Eye detection using a deformable template in static images

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1 Ey dtction using a dformabl tmplat in static imags Frnando Jorg Soars Carvalho Dpartamnto d Matmática, Instituto Suprior d Engnharia do Porto R. Dr. Brnardino d Almida, Porto Portugal -mail: fjc@isp.ipp.pt João Manul R. S. Tavars Lab. d Óptica Mcânica Exprimntal, Instituto d Eng. Mcânica Gstão Industrial Dp. d Engnharia Mcânica Gstão Industrial, Faculdad d Engnharia da Univrsidad do Porto Rua Dr. Robrto Frias, s/n Porto Portugal -mail: tavars@f.up.pt ABSTRACT: In this papr, w prsnt a mthodology that uss a dformabl tmplat to dtct th human y in static imags. Gomtrically, th usd tmplat is rprsntd by two distinct ntitis: a circumfrnc, that dfins th iris contour; and two parabolas, on concav and othr convx, that dfin rspctivly, th abov and blow contours of th y. Th gomtrical shap of th usd tmplat is controlld by a st of lvn control paramtrs that allows its chang in scal, position and orintation. To procss th matching btwn th y, rprsntd in th input imag, and th tmplat usd, w considr information obtaind from four nrgy filds. Thn, to procss th dynamic updat of th tmplat paramtrs, w us an nrgy function, basd on thos nrgy filds, that charactrizs th cost of th tmplat dformation. During ach of th svn procssing phass, w sarch itrativly for th bst combination paramtrs valus that minimiz th nrgy cost of th tmplat dformation. In this papr, w illustrat th functionality of this mthod by prsnting som xprimntal rsults, and prsnt som conclusions and prspctivs of futur work as wll. 1 INTRODUCTION In Computational Vision domain, on of th main dvlopmnt aras is rlatd with th dtction of facs, ithr in static imags or along imag squncs. In this ara, th fac can b dtctd as a whol, using, for xampl, a gomtric contour that dfins it in a global mannr, lik a balloon, or th sam dtction can b accomplishd by idntifying crtain facial faturs, as th y, th mouth, th ylids or th chin. Th mthodologis dvlopd for fac dtction «ar usually dfind in function of th mannr th fac is xpctd to appar in th input imags. Thus, for xampl, som xistnt mthodologis considr that th fac should appar in th input imags without facial hair and glasss, in a frontal position, without partial occlusion, tc. In (Yang t al. 00, is prsntd on of th most known survys about th xistnt works rlatd with fac dtction in imags. In that work, th xistnt mthodologis ar dividd into four catgoris: 1 basd on knowldg; basd on invariant faturs; 3 basd on apparanc; and 4 basd on tmplat matching. In th prsnt work, w had a spcial intrst in xploring th mthodologis basd on tmplat matching. Commonly, ths particular mthodologis us tmplats that try to rprsnt th fac to b dtctd compltly or by using just som faturs of it. Usually, th dtction procss is lad by a dynamic procss for matching th usd tmplat in th input imag; som xampls of rlatd works that can b considrd in this fild ar: cross corrlation, s for xampl (Carvalho & Tavars 005b; dformabl tmplats, as in (Yuill t al. 199, (Yuwn Wu t al. 003 and (Carvalho & Tavars 005a, for instancs; and circular pattrns dtction using Hough transform, as is don, for xampl, in (Tonnis t al. 00. In th dformabl tmplats ara, (Yuill t al. 199 dscribs a mthod that allows th dtction and xtraction of facial faturs, lik th y and th mouth. Thus, considring th similarity btwn th contours of thos faturs and som prdfind mathmatical modls, it is possibl to rprsnt thos facial faturs using gomtrical shap contours that ar usually known as dformabl tmplats. Onc th usd dformabl tmplats ar paramtrizd, th updat of thir paramtrs allows thir global dformation, and so th flxibility to chang thir scal, position and orintation in th imag spac. Frquntly, to lad th dynamic matching procss of th dformabl tmplat in th input imag, four diffrnt typs of th nrgy filds ar usd, that ar obtaind from th original imag. Th four nrgy filds considrd ar: intnsity dgs, intnsity vallys, intnsity paks, and intnsity gry lvls. Th filds considrd ar th rsult of th application of spcific morphologic oprators on th input imag,

2 in ordr to nhanc som important aspcts of th faturs to b dtctd. For xampl, th iris of th human y has a strong intnsity vally, bing vry asy to idntify its prsnc in that fild. Thrfor, this fild has th capacity to attract th tmplat usd to its corrct position. Thus, th y and th mouth dtction in th input imag consist on th dynamic and itrativ updat of th paramtrs of th usd tmplat by matching th sam on in th nrgy filds govrnd by an nrgy function. This nrgy function is dfind by a sum of svral primitivs that uss information obtaind from th nrgy filds, and allows also th charactrization of th matching cost during th tmplat dformation. Thus, a low matching cost assurs that th corrspondnc btwn th tmplat usd and th facial fatur to b dtctd is adquat, and consquntly that a corrct dtction was achivd. Othrwis, if th matching cost is high, thn th tmplat gomtry is vry diffrnt from th facial fatur to b dtctd and so th matching is not appropriat. Usually, th tmplat matching procss in th input imag is stratgically dfind by a st of procssing phass, and givn an initial st of paramtrs valus, is it vry probably that th st of final valus obtaind is considrably diffrnt of th initial on. In this work, w considr th mthod proposd in (Yuill t al. 199, for th dtction of th human y in static imags, and prsnt th dscription of th most rlvant stps of this mthod as wll as som illustrativ xprimntal xampls. This papr is organizd as follows: in th nxt sction, w prsntd th tmplat and nrgy filds usd in our work; thn, in sction 3, w dscribd th usd nrgy function, th matching procss, and th updat of th tmplat paramtrs; in sction 4, som xprimntal rsults ar prsntd; and finally, in th last sction, w addrssd som conclusions and prspctivs of futur work. othr blow, Equation 8, cntrd in (x,y, bing thir maximum width b, thir maximum hight a, masurd btwn th abov contour and th cntr, thir maximum hight c, calculatd btwn th blow contour and th cntr, and angl t thir orintation; finally, two pak points, P 1 and P, that ar usd in Equations 5 and 6, and corrspond to th cntrs of th sclra. Th position of ths points, P 1 and P, allow a corrct dtrmination of th tmplat orintation. Morovr, for th dtrmination of th tmplat orintation, is considrd two units vctors: ( cos( t sn( t 1=,, (1 ( sn( t, cos( t =. ( Thus, any point u in th imag spac (x,y, can b rprsntd as: u = x + y, (3 1 thn, around th tmplat cntr (x,y, th pak points P 1 and P, can b usd in Equations 5 and 6: u u ( x + P cos ( t y + P sn( t =, (5 1 1, 1 ( x P cos( t y P sn( t =. (6, Finally, to rprsnt th two parabolic sctions, w us th quations: a y= y a ( x x +, (7 b c y= y c ( x x +. (8 b EYE TEMPLATE AND ENERGY FIELDS.1 Ey Tmplat Th tmplat usd for th y dtction in an input imag is gomtrically rprsntd by: a circumfrnc, that dfins th iris contour and is controlld by thr paramtrs; and two parabolas, on concav and othr convx, that dfin rspctivly, th abov and blow contours of th y, and ar controlld by ight paramtrs, Figur 1. Considring a total of lvn paramtrs, and th imag spac (x,y, th tmplat paramtrization consists of th following lmnts: a circl, of radius r and cntr (xc,yc, that dfins th boundary btwn th iris and th whit part of th y (sclra; two parabolic sctions, on abov, Equation 7, and Figur 1. Th dformabl tmplat usd in this work is dfind by a st of lvn control paramtrs: a, b, c, x, y, xc, yc, P, P, t.. Enrgy filds In this work, ar usd four typs of nrgy filds, all obtaind from th input imag: intnsity dgs, intnsity vallys, intnsity paks, and intnsity gry lvls, Figur.

3 c d Figur. Rprsntativ imags of th nrgy filds considrd: intnsity dgs (a, intnsity vallys (b, intnsity paks (c and intnsity gry lvls (d. In this work, w us th Canny dg dtctor for nhancing th aras of th input imag that prsnt highst intnsity contrasts; that is, th dtction of th contours prsntd in th sam imags. Th tmplat usd is thn attractd by th dgs of th nrgy filds considrd; which, usually, allows fin adjustmnts of th tmplat usd. Thus, th iris tmplat is attractd by th vallys nrgy fild; bing charactrizd to contain a highr gradint insid th iris ara, which was usd to find th corrct iris location. Thrfor, th paks of th nrgy filds contain strong gradints insid th sclra, which allow th attraction of th pak points P 1 and P to th cntr of th y, giving consquntly th corrct orintation of th tmplat. Finally, th intnsity gry lvls nrgy fild contains gnric information about th brightnss intnsitis distribution, and is gnrically usd to updat all tmplat paramtrs. Th four nrgy filds considrd, Figur, ar thn filtring using a Gaussian filtr, in ordr to sprad th nrgy valus, nabling thrfor th attraction of th tmplat from largr distancs, Figur 3. 3 DEFORMABLE TEMPLATES METHOD In this sction, is prsntd a dscription of th usd mthod and th dfinition of th nrgy function, as wll as th followd stratgy to dtct th y itrativly in th input imag by using th principl of nrgy minimization. c d Figur 3. Rprsntativ imag of th nrgy filds obtaind aftr using a Gaussian filtr: intnsity dgs (a, intnsity vallys (b, intnsity paks (c and intnsity gry lvls (d. 3.1 Th Enrgy function for y tmplat Th total nrgy E, is th sum of svral primitivs involving th nrgy filds φ, dscribd in th prvious sction, and givn by: E = E + E + E + E + E, (9 v p i prior whr E v is th intnsity vallys nrgy, E th intnsity dgs nrgy, E p th intnsity paks nrgy, E i th intnsity gry lvls nrgy, and E prior th intrnal nrgy. During th matching procss, th nrgy E v should b maximizd insid a circumfrnc, and its valu is calculatd by th sum of th nrgy vallys insid th sam circumfrnc dividd by its ara: c1 Ev = v( uda A φ, (10 1 Rc whr C 1 rprsnts a wight constant, A 1 th circumfrnc ara, and Rc th intrior domain of th circumfrnc cntrd in (xc,yc. Th nrgy E, should also b maximizd and its valu is th sum of th nrgy dgs ovr th boundaris of th parabolas and th circumfrnc usd in th tmplat divid by thir lngths: E v c3 ( u ds ( uds c = L φ L φ, (11 1 Cb Pb whr C rprsnts a wight constant, L 1 th circumfrnc primtr, L th lngths of th parabola arcs, and Cb and Pb, rprsnt th boundaris of th circumfrnc and of th parabolas, rspctivly.

4 Th nrgy E i, has two distinct trms: a first on, rlatd with th minimization of th total brightnss insid th circumfrnc, divid by its ara, and a scond on, associatd with th minimization of th total brightnss insid th sclra zon, divid by its ara as wll. That is: c5 ( u da i( uda c4 Ei = i A φ A φ, (1 1 Rc Rs whr C 4 and C 5 rprsnt wight constants, A 1 and A th aras of th circumfrnc and of th sclra rspctivly, and Rc and Rs th corrspondnt aras domain. Considring th position of th two paks points P 1 and P, th nrgy E p, should b minimizd using: r r E = c φ u+ P + φ u P, (13 p ( p( 1 1 p( 1 6 whr C 6 rprsnts a wight constant. Finally, th nrgy E priori is usd to avoid that th tmplat usd closs on itslf: E p k1 = k + P ( x x + ( y y k 1 + P1 ( r+ b c 1 + ( r+ b k3 + c ( b r whr k 1, k, k 3 rprsnt wight constants. 3. Matching procss, (14 Th matching procss usd is dfind by th dynamic updat of th tmplat paramtrs, which is procssd by an optimal mthod: th stpst dscndnt gradint. For xampl, during th updat of th iris radius w us: r _ old ' = r _ nw+ dt r t, (15 whr r_nw is th radius valu of th nw itration, r_old th radius of th prvious itration, dt th tim stp, and r (t th variation rat of th radius in tim, translatd by th symmtrical variation rat of th total nrgy considring a small radius variation: ' r t = dr dt E =. (16 r Finally, for ach dscnt stp is calculat d total nrgy E, considring th nw st of obtaind paramtrs, and th bst matching is found whn th variation btwn two conscutivs nrgy stps is lss than a prdfind tolranc. That mans that th variation paramtrs ar vry small, which could indicat th corrct y dtction in th input imag. In Computational Vision, this procdur is usually known as th minimization nrgy principl. 3.3 Paramtrs updat To updat all paramtrs of th tmplat usd, th computational algorithm dvlopd is dividd into svn procssing phass. First, it is ncssary to dfin a st of initial paramtrs valus to b usd as input in our computational algorithm. Thus, w considr that: x=xc, y=yc, P1=r, P=-r, t=0, a=r, b=r, c=r. W should not that th initial valus chosn for xc, yc and r, must b carfully dfind rflcting proprly th siz of th facs in th input imag. Thn, in th first phas of our computational matching algorithm, w us th intnsity vallys fild to allow that th tmplat taks a clos position to th iris cntr, bing th nrgy wightd by constant C 1. In th nxt procssing phas, th radius and th cntr of th iris ar updat, using th vallys, th gry lvls, and dgs intnsity filds, kping constant C 1 with th prvious valu and incrasing th wight of constants C and C 4. This procdur prmits th scaling of th circumfrnc of th tmplat usd to th corrct siz of th iris. In th third phas, prvious constant valus ar incrasd again allowing th fitting of th tmplat to th iris by a fin tuning approach. To dtrmin th corrct angl rotation of th tmplat usd, w considr th fourth phas of our algorithm, using only th intnsity paks fild, wightd by constant C 6. In this phas, th paramtrs to updat ar: th tmplat cntr (x,y, th pak points P 1 and P, and th rotation angl t. Th fifth phas, of our computational procdur, uss th dgs, gry lvls, and paks intnsity filds. This phas bgins th procss of scaling th parabolas to thir corrct position. Th paramtrs that ar updat during this phas ar: pak points P 1 and P, rotation angl t, y cntr (x,y, and y width b. In th sixth phas, using th sam nrgy filds of th last phas, thr paramtrs ar updat: y width b, and hights a and b. Finally, in th svn and last phas of our computational algorithm, all considring nrgy filds ar usd in ordr to updat th lvn paramtrs of th tmplat usd simultanously. 4 EXPERIMENTAL RESULTS Th Tabl 1, prsnts th obtaind rsults considring th first thr procssing phass of our computational algorithm, using as input imag th on prsntd in Figur 4a. In Figur 4b, is rprsntd th path fallowd by th tmplat usd during th first updat procssing phas, which allows th dtrmination of th iris cntr.

5 Tabl 1. Rsults of th paramtrs updat during th phass 1, and 3. Paramtrs Updat procssing phass Units t radians x y xc yc P Pixls - P a b c r During th fourth procssing phas, as is indicatd in Tabl, w updat itrativly fiv paramtrs: orintation angl t, pak points P 1 and P, and cntr of th tmplat. Th rsults obtaind in this phas ar showd in Figur 6a. In addition to th fiv paramtrs alrady considrd in th fourth phas, is also updat th tmplat width, through th paramtr b, during th fifth phas procssing. This updat accomplishs th first approximation of th tmplat to th y cornrs. Tabl. Rsults of th paramtrs updat during th phass 4, 5, 6 and 7. Paramtrs Updat procssing phass Units t radians x y xc yc P Pixls - P a b c r Figur 4. An input imag (a and th path fallowd by th tmplat usd in th iris cntr dtction during th first procssing phas (b. (Th start point is rprsntd in rd and th nd point in grn. Th path fallowd by th tmplat usd during th nxt two procssing phass is rprsntd in Figur 5. Thus, in th scond phas, Figur 5a, th paramtrs rlatd to th iris cntr and to its radius ar dtrmind. In th third phas, Figur 5b, it is just don th fin adjustmnt of th iris radius. Figur 5. Updat of th iris cntr and its radius during th scond procssing phas (a, and th radius fin adjustmnt during th third procssing phas (b. Figur 6. Updating of th paramtrs of th tmplat usd during th fourth procssing phas (a - location and orintation and during th fifth procssing phas (b - location, orintation and width. (Th rd colour rprsnts th start positions and th grn colour th final position. In th sixth phas of our computational procssing, ar only updat th paramtrs that allow th scaling of th abov and th blow contours of th parabola includd in th tmplat. This is just an opration of fin adjustmnt of th tmplat to th y rprsntd in th input imag, as is illustratd in Figur 7a. In figur 7b, w show th bst fit foundd during th svn an last phas of our matching algorithm, and in th Figur 8, w prsnt th tmplat matchd in th input imag with all its control paramtrs idntifid. W tstd also our matching algorithm on th imag usd to illustrat th nrgy filds in th scond sction of this papr, Figur 3, considring th sam constants valus and tim stps usd in th prvious xprimntal xampl. Although, th diffrnc in scal that th two input imags prsnt, th dtction obtaind can still b considr as satisfactory, as can bn vrify in Figur 9. Of cours, that a bttr rsult can b obtaind on this input imag if w slctd a mor suitabl st of constants valus and tim stps.

6 5 CONCLUSIONS AND PERSPECTIVES OF FUTURE WORK Figur 7. Fin updat of th tmplat usd during th sixth procssing phas (a and th final matching obtaind aftr th last phas (b. Having in mind th obtaind rsults, w can considr that th mthodology prsntd in this papr allows th adquat dtction of th human y in input imags. Th algorithm dvlopd convrgs vry fast and givs good rsults whn ar usd adquat nrgy wight constants. But, it still works fin vn whn th input imags hav facs with diffrnt scals and th initial paramtrs ar not spcially tund for thm. Th disadvantags that th mthodology prsnts consist on th ncssity to dfin an adquat st of initial paramtrs for th tmplat, and that tmplat is initially placd nar th y to b dtctd in th input imag. As futur works, w intnd to dvlop a mchanism to automatically adjust th nrgy wight constants, applying th mthodology considrd in this work to imags with facs prsnting diffrnt scals, and apply this mthodology in th tracking of th human y in imag squncs. 6 ACKNOWLEDGMENTS Figur 8. Tmplat usd matchd in th input imag using our computational algorithm with its all control paramtrs idntifid. Th prsntd work was partially don in th scop of th projct Sgmntation, Tracking and Motion Analysis of Dformabl (D/3D Objcts Using Physical Principls, with rfrnc POSC/EEA-SRI/55386/004, financially supportd by FCT - Fundação para a Ciência a Tcnologia in Portugal. REFERENCES Figur 9. Ey tmplat match found using our dtction algorithm on imag of Figur 3. Carvalho, Frnando Jorg Soars & Tavars, João Manul R. S. 005a. Dtcção Extracção d Caractrísticas do Olho Humano a partir d um Modlo Protótipo Dformávl. At Encontro Nacional d Visualização Cintífica, Espinho, Portugal. Carvalho, Frnando J. S. & Tavars, João M. R. S. 005b. Mtodologias para idntificação d facs m imagns: introdução xmplos d rsultados. At Congrsso d Métodos Numéricos n Ingniría 005, Granada, España. Tonnis, K. & Bhrns, F. & Aurnhammr, M. 00. Fasibility of hough-transform basd iris localisation for ral-timapplication. In Procdings of th 16th Intrnational Confrnc on Pattrn Rcognition (ICPR 0, Qubc, vol., pp Yuill, A. & Hallinan, P. & Cohn, D Fatur Extraction from Facs Using Dformabl Tmplats. Intrnational Journal of Computr Vision 8, pp Yang, Ming & Krigman, David J. & Ahuja, Narndra 00. Dtcting Facs in Imags: A Survy. IEEE Transactions on Pattrn Analysis and Machin Intllignc 48(1, pp Wu, Y. & Liu, H. & Zha, H A Nw Mthod of Human Eylids Dtction Basd on Dformabl Tmplats. In Proc. 003 Sino-Kora Symp. On Intllignt Systms, pp.49-54, Guangzhou, China, Nov. 18.