ages n arbtrary vews and there s no user nteracton n the whole process. n our experents, we used face ages wth dfferent poses to autoatcally construct the personalzed 3D faces. Fgure 5 and Fgure 6 show a seres of experental results. Fgure 5 shows the syntheszed results based two ages of Bll Gates, and the generated face ages n dfferent vews deonstrate the good realstc property of the reconstructed 3D face odel. Moreover, we also conducted the experents to reconstruct the 3D face odels of the twelve persons n our lab. All the results show the good perforance of our proposed algorth n Fgure 6. Fgure 4 copares the realstc property of the results fro sngle and ultple ages. t shows the superor perforance of our proposed algorth. he whole process to construct a head odel fro face ages costs less than seconds on a C wth V.8 GHz processor, whch s tens of tes faster than the 3D face reconstructon processng proposed by Vetter [3], and several tes faster than the work of Zhang []. he te cost n 3D face geoetry reconstructon process s about.6 seconds and t s uch faster than Vetter s [3] ethod. he orphable odel used n our fraework s uch ore realstc than the artfcal 3D shape odel proposed by Zhang []. n the orphable odel, we utlze about 89 vertces, whch s a an source of te expendture. We can decrease the total nuber of 3D face vertces to speed up our fraework. Moreover, Zhang s work s vdeo based and as at utlzng the nforaton between adjacent fraes, thus the nuber of total ages used to reconstruct the 3D face odel s very large. n our work, the nuber of nput ages s arbtrary. 6. Conclusons and future work We have proposed a novel fraework to construct personalzed 3D face odel by fusng ultple face ages. he experental results showed the realstc of the reconstructed 3D face odels. Copared wth other related works, ths fraework has the followng advantages: ) t s effcent, autoatc and no user nteracton s requred; ) the reconstructed 3D face odel s ore realstc owng to co-enhanceent of the ultple ages; and 3) the algorth s robust to pose varaton as a result of the dynac correspondence approach. he realstc 3D face reconstructon by fusng ultple D ages has any applcatons ncludng 3D odel based ult-vew face recognton, and vrtual realty n 3D gae. Currently, we are explorng to effcently perfor the face recognton n varant poses. roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

7 Fgure 4. he coparson between the 3D face odels reconstructed fro one and ultple ages. op row: left s the orgnal ages, ddle s the reconstructon result fro the left age, and rght s the reconstructon result fro ultple ages; the ddle row and botto row are the detals coparsons between the 3D odels fro one and ultple ages. t shows that the result fro ultple ages s uch ore realstc. Fgure 5. 3D face reconstructon fro two face ages of Bll Gates. Fgure 6. 3D face reconstructon fro two face ages. roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE

8 References [] V. Blanz and. Vetter. A orphable odel for the synthess of 3D-faces. n SGGRAH 99 Conference3 roceedngs, os angeles, pages 87-94, 999. [] D. DeCarlos, D. Metaxas, and M. Stone. An anthropoetrc face odel usng varatonal technques. n Coputer Graphcs roceedngs SGGRAH 98, pages 67 74, 998. [3] S. Daola. Extendng the range of facal types. Journal of Vsualzaton and Coputer Anaton, (4):9 3, 99. [4] A.Hll,.F.Cootes, C.J.aylor. "Actve Shape Models and the shape approxaton proble." age and Vson Coputng. 4 (8) Aug. 996 pp [5] B.K..Horn. Closed-for soluton of absolute orentaton usng unt quaternons. Journal of the Optcal Socety of Aerca,4(4):69-64,Apr.987. [6] Y. X. Hu, D.. Jang, S. C. Yan, e Zhang, H.J. Zhang. "Autoatc 3D Reconstructon for Face Recognton", n FG4 roceedngs, pages , 4.. [7] Kn-Man a and Hong Yan, An Analytc-to-Holstc Approach for Face Recognton Based on a Sngle Frontal Vew, AM98, Vol, No7,page [8] J.. ews. Algorths for sold nose synthess. n SGGRAH 89 Conference proceedngs, pages ACM, 989. [9] H., S.C. Yan,.Z. eng. Robust Mult-vew Face Algnent wth Edge Based exture, subtted to Journal of Coputer Scence and echnology, 4. [] u, Z., Zhang, Z., Jacobs, C. and Cohen, M. (). Rapd odelng of anated faces fro vdeo, roc. 3rd nternatonal Conference on Vsual Coputng, Mexco Cty, pp Also n the specal ssue of he Journal of Vsualzaton and Coputer Anaton, Vol.,. [] F.. arke. Coputer generated anaton of faces. n ACM Natonal Conference. ACM, Noveber 97. [] F.. arke. A araetrc Model of Huan Faces. hd thess, Unversty of Utah, Salt ake Cty, 974. [3] S. Rodhan, V. Blanz, and. Vetter. Face dentfcaton by fttng a 3d orphable odel usng lnear shape and texture error functons. n Coputer Vson ECCV, volue 4, pages 3-9,. [4] N.Magneneat-halann, H. Mnh,M. Angels, and D. halann. Desgn, transforaton and anaton of huan faces. Vsual Coputer, 5:3 39, 989. [5] M. ppng and C. Bshop. "robablstc prncpal coponent analyss" echncal Report NCRG/97/, Neural Coputng Research Group, Aston Unversty, Brngha, UK, Septeber 997. [6] J.. odd, S. M. eonard, R. E. Shaw, and J. B. ttenger. he percepton of huan growth. Scentfc Aercan, 4:6 4, 98. [7]R.Zhang,.S.a,J.E.Cryer,M.Sha, ShapeFro Shadng: A Survey, EEE rans. On AM, (8). pp [8] H. H. S. p and -J. Yn, "Constructng a 3D Head ndvdualzed Model fro wo Orthogonal Vews", he Vsual Coputer, Vol, No. 5, pp , 996. roceedngs of the th nternatonal Multeda Modellng Conference (MMM 5) 55-55/5 $. 5 EEE