Markerless Tracking using Planar Structures in the Scene

Transcription

1 aklss Tacking using Plana Stuctus in th Scn Gills Simon, Andw W. Fitzgibbon and Andw Zissman gs,awf,az obots.ox.ac.uk Robotics Rsach Goup, Dpatmnt of Engining Scinc, Univsity of Oxfod, 19 Paks Road, Oxfod OX1 3PJ, Unitd ingdom vgg Abstact W dscib a maklss cama tacking systm fo augmntd ality that opats in nvionmnts which contain on o mo plans. This is a common spcial cas, which w show significantly simplifis tacking. Th sult is a pactical, liabl, vision-basd tack. Futhmo, th tackd plan imposs a natual fnc fam, so that th alignmnt of th al and vitual coodinat systms is ath simpl than would b th cas with a gnal stuctu-and-motion systm. ultipl plans can b tackd, and additional data such as 2D point tacks a asily incopoatd. 1 Intoduction To ffctivly implmnt augmntd ality in unstuctud nvionmnts ith in waabl had-mountd displays, o whn augmnting achiv footag (.g. fo spcial ffcts th pimay uimnt is accuat, liabl, fast position tacking. Only optical tchnologis appa to off th uid accuacy, but unstuctud nvionmnts do not pmit th placmnt of tagts [31] o th ppaation of 3D modls of th nvionmnt a-pioi. Achiv footag also psnts spcial difficultis in augmntd ality. Gnally, cama calibation is unavailabl, o at bst inaccuat. aks a not availabl, and 3D masumnts a not asily obtaind fo points visibl in th povidd imags. On th oth hand, post-hoc augmntation of achiv footag is oftn uid, fo xampl in achitctual visualisation, in post-poduction, o vn whn p-shoot planning is found to b in o. Although movmatching tchnius fom photogammty and comput vision may b usd to comput th cama motion, such tchnius a cuntly difficult to us and xtmly tim-consuming, whil automatic mthods [1, 3, 12, 21] a not yt widly availabl, and a fa fom bing al-tim. Evn if an automatic, gnal-pupos movmatch w availabl, th mains th non-tivial task of aligning th systm s abitaily chosn coodinat fam with that of th augmnting obcts. In this pap, w dscib a vision-basd position tack which simplifis th gnal cama-tacking poblm in th cas wh th is a plana sufac visibl somwh in th scn. Som xampls a shown in figu 1. Bcaus this is a spcial cas of th gnal poblm, it is asi to solv, and thfo allows mo liabl and fast solutions. Howv, it is also a vy common spcial cas; th gound plan, o a wall is oftn visibl thoughout th scn; and indoos, th ciling is oftn adily tackd. W show that th systm pfoms as wll as gnalmotion tacks, but is mo liabl and fast. An xampl implmntation is psntd, but th basic tchnology of automatic homogaphy tacking is wll stablishd in th boadcast industy so altim solutions to th plan tacking poblm alady xist. 2 Backgound Bfo dscibing ou plan-spcific tack, w viw th cunt statgis fo maklss AR. Ths may b dividd into two main catgois: modl-basd tacking and mov-matching. All statgis dpnd on making cospondnc btwn 3D wold fatus and 2D imag fatus, and idally, on making such cospondnc automatic. 2.1 odl-basd tacking Th most common appoach fo daling with unstuctud nvionmnts is to impos som stuctu post-hoc.

2 &, JI H H H Figu 1. Exampl scns with plana lmnts. Ou algoithm automatically tacks th plan and covs cama position. Accuacy is at o na th lvl of a full-scn stuctu and motion solution. In addition, th plan povids a natual coodinat systm fo augmntation. By idntifying fatus in th imags fo which al-wold coodinats can b masud, a cospondnc btwn 3D and 2D is st up. Exampls includ stt lamps and 3D cuvs in [5, 27] and th hoizon in [4]. Pos-stimation tchnius [8, 10] can thn b usd to stimat th cama position. Futh modl-basd systms a dscibd in [18, 19, 26, 29, 30]. W now dscib point-basd pos stimation in od to situat ou wok and intoduc ou notation. Fo ach nw vido fam, w a givn a st of 3D points whos coodinats a known, and a cosponding st of 2D points. W psnt all uantitis in homognous coodinats, so is a 3-vcto, and X Y Z. Th cama position is psntd as a poction matix P R! wh R is a "# otation matix, and is th tanslation of th cama. Th matix psnts th intnal calibation paamts of th cama: $%& (*, & -. / (5 -. is focal lngth; is pincipal point; is aspct atio; is skw In most cass, th intnal paamts may b assumd known, but somtims (.g. whn daling with achiv footag thy must b stimatd fom th data. Th pos stimation task is to comput P, givn th 2D-3D cospondncs 6879 P th homognous scal factos 7 a unknown a-pioi, so must b stimatd simultanously with R and. Th statgy is to fist stimat P using a lina mthod, and thn nonlinaly minimiz th poction o wh >C DE DE GF AF H F : R ;=< IJ IJ?>A P B F H FL AF H FL Fo a modat numb of points, this pocss can b mad to un uickly, uiing of th od of 50ms p fam. Th pimay advantag of modl-basd tacking is high pcision, and absnc of dift: as long as (a subst of th ky points a visibl, th systm is always gisting dictly to th scn. Futhmo, th coodinat systm is wll dfind bfohand. Howv, it is commonly tu that fw points a availabl fo gistation, so th tacking suffs fom high-funcy itt, as nois in th imag masumnts coupt th stimatd pos. o impotantly, th tchniu uis significant manual intvntion to constuct th modl. In many al-wold cass, a 3D modl is difficult to obtain, o masuabl fatus may not b asily dtctabl. 2.2 ov-matching A tchnology which appas to off significant possibilitis fo gnal, accuat gistation is known as stuctuand-motion stimation, o mov-matching [1, 2, 3, 12, 24]. Such systms simultanously stimat cama motion, and th 3D stuctu of th imagd scn. Ths systms pmit xtmly accuat gistation, with accuacis of aound 0.2 pixls, and ngligibl itt. Howv, thy hav a numb of disadvantags that man that thy a not likly to b suitabl fo al-tim implmntation in th na futu. 2

3 Fist, thy a slow, and high accuacy is only achivd by a batch bundl adustmnt [12]. This pcluds a suntial implmntation, as is uid fo autonomous, o longunning applications. Scond, th coodinat systm chosn will b abitay, gnally aligning th wold coodinat systm with th fist cama. Thfo, th computd motion is lativ ath than absolut, which mans that in od to inst vitual obcts th systms must b manually alignd. This is difficult unlss som fatu cospondncs a mad btwn th covd 3D stuctu and th augmnting modls. Anoth algoithm fo stuctu-and-motion basd augmntd ality tacking was potd by Numann t al. [24]. In thi systm, optical flow is usd to comput diffntial motion stimats, which a intgatd to giv cama pos. Ou systm might b considd a spcial cas of this w comput diffntial motion stimats fo th plan, and thn us ths stimats to comput th cama motion. Howv, ou systm dos not assum that th int-fam motion is small, and can thfo b usd in situations wh a fast-moving cama would mak optic flow difficult to comput. 2.3 Spcial-cas tchnius Som intsting cnt wok looks at impoving AR using spcial gomtic constuctions that a found in th scn [20, 28]. In ths woks, constaints a obtaind fom stuctus typically found in man-mad nvionmnts. Fo xampl, sts of paalll o othogonal lins can b usd to dtmin th 3D fnc fam, and comput o fin tacking. 3 Plana-sufac tacking In this pap, w consid an appoach which boows somthing fom ach of th abov. W dscib what is ssntially an automatic mov-match fo scns which contain plana stuctus. W a thus, lik [20], using a limitd typ of scn. In ou cas, howv, th limitation is slight w ui that a plan o plans b visibl in th scn. This is commonly tu of indoo nvionmnts, wh a txtud ciling o gound plan is visibl. Outdoos, vn ough gound (viz. th gass in Figu 1, povids a good fnc fo th systm. Th sam plan nd not b visibl thoughout th sunc, as th algoithm can hand off tacking fom on plan to th nxt. Lik mov-matching, th computation of lativ motion fom fam to fam is compltly automatic, but th poposd appoach is significantly mo liabl, fo asons discussd in N 4.4. Tacking of a plan confs anoth advantag. A canonical coodinat systm is automatically Initialization: 1. anually indicat th plana gion in imag. 2. Dtct intst points in imag. 3. Initializ cama calibation. Stady stat, computing H fom fam O to O 1. Dtct P intst points in fam O st Q UWVX SRTF UY F. 2. atch intst points fom fam O to O gnats a st of cospondncs U[Z., giving th. This ]. \R6F 3. Fom th st of cospondncs, obustly comput SRTF H (N Comput pos fom H SRTF (N 3.3. Figu 2. Algoithm summay. catd within th scn, which gatly simplifis th alignmnt of th systm s automatically chosn fnc fam and any fam attachd to an augmnting modl. A fw mous clicks a nough to st th coodinat fam, and it may b changd at any tim without stating th algoithm. An ovviw of th algoithm is shown in Figu 2. Th basic pimitivs usd a intst points [14, 23], which a automatically computd fo ach input imag. Ths intst point opatos hav th dsiabl popty that th 2D points thy gnat oftn cospond to 3D points in th wold. By obtaining multipl imags of a 3D point, w glan infomation about th stuctu of th wold, and about th motion of th cama. Th tansfomation which modls th 2D movmnt of coplana points und pspctiv poction is givn by a ^_ plana homogaphy. Fom th plana homogaphy, w can asily comput th cama position and otation, which povids th motion stimats. In th following, w fist dvlop th mathmatical modl usd by th systm, and thn dscib ou implmntation. Finally w commnt on liability in compaison with gnal motion stimation, and with spct to th wll-known singulaitis of pos stimation fom coplana points. 3.1 ultipl viws of a plan Fo most of this pap, w may choos coodinats so that w a tacking th Z plan. Thfo, a 3D point on th plan has th fom X Y, and is dfind by ust two coodinats X and Y. It is poctd into imag 3

4 JI JI EhhhhhhhhhhD y y F O via th `a poction matix P, yilding th masud 2D point P bdc F c bdc F c H DE c gf f IJ X Y hhdex Y IJ X Y wh th kl matix H is a plana homogaphy 1 which tansfoms points on th wold plan to th O th imag plan. Th subscipt H fs to th wold coodinat systm. Th is a on-to-on cospondnc btwn th two plans, so a point m n on th imag can b back-poctd onto th wold plan by multiplying it by H po F H. Now, in ou cas, th wold coodinat systm is not known, so w SR6F cannot masu H dictly. Howv, w can masu H, th homogaphy that maps th imags of points on th plan fom fam O to fam O. This matix is givn by \R6F H SRTF H H o F \R6F Now, H lats imag coodinats of fatus that w can masu. Indd, givn SR6F fou o mo cosponding points, w can comput H fom imag data alon. 3.2 Computing \R6F H Spcifically, if 5 and \R6F m5 a imags of th sam 3D point on th plan, thi coodinats a latd by 5 87 H \R6F wh 7 is th unknown homognous scal facto. Now, coss-multiplying th thid componnts of ach sid and witing th componnts of th homogaphy as FF tc, w obtain \R6F th lina systm of two uations fo th lmnts of H s F t FuF F F s F t F Givn fou such cospondncs, w obtain au matix uation of th fom Av xw, wh v is ust th componnts 1 Also known as collination, o plan pspctiv tansfomation. JIi i nf F 9y y GF F *y y *F nf F nf * * y 9y y 9y 5F F F F 5 5 y y y y Figu 3. Componnts of th matix A. 9 U stackd into a 9-lmnt vcto. Th matix A is shown in figu 3. Th solution v is th null spac of A, which may b computd using th singula valu dcomposition [13]. o dtails, in paticula on data nomalization, a givn in [16]. 3.3 Computing P Suppos fo a momnt that w knw th mapping fom wold coodinats to on of th fams of th sunc, say fam. ] This mapping is th homogaphy H. W can R6F masu H ] fo any pai of fams sz z fom tackd points, and thfo w can comput H H o F H o F H o F Finally, using th known valu of H, w obtain H H H Now call that H b c F c f If th calibation (i.. is known (s N 3.5, thn w can asily xtact c F and c fom th fist two columns of o F H. Thn, bcaus R must b a otation matix, w know its columns must b othonomal, so c is givn by th coss poduct c F }c. Thfo w can wit P b~c F c mc F c f Thus, if w know H, w can comput cama positions fo vy fam of th \R6F sunc, using only th fam-to-fam homogaphis H 3.4 Computing H : Aligning th al and vitual coodinat systms In od to coctly align th al and vitual coodinat systms, w nd to know th mapping btwn on imag plan and th wold plan. This mapping is spcifid by th plana homogaphy H, and may b dividd into mtic and poctiv componnts. Th mtic componnt fs 5F 5 5 JIiiiii iiiii 4

5 & c & JI JI & U to th abitay choic of Euclidan coodinats in th plan, and th ovall scal, which can nv b dtmind fom th imags alon. Th poctiv componnt concns th othogonality of th coodinat axs. W will dscib two ways of aligning th fnc fams. Th simplst way of stting th fam is to us th mous to slct 4 points on a ctangl in th scn [17]. Th fou points a thn assignd th wold coodinats of th ctangl, C, C,, wh is th (unknown aspct atio of th wold ctangl. Fo th momnt, assum. Witing ths points as m ] ], and with th cosponding mous-slctd coodinats dnotd m5] ], w may us th mthod dscibd abov to comput th homogaphy H which lats ths two sts of points, i.. ] 7 ] H ]. Now, bcaus w know, and obsving that th ffct of non-unit is to pmultiply th wold coodinats X Y by th diagonal matix D diag C w hav H H D c F c o F H cf!!, Thfo is givn by th atio of th lngths of th fist two columns vƒf of o F H. Thus, th algoithm is: 1. Comput H which maps th unit sua to m5] ]. 2. Comput ĈŠ. ˆŒ! 3. Comput H HDo F H diag F. Howv, it is inconvnint to spcify fou points in od to fix th coodinat fam. Th minimum possibl is two on to st th oigin, and th scond to indicat th diction of, say, th X axis and th ovall scn scal. This can b don in a singl mous gstu, wh th button down indicats th oigin, and th button las is at a point dfind to b on th wold plan. 3.5 Computing If th intinsic paamts of th cama a unknown, thy can b appoximatd by using two sts of paalll lins [6, 22] (.g. th ctangl in Np and fixing skw to 0, aspct atio to 1 and pincipal point to th cnt of th imag. W now show how to comput th focal lngth. b th vanish- Lt Ž * and m ing points of th sts of lins. As th dictions o F Ž and o F a othogonal, w hav Ž T o T o F, that is IJDE 5. which povids and hnc &. 3.6 Hand-off Th pvious discussion assums that th sam plan is bing tackd thoughout th sunc. Whil this may b fasibl in som situations, in many nvionmnts it is a sious limitation. Howv, it is asy to switch tacking fom on plan to anoth at any point, poviding both plans a sn simultanously in a minimum of two fams. This hand-off pocdu is lativly simpl. Imagin, fo conctnss, that w a tacking th gound plan in th plaza sunc. Aft som tim, th font wall of th building povs a mo liabl choic (s N 4.3. To automatically commnc tacking using th nw plan, w only nd to tansf th coodinat-systm alignmnt. This is asily don by andomly choosing th points on th nw plan, which a tackd ov two viws, O and, say. Call th points and thi cospondnts ] and ], fo z. Bcaus th unning (gound-plan tack is poviding P matics, w hav P U and P. Thn w can us standad sto tiangulation [16] to comput th 3D wold coodinats ]. Bcaus w hav wold coodinats of ], w can adily comput H nw, and continu tacking using th nw plan. Not that O and a not ncssay adacnt. In fact, O and should b fa apat, say th fist and last fams in which both plans w sn. 3.7 Incopoating off-plan tacks Anoth impovmnt to th systm is to allow individual points off th plan to b tackd, and includd in th motion stimat. Cuntly w implmnt this by using th plan-computd P matics to initializ a bundl adustmnt [7, 11]. In Figu 6 th camas w impovd by incopoating som two-viw cospondncs fom th obct silhoutt. 4 Implmntation Th pvious sction has discussd th thoy of planbasd tacking. W now povid som dtails of ou implmntation. Unsupisingly, a liabl imag-basd plan tack is th most impotant componnt of th systm. Luckily, plan tacking is a lativly asy poblm, and indd commcial systms a availabl which povid altim homogaphis fo liv boadcast [25]. 5

6 š Figu 4. Stps in th algoithm. (1 Th plan to b tackd is oughly indicatd with th mous, with th cama stationay. (2 Automatic fatu dtction and tacking. (3 Stting th coodinat systm by indicating 4 points on a ctangl. At no point aft (1 nd th cama b stationay, no tacking intuptd. 4.1 Robust computation of H \R6F Ou systm is basd on that dscibd in [16], using th succssful RANSAC paadigm. Consid two imags, with points in th fist lablld, and thos in th scond. Th pocdu is: 1. Dtct intst points in both imags. Ou implmntation uss public-domain cod fo th Hais con dtcto [15], fom Th two sts a Q U V UY X F and Q ] V X^ ] Y F. Typically, paamts a st so that about 500 cons a computd in th full imag, with popotionally fw in th tacking gion. 2. atch intst points: Fo ach point U, choos th point ] in th nxt fam which maximizs th coss-colation in a _ window. This gnats a st of cospondncs U Z ]. Typically, ach pixl is compad with 10 oths fo a maximum imag movmnt of 50 pixls. 3. Robust stimation of H: Fom th st of cospondncs, andomly sampl substs of fou Z pais. Fo ach sampl, comput H as in Np. Each candidat H is tstd against all th cospondncs by computing th distanc btwn and H. W choos th H fo which th most pais a within a thshold of say pixls. This pocss givs a valu fo H and a st of inli cospondncs. A nonlina minimization of poction o ov th inlis is found to significantly duc itt. 4.2 Initialization Th systm as cuntly implmntd uis that th plan b appoximatly spcifid bfo tacking commncs. Con dtction and matching a thn stictd to this gion, and whn th fam-to-fam homogaphy is computd, th gion is tansfomd to th nw imag. Ths stps can b impovd in \R6F a fw ways: (1 bcaus of th obust computation of H, th plan nd only b vy appoximatly indicatd; (2 ath than tansfoming th polylin bounday of th gion, w can gath all inlis to th homogaphy, and st th bounday to th convx hull of th 2D points. This will allow th gion to xpand and contact as ncssay though th sunc. 4.3 Automatic plan dtction Th RANSAC pocdu dscibd in Nu can b applid on th full imag, giving th homogaphy that cosponds to th lagst st of coplana points. Thfo, th initial indication of th plan can b omittd if th is only on plan in th scn, o if th lagst plan is th on w wish to tack. oov, this automatic plan dtction can b usd to choos th most liabl plan fo th hand-off pocdu. 4.4 Rliability issus Plan tacking of intst points has an impotant liability advantag ov tacking points undgoing gnal motion. In gnal motion tacking, th lationship btwn points in succssiv fams is dscibd by th fundamntal matix [9]. Fo a givn point in th fist viw, th cosponding point in th scond viw must li on 6

7 š š Figu 5. Augmntation sults, stanislas sua. Jitt and dift a sub-pixl ov this 40-fam sunc. F. Assum th imag hight is 500 pixls. If w consid, as an xampl, a cas wh th pipola lin is hoizontal and an accptanc thshold of œ pixls, thn 1% of andomly dtctd points will b viabl matchs fo. Fo homogaphy matchs, on th oth hand, th tansf is xact, so th cosponding point must li in a cicl of adius cntd on H, a gion which is only. of th imag aa. Thfo, ogu matchs a significantly lss likly fo homogaphy tacks. Th mao souc of o in th systm as dscibd is dift. Th is ffctivly zo itt, vn fo points fa fom th plan, du to th accuacy of homogaphis computd fom hundds of con fatus. On th oth hand, th pos fo ach nw fam is computd by multiplying th homogaphis fo ach of th pvious fams, so os will accumulat ov tim. Ths os can b amlioatd in a fw ways, but th most impotant is th matching of points fom th fist fam to fam O whnv possibl. This is simplifid bcaus th computd homogaphy H is availabl, ducing th sach gion. Howv, bcaus th will b significant pspctiv distotion btwn th two fams, it is ncssay to wap th imags using th homogaphy in od to comput th coss-colation scos. th pipola lin, gnatd by 5 Rsults Th sults of applying th poposd systm to th plaza sunc a shown in figu 5. In this cas, th gound plan was tackd, and a 3D modl supimposd on th sunc to valuat th gistation accuacy. Th movi sunc is availabl at vgg/isa/a.mpg. Th ad can notic that th is no pcptibl dift o itt. Th scond xampl, in figu 6, is an outdoo scn, with a hand-hld cama cicumnavigating a Hny oo sculptu. Th gass povidd sufficint txtu to tack th plan, thanks in pat to th inhnt obustnss of homogaphy tacking. Rgistation on this sunc is also good, with low itt, but dift of a fw pixls. 6 Discussion W hav psntd a maklss optical tack fo augmntd ality, which povids accuat and liabl sults fo scns which includ plana stuctus. Th nw mathmatical contibutions a th famwok fo uncalibatd plan tacking, and cama covy th fom. A pliminay implmntation yilds sults compaabl in accuacy with full stuctu-and-motion mthods but with btt liability. In addition, aligning th al and vitual coodinat systms is gatly simplifid by th idntification of th plan. Lik any vision-basd tack, ou systm will fail if th lighting conditions a unfavouabl, o th tackd plan gos out of viw. Howv, th nti plan dos not hav to b visibl at any tim, and th systm can mov fom on plan to anoth to maintain tacking. This maks it applicabl in a wid ang of nvionmnts. Of cous, a hybid systm would incas obustnss paticulaly in hand-off btwn plans which cannot b sn simultanously. Rfncs [1] A. J. Azabayani, B. Hoowitz, and A. Pntland. Rcusiv stimation of stuctu and motion using lativ ointation constaints. In Poc. CVPR, pags , [2] R. Azuma, J. W. L, B. Jiang, J. Pak, S. You, and U. Numann. Tacking in unppad nvionmnts 7

8 Figu 6. Augmntation sults, Hny oo. Jitt is sub-pixl, dift of th od of a fw pixls. Ths woks a poducd by pmission of th Hny oo Foundation. fo augmntd ality systms. IEEE Tansactions on Comput Gaphics, [3] P. A. Badsly, P. H. S. To, and A. Zissman. 3D modl auisition fom xtndd imag suncs. In Poc. ECCV, pags , [4] R. Bhing. Impoving th pcision of gistation fo augmntd ality in an outdoo scnaio by visual hoizon silhoutt matching. In Fist IEEE Wokshop on Augmntd Rality (IWAR 98, [5].-O. Bg, B. Wobl-Dautcout, S. Ptitan, and G. Simon. ixing Synthtic and Vido Imags of an Outdoo Uban Envionmnt. achin Vision and Applications, 11(3, [6] B. Capil and V. To. Using vanishing points fo cama calibation. IJCV, pags , [7] G. Coss, A. W. Fitzgibbon, and A. Zissman. Paallax gomty of smooth sufacs in multipl viws. In Poc. ICCV, pags , Sp [8] D. Dmnthon and L. Davis. odl Basd Obct Pos in 25 Lins of Cod. IJCV, 15: , [9] O. Faugas. What can b sn in th dimnsions with an uncalibatd sto ig? In Poc. ECCV, LNCS 588, pags Sping-Vlag, [10]. A. Fischl and R. C. Bolls. Random sampl consnsus: A paadigm fo modl fitting with applications to imag analysis and automatd catogaphy. Comm. AC, 24(6: , [11] A. W. Fitzgibbon, G. Coss, and A. Zissman. Automatic 3D modl constuction fo tun-tabl suncs. In R. och and L. Van Gool, ditos, 3D Stuctu fom ultipl Imags of Lag-Scal Envionmnts, LNCS 1506, pags Sping-Vlag, Jun [12] A. W. Fitzgibbon and A. Zissman. Automatic cama covy fo closd o opn imag suncs. In Poc. ECCV, pags Sping-Vlag, Jun [13] G. H. Golub and C. Van Loan. atix Computations. Th John Hopkins Univsity Pss, Baltimo, D, scond dition, [14] C. J. Hais and J.. Pik. 3D positional intgation fom imag suncs. In Alvy Vision Conf., pags , [15] C. J. Hais and. Stphns. A combind con and dg dtcto. In Alvy Vision Conf., pags , [16] R. I. Hatly and A. Zissman. ultipl Viw Gomty in Comput Vision. Cambidg Univsity Pss, ISBN: , [17]. Jthwa, A. Zissman, and A. W. Fitzgibbon. Raltim panoamic mosaics and augmntd ality. In Poc. BVC, pags , [18] D. oll,. Daniilidis, and H. H. Nagl. odl- Basd Obct Tacking in Taffic Scns. In Poc. ECCV, volum 588, pags , [19] D. oll, G. link, E. Ros, D. Bn, R. Whitak, and. Tucyan. Ral-tim vision-basd cama tacking fo augmntd ality applications. In AC Symposium on Vitual Rality, Softwa and Tchnology (VRST-97,

9 [20]. N. utulakos and J. R. Vallino. Calibation-f augmntd ality. IEEE Tans. on Visualization and Comput Gaphics, 4(1:1 20, [21] S. Lavau. Géométi d un systèm d P caméas. Théoi, stimation t applications. PhD thsis, IN- RIA, [22] D. Libowitz and A. Zissman. Combining scn and auto-calibation constaints. In Poc. ICCV, Sp [23] H. P. oavc. Towads Automatic Visual Obstacl Avoidanc. In IJCAI, [24] U. Numann, S. You, Y. Cho, J. L, and J. Pak. Natual fatu tacking fo augmntd ality. IEEE Tansactions on ultimdia, 1(1:53 64, a [25] Pincton Vido Imag. Poduct showcas, [26] S. Ravla, B. Dap, J. Lim, and R. Wiss. Tacking Obct otion Acoss Aspct Changs fo Augmntd Rality. In ARPA Imag Undtanding Woshop, Palm Sping (USA, Aug [27] G. Simon and.-o. Bg. A two-stag obust statistical mthod fo tmpoal gistation fom fatus of vaious typ. In Poc. ICCV, pags , [28] R. A. Smith, A. W. Fitzgibbon, and A. Zissman. Impoving augmntd ality using imag and scn constaints. In Poc. BVC, pags BVA Pss, [29] D. Stick, G. link, and D. Rins. A fast and obust lin-basd optical tack fo augmntd ality applications. In Fist IEEE Wokshop on Augmntd Rality (IWAR 98, [30]. Unohaa and T. anad. Vision basd obct gistation fo al tim imag ovlay. Jounal of Computs in Biology and dcin, [31] G. Wlch and G. Bishop. SCAAT: Incmntal tacking with incomplt infomation. In Poc. AC SIG- GRAPH,