IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 775 Fac Rcognition by Elastic Bunch Gaph Matching Launz Wiskott, Jan-Mac Fllous, Nobt Küg, and Chistoph von d Malsbug Abstact W psnt a syst fo cognizing huan facs fo singl iags out of a lag databas containing on iag p pson. Facs a psntd by labld gaphs, basd on a Gabo wavlt tansfo. Iag gaphs of nw facs a xtactd by an lastic gaph atching pocss and can b copad by a sipl siilaity function. Th syst diffs fo th pcding on [1] in th spcts. Phas infoation is usd fo accuat nod positioning. Obct-adaptd gaphs a usd to handl lag otations in dpth. Iag gaph xtaction is basd on a novl data stuctu, th bunch gaph, which is constuctd fo a sall st of sapl iag gaphs. Indx Ts Fac cognition, diffnt poss, Gabo wavlts, lastic gaph atching, bunch gaph, ARPA/ARL FERET databas, Bochu databas. 1 INTRODUCTION THE syst psntd h is basd on a fac cognition syst dscibd in [1]. In this pcding syst, individual facs w psntd by a ctangula gaph, ach nod labld with a st of coplx Gabo wavlt cofficints, calld a t. Only th agnituds of th cofficints w usd fo atching and cognition. Whn cognizing a fac of a nw iag, ach gaph in th odl gally (databas) was atchd to th iag spaatly and th bst atch indicatd th cognizd pson. Rotation in dpth was copnsatd fo by lastic dfoation of th gaphs. W hav ad th ao xtnsions to this syst in od to handl lag gallis and lag vaiations in pos, and to incas th atching accuacy, which povids th potntial fo futh tchniqus to ipov cognition at. Fistly, w us th phas of th coplx Gabo wavlt cofficints to achiv a o accuat location of th nods and to disabiguat pattns which would b siila in thi cofficint agnituds. Scondly, w ploy obct adaptd gaphs, so that nods f to spcific facial landaks, calld fiducial points. Th coct cospondncs btwn two facs can thn b found acoss lag viwpoint changs. L. Wiskott was with th Institut fo Nual Coputation, Ruh- Univsity Bochu, D-44780 Bochu, Gany (http://www.nuoinfoatik.uh-uni-bochu.d), whn this sach was pfod. H is now at th Coputational Nuobiology Laboatoy, Th Salk Institut fo Biological Studis, San Digo, CA 9186-5800. E-ail: wiskott@cnl.salk.du. J.-M. Fllous was with th Coput Scinc Dpatnt, Univsity of Southn Califonia, Los Angls, CA 90089 whn this sach was pfod. H is now at th Voln Cnt fo Coplx Systs, Bandis Univsity, Waltha, MA 054-9110. E-ail: fllous@caal.ccs.bandis.du. N. Küg and C. von d Malsbug a with th Institut fo Nual Coputation, Bochu. Chistoph von d Malsbug is also with th Coput Scinc Dpatnt, Univsity of Southn Califonia, Los Angls. E- ail: {nkug, alsbug}@nuoinfoatik.uh-uni-bochu.d. Manuscipt civd 19 Ap. 1996; visd 3 Ap. 1997. Rcondd fo accptanc by R. Szliski. Fo infoation on obtaining pints of this aticl, plas snd -ail to: tanspai@coput.og, and fnc IEEECS Log Nub 105030. 016-888/97/$10.00 1997 IEEE
776 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 Thidly, w hav intoducd a nw data stuctu, calld th bunch gaph, which svs as a gnalizd psntation of facs by cobining ts of a sall st of individual facs. This allows th syst to find th fiducial points in on atching pocss, which liinats th nd fo atching ach odl gaph individually. This ducs coputational ffot significantly. A o dtaild dsciption of this syst is givn in []. THE SYSTEM.1 Jts A t is basd on a wavlt tansfo, dfind as a convolution of th iag with a faily of Gabo knls [3] y F IL bg H K NM k kx s x = xp - xp ik x - xp - s G (1) s J in th shap of plan wavs with wav vcto k, stictd by a F H G IO K J QP Gaussian nvlop function with lativ width s = p. W ploy a disct st of fiv diffnt spatial fquncis and ight ointations. Fo iags of siz 18 18 pixls, th lowst and highst fquncy hav a wavlngth of 16 and fou pixls, spctivly. Th last t in (1) aks th knls DC-f, i.., th intgal z y bg xdx vanishs. This is known as a wavlt tansfo bcaus th faily of knls is slf-siila, all knls bing gnatd fo on oth wavlt by dilation and otation. A t - is dfind as th st {- } of 40 coplx Gabo wavlt cofficints obtaind fo on iag point. It can b wittn as - = a xp(if ) with agnitudsabg, x which slowly vay with position, and phass f bg, x which otat with a at st by th spatial fquncy o wav vcto k of th knls. Du to this phas otation, ts takn fo iag points only a fw pixls apat hav vy diffnt cofficints, although psnting alost th sa local fatu. This can caus sv pobls fo atching. W thfo ith igno th phas o copnsat fo its vaiation xplicitly. Th siilaity function 6 -- = b g a Âa Âa  aa ignos phas [1]. With a t -' takn at a fixd iag position and ts - = -bg x takn at vaiabl positionx, 6ac-bg x - h is a sooth function with local optia foing lag attacto basins (s Fig. 1), lading to apid and liabl convgnc with sipl sach thods such as gadint dscnt o diffusion. Using phas has two advantags. Fistly, phas infoation is quid to disciinat btwn pattns with siila agnituds, should thy occu. Scondly, sinc phas vais so quickly with location, it povids a ans fo accuat t localization in an iag. Assuing that two ts - and - f to obct locations with sall lativ displacnt d, th phas shifts can b appoxiatly copnsatd fo by th ts dk, lading to a phassnsitiv siilaity function () Fig. 1. Siilaitis 6 a (-, - ) (dashd lin) and 6 f (-, - ) (solid lin) with t - takn fo th lft y of a fac, and t - takn fo pixl positions of th sa hoizontal lin. Th dottd lin shows th stiatd displacnt dc- -h (dividd by ight to fit th odinat ang). Th ight y is 4 pixls away fo th lft y, gnating a local axiu fo both siilaity functions and zo displacnt clos to d x = -4. 6 -- = f b g  aa cos f - f - dk   a a (3) In od to coput it, th displacnt d has to b stiatd. This can b don by axiizing 6 f in its Taylo xpansion aound d = 0, which is a constaind fit of th two-dinsional d to th 40 phas diffncs f - f [], [4]. Lag displacnts of up to ight pixls can b stiatd if th phass of high fquncy cofficints a coctd by ultipls of p dpnding on th dispaity stiatd fo low fquncy cofficints. It is a gat advantag of this scond siilaity function that it yilds this displacnt infoation. Pofils of siilaitis and stiatd displacnts a shown in Fig. 1.. Gaphs A labld gaph * psnting a fac consists of N nods connctd by E dgs. Th nods a locatd at facial landaks x, n n = 1,..., N, calld fiducial points,.g., th pupils, th cons of th outh, th tip of th nos, th top and botto of th as, tc. This fac gaph is obct-adaptd sinc its gotical stuctu is adaptd to th stuctu of th obct (s Fig. ). Th nods a labld with ts - n. Th dgs a labld with two-dinsional distanc vctos Dx x x = n -, n = 1,..., E, wh dg conncts nod n with n. (W f to th gotical stuctu of a gaph, unlabld by ts, as a gid.) Gaphs fo diffnt had pos diff in goty and local fatus (ts). Although th fiducial points f to cosponding obct locations, so ay b occludd, and ts as wll as distancs vay du to otation in dpth. To b abl to copa gaphs of diffnt poss, w anually dfind points to associat cosponding nods in th diffnt gaphs. In od to xtact iag gaphs autoatically fo nw facs, on nds a gnal psntation ath than odls of individual
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 777 facs. This psntation should cov a wid ang of possibl vaiations in th appaanc of facs, such as diffntly shapd ys, ouths, o noss, diffnt typs of bads, vaiations du to sx, ag, and ac, tc. It is obvious that it would b too xpnsiv to cov ach fatu cobination by a spaat gaph. W instad cobin a psntativ st of M individual odl gaphs * % ( = 1,..., M) into a stack-lik stuctu, calld a fac bunch gaph (FBG) (s Fig. 3). Each odl gaph has th sa gid stuctu and th nods f to idntical fiducial points. A st of ts fing to on fiducial point is calld a bunch. An y bunch, fo instanc, ay includ ts fo closd, opn, fal, and al ys tc. to cov ths local vaiations. Th cosponding FBG % is thn givn th sa gid stuctu as th individual gaphs, its nods a labld with th bunchs of ts - % n and its dgs a labld with th % % avagd distancs Dx =Â Dx / M. Duing th location of fiducial points in a nw iag of a fac, th pocdu dscibd blow slcts th bst fitting t, calld th local xpt, fo th bunch ddicatd to ach fiducial point. Thus, th full cobination of ts in th bunch gaph is availabl, coving a uch lag ang of facial vaiation than psntd in th constituting odl gaphs thslvs. Fig.. Obct-adaptd gids fo diffnt poss. Th nods a positiond autoatically by lastic bunch gaph atching. (Th gids usd in Sction 3 fo th FERET databas had about 14 additional nods which a not shown h fo siplicity.) On can s that, in gnal, th atching finds th fiducial points quit accuatly. But ispositioning occud, fo xapl, fo th fac in th cnt. Th chin was not found accuatly; th lftost nod and th nod blow should b at th top and th botto of th a, spctivly..3 Elastic Bunch Gaph Matching A fist st of gaphs is gnatd anually. Nods a locatd at fiducial points and dgs btwn th nods as wll as cospondncs btwn nods of diffnt poss a dfind. Onc th syst has an FBG (possibly consisting of only on anually dfind odl), gaphs fo nw iags can b gnatd autoatically by lastic bunch gaph atching. Initially, whn th FBG contains only fw facs, it is ncssay to viw and coct th sulting atchs, but onc th FBG is ich nough (appoxiatly 70 gaphs) on can ly on th atching and gnat lag gallis of odl gaphs autoatically. Matching a FBG on a nw iag is don by axiizing a gaph siilaity btwn an iag gaph and th FBG of idntical pos. It dpnds on th t siilaitis and a topogaphy t, which taks into account th distotion of th iag gid lativ to th FBG gid. Fo an iag gaph *, with nods n = 1,..., N and dgs = 1,..., E and an FBG % with odl gaphs = 1,..., M th siilaity is dfind as, 1 x - x, % l D D 6 % *,% = Âax 6-Q, -Q- N f EÂ % n Dx, % (4) wh l dtins th lativ ipotanc of t siilaitis and th topogaphy t. - n a th ts at nod n and Dx a th distanc vctos usd as labls at dgs. Sinc th FBG povids sval ts fo ach fiducial point, th bst on is slctd and usd fo copaison. Ths bst fitting ts sv as local xpts fo th iag fac. A huistic algoith is usd to find th iag gaph which axiizs th gaph siilaity function. Fist, th location of th fac is found by a spas scanning of th FBG ov th iag. Thn, th FBG is vaid in siz and aspct atio to adapt to th ight foat of th fac. Ths stps a of no cost in th topogaphy t of th siilaity function bcaus th dg labls a tansfod accodingly. Finally all nods a ovd locally and lativ to ach oth to optiiz th gaph siilaity futh. Only nod locations with sall stiatd dispaity a considd. This local distotion is constaind by th topogaphy t. Sinc in th FERET databas facs vay in siz by a facto of th, th atching is don twic. In th fist atching stp th siz and location of th fac is dtind and th fac iag noalizd in siz. Th scond atching stp is usd to find th Fig. 3. Th Fac Bunch Gaph (FBG) svs as a gnal psntation of facs. Each stack of discs psnts a t. Fo a bunch of ts attachd to a singl nod only th bst fitting on is slctd fo a atch, indicatd by gay shading. fiducial points fo cognition. Th two stps us diffnt FBGs with diffnt phasis and nub of nods. Th fist stp quis sval FBGs of diffnt siz, th bst fitting on of which is usd fo siz stiation. Each iag has a labl which indicats th pos, so that pos dos not nd to b dtind autoatically, though ou syst is abl to dtin pos autoatically in th sa way as siz is stiatd [5]. Th two stps togth tak lss than 30 sconds on a SPARCstation 10-51. Fig. shows so autoatically positiond gids..4 Rcognition Aft having xtactd odl gaphs fo th gally iags and iag gaphs fo th pob iags, cognition is possibl with lativly littl coputational ffot by copaing an iag gaph to all odl gaphs and slcting th on with th highst siilaity valu. Th siilaity function w us h fo copaing
778 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 TABLE 1 RECOGNITION RESULTS FOR CROSS-RUNS BETWEEN DIFFERENT GALLERIES Modl Gally Pob Iags Fist Rank Fist 10 Ranks # % # % 50 fa 50 fb 45 98 48 99 50 h 181 hl 103 57 147 81 50 p 50 pl 10 84 36 94 49 fa 1 fb 171 hl 79 h 44 18 111 44 171 hl 79 h 49 fa 1 fb 4 17 95 38 170 hl 80 h 17 pl 33 p 9 67 7 17 pl 33 p 170 hl 80 h 31 1 80 3 Th diffnt copositions in th fou botto ows a du to th fact that not all poss w availabl fo all popl. Th tabl shows how oftn th coct odl was idntifid as ank on and how oftn it was aong th fist 10 (4 pcnt). gaphs is an avag ov th siilaitis btwn pais of cosponding ts. So ts in on pos ay not hav a cosponding t in th oth pos bcaus of occlusions. W us th t siilaity function without phas h. It tund out to b o disciinativ, possibly bcaus it is o obust with spct to chang in facial xpssion and oth vaiations. Gid distotions a not takn into account. This gaph siilaity inducs a anking of th odl gaphs lativ to an iag gaph. A pson is cognizd coctly if th coct odl yilds th highst gaph siilaity, i.., if it is of ank on. A copaison against a gally of 50 individuals took slightly lss than a scond. 3 EXPERIMENTS On st of tsts was don on th ARPA/ARL FERET databas povidd by th US Ay Rsach Laboatoy. Th poss usd h a: nutal fontal viw (fa), fontal viw with diffnt facial xpssion (fb), half-pofil ight (h) o lft (hl) (otatd by about 40 $ -70 $ ), and pofil ight (p) o lft (pl) (s Fig. fo xapls). Th siz of th facs vais by about a facto of th, which was copnsatd fo by th fist atching stp. Th foat of th oiginal iags is 56 384 pixls, 56 gay lvls. Rcognition sults a shown in Tabl 1. Th cognition at is vy high fo fontal against fontal iags (fist ow). This is ainly du to th fact that in this databas two fontal viws show only littl vaiation, and any fac cognition syst should pfo wll und ths cicustancs. S sults on th Bochu databas fo a o challnging tst. Bfo copaing lft against ight poss, w flippd all lft pos iags ov. Sinc huan hads a bilatally sytic to so dg, and sinc ou psnt syst pfos pooly on such lag otations in dpth (s blow), w pocdd und th assuption that it would b asi to dal with diffncs du to facial asyty than with diffncs causd by substantial had otation. This assuption is bon out at last by th high cognition at of 84 pcnt fo ight pofil against lft pofil (thid ow). Th shaply ducd cognition at of 57 pcnt (scond ow) whn copaing lft and ight half-pofils could b du to inhnt facial asyty, but th o likly ason is th poo contol in otation angl in th databas visual inspction of iags shows that ight and lft otation angls ay diff by up to 30 $. Whn copaing half pofils with ith fontal viws o full pofils anoth duction in cognition at is obsvd (although vn a coct cognition at of 10 pcnt out of a gally of 50 is still high abov chanc lvl, which would b 0.4 pcnt!). Th sults a asytical, pfoanc bing btt whn fontal o pofil iags sv as odl gally ath than if half-pofils a usd. This is du to th fact that both fontal and pofil poss a uch o standadizd than halfpofils, fo which th angl vais btwn 40 $ and 70 $. W intpt this as bing du to th fact that siilaity is o snsitiv to dpth-otation than to int-individual fac diffncs. Thus, whn copaing fontal pob iags to a half-pofil gally, a 40 $ half-pofil gally iag of a wong pson is oftn favod ov th coct gally iag if, in th latt, th had is otatd by a lag angl. A lag nub of such fals positivs considably dgads th coct-cognition at. In ths xpints w also flippd all lft pos iags ov, so that to a lag xtnt th cognition was not only don acoss pos but also acoss io flction. A scond st of tsts has bn don on th Bochu databas [1]. It contains nutal fontal viws (fa), fontal viws with diffnt facial xpssion (fb), 11 $ otatd poss (fd to as 15 $ in [1] bcaus th gaz is at 15 $, but th had otation is lss), $ otatd poss. Fo th Bochu databas w did not us th noalization stag, bcaus facs vaid only littl in siz. W usd 108 nutal fontal viws as a odl gally and th oth iags as pob gallis. Th cognition ats fo gallis fb, 11 $, and $ w 91 pcnt, 94 pcnt, and 88 pcnt, spctivly. On th sa gallis th pcding syst [1] achivd 9 pcnt, 97 pcnt, and 85 pcnt. Thus th ovall pfoanc is th sa. Th pfoanc on th fb-gally is wos than fo th cosponding fb-gally of th FERET databas, bcaus th Bochu databas shows o vaiation in facial xpssion, so facs bing vn half covd by a hand o hai. W hav intoducd phas infoation in od to ipov atching accuacy. W hav tstd th accuacy on th Bochu databas by atching a fac bunch gaph to iags fo which all fiducial points w contolld anually. W always lft th pson on th iag out of th fac bunch gaph, so that no infoation about that paticula pson could b usd fo atching. W an th sa algoith with phas infoation and without phas infoation, i.., all phass st to zo. Matching accuacy was calculatd as th an Euclidan distanc btwn atching positions and anually contolld fnc positions. It was 1.6 and 5. pixls with and without phas, and th histogas had thi axiu at on and fou pixls distanc, spctivly. Th iags had a siz of 18 18 pixls. 4 CONCLUSION Th syst psntd is gnal and flxibl. It is dsignd fo an in-class cognition task, i.., fo cognizing bs of a known class of obcts. W hav applid it to fac cognition but th syst is in no way spcializd to facs and w assu that it can b dictly applid to oth in-class cognition tasks, such as cognizing individuals of a givn anial spcis, givn th sa lvl of standadization of th iags. In contast to any nual ntwok systs, no xtnsiv taining fo nw facs o nw obct classs is quid. Only a odat nub of typical xapls hav to b inspctd to build up a bunch gaph, and individuals can thn b cognizd aft stoing a singl iag.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 779 W tstd th syst with spct to otation in dpth and diffncs in facial xpssion. So xpints includd io flction. W did not invstigat obustnss to oth vaiations, such as illuination changs o stuctud backgound. Th pfoanc is high on facs of sa pos. W also showd obustnss against otation in dpth up to about $. Fo lag otation angls th pfoanc dgads significantly. Ou syst pfos wll copad to oth systs. Rsults of a blind tst of diffnt systs on th FERET databas w publishd in [6] and [7]. In copaison to th syst [1], on th basis of which, w hav dvlopd th syst psntd h w hav ad sval ao odifications. W now utiliz wavlt phas infoation fo accuat nod localization. Pviously, nod localization was ath ipcis. W hav intoducd th potntial to spcializ th syst to spcific obct typs and to handl diffnt poss with th hlp of obct-adaptd gids. Th fac bunch gaph is abl to psnt a wid vaity of facs, which allows atching on fac iags of unsn individuals. Ths ipovnts ak it possibl to xtact an iag gaph fo a nw fac iag in on atching pocss. Evn if th pson of th nw iag is not includd in th FBG, th iag gaph liably fs to th fiducial points. This considably acclats cognition fo lag databass sinc fo ach pob iag, coct nod positions nd to b sachd only onc instad of in ach attptd atch to a gally iag, as was pviously ncssay. W did not xpct, and th syst dos not show, an ipovnt in ts of cognition ats copad to th pcding syst. Th incasd atching accuacy, th obct adaptd gaphs, and th fac bunch gaph povid th basis fo futh ipovnts. In an xtnsion of th syst psntd h, Küg has dvlopd a thod fo laning wights phasizing thos nods which a o disciinativ and o obust against nois [8]. On odl gallis of siz 130 150 and pob iags of diffnt pos, an avag ipovnt of th fist ank cognition ats of 6.5 pcnt has bn achivd, fo a an pfoanc of 19.8 pcnt without to 6.3 pcnt with wights. Anoth individual tatnt of th nods has bn dvlopd by Mau and von d Malsbug [9]. Thy applid lina t tansfoations to copnsat fo th ffct of otation in dpth. On a fontal pos gally of 90 facs and half pofil pob iags an avag ipovnt of th fist ank cognition at of 15 pcnt was achivd, fo 36 pcnt without otation to 50 pcnt and 53 pcnt with otation, dpnding on which pos was otatd. In [10], th bunch gaph tchniqu has bn usd to faily liably dtin facial attibuts fo singl iags, such as sx o th psnc of glasss o a bad. If this tchniqu was dvlopd to xtact indpndnt and stabl psonal attibuts, such as ag, ac, o sx, cognition fo lag databass could b ipovd and considably spdd by pslcting cosponding sctos of th databas. Futu sach on th basic syst will hav to focus on placing th anual stps in th initial phas by autoatic pocdus. Th anual slction of fiducial points could b placd by gouping salint points on th basis of coon otion [11]. Monitoing a otating obct by continuously applying lastic bunch gaph atching can thn val which nods f to cosponding fiducial points in diffnt poss [1]. S [] fo a o dtaild discussion. Mau and Jan Vobüggn fo additional tsts on th Bochu databas. Fo th xpints w hav usd th FERET databas of facial iags collctd und th ARPA/ARL FERET poga and th Bochu gally collctd at th Institut fo Nual Coputation, Ruh-Univsity Bochu. This wok has bn suppotd by gants fo th Gan Fdal Ministy fo Scinc and Tchnology (413-5839-01 IN 101 B9) and fo ARPA and th U.S. Ay Rsach Lab (01/93/K-109). REFERENCES [1] M. Lads, J.C. Vobüggn, J. Buhann, J. Lang, C. von d Malsbug, R.P. Wütz, and W. Konn, Distotion Invaiant Obct Rcognition in th Dynaic Link Achitctu, IEEE Tans. Coputs, vol. 4, no. 3, pp. 300 311, 1993. [] L. Wiskott, J.-M. Fllous, N. 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Sping Vlag, July 1996. ACKNOWLEDGMENTS W wish to thank Iving Bidan, Ladan Shas, Michal Lyons, and Thoas Mau fo vy fuitful discussions and thi hlp in th tsts on th FERET databas. Many thanks go to Thoas