ROAD SURVEY BY KALMAN FILTER RECTIFICATION OF IMAGE SEQUENCES ACQUIRED WITH A MONOSCOPIC LOW-COST MMS

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1 OAD SUVEY BY KALMAN FILE ECIFICAION OF IMAGE SEQUENCES ACQUIED WIH A MONOSCOPIC LOW-COS MMS Domenico Visinini Deparmen of Georesources & erriory, Universiy of Udine, via Coonificio, 4 I-3300 Udine, Ialy domenico.visinini@uniud.i KEY WODS: Sequences, Dynamic, Orienaion, Maching, ecificaion. ABSAC his paper proposes a mehod for a mosaic digial represenaion of a road by means of a Kalman filer based recificaion of a monoscopic image sequence acquired wih a low-cos MMS wihou INS sensors. he fronal images of he road acquired by a poining ahead-down camera are recified ono he road surface by means of a homographic ransformaion among image and ground planes. As basic idea, he exernal/homographic parameers consiue he unknown sae vecor of a Kalman filer pseudodynamic model, describing is evoluion wih respec o he covered disance, wih observaion equaions given from image coplanariy and collineariy condiions and GPS kinemaic measures. o make easy he relaive orienaion among images, an original Kalman filer maching is exploied: once seleced some lane rac poins in he firs image, he homologous poins in he second image are so auomaically deeced. Exploiing only near poins in he lower par of he images, a high-scale opical model wih a srong geomerical consisency is achieved: herefore, a reliable recificaion of he image sequence can be expeced. his mehod has been implemened in a Malab language program making possible he recificaion of he image sequence by a digial resampling wih auomaic mosaicking ono finie planes modeling he road surface. Firs numerical experimens wih real daa of our MMS prooype have given saisfacory resuls here described and analyzed.. INODUCION In hese lass years, he phoogrammeric survey echnology by means of a Mobile Mapping Sysem (MMS), ha is erresrial vehicles equipped wih GPS, INS, CCD on oher inegraed sensors, presens an increasing developmen and ineresing applicaions, mainly o 3D-survey he geomery and he pavemen characerisics of roadways. his advanced echnique, involving compleely differen measuring sensors (saellie, inerial, odomeer, imaging, ec), is characerized by los of analyical, mehodological, and echnological sub-aspecs. Obviously, his paper only briefly hins o some of hem: he ineresed reader can invesigae in deph wihin he wide available lieraure. One can sar jus from he proceedings of he previous Inernaional Symposiums on Mobile Mapping echnology (Ohio Sae Universiy, 995; Li and Murai, 999; El-Sheimy, 200; ao, 2004) and from he recen volume of ao and Li (2007). As general expecaion on he echnology, knowing he high level of echnological insrumens and analyical models involved in acquiring and processing MMS daa, a high efficiency survey in erms of correcness, accuracy, reliabiliy, compleeness, and produciviy is realisically expeced. his work of his paper fis in he philosophy of our researches ( ) devoed o envelop/asses a simplified MMS equipped wih only one CCD camera, a GPS receiver, an odomeer, bu wihou INS sensors (secion 2). he so-called coplanariy condiion, linking homologous poins of successive images, is he essenial analyical ool o acually achieve a survey wih such low-cos MMS (secion 3) he exernal/homographic parameers consiue he unknown sae vecor of a Kalman filer pseudo-dynamic model, describing is geomeric evoluion in he sequence (secion 4). For he orienaion problem (subsecion 4.), he filer sae equaions are obained by means of cubic spline funcions. he updaing observaions are mainly provided from image coordinaes of homologous road lane poins in successive images. Oher wo kinds of observaions are used: kinemaic GPS measures acquired in he sho insans and, if repored in a digial map, road edge corner submied o he collineariy condiion among image and carographic coordinaes. Also a maching Kalman filer based is applied (subsecion 4.2): once seleced some lane poins in he firs image, he homologous poins in he second one are auomaically found. hus for each couple of images, he orienaion and he maching problems are recursively and dynamically solved (secion 5). Using only poins in he lower par of he images, far o he vanishing poin, a high-scale opical model wih srong geomerical consisency is achieved. he fronal images of he road acquired by a poining aheaddown camera are recified ono he road surface by a homographic ransformaion among image and ground planes (secion 6). hanks o he implemenaion in Malab language, he image lower pars are recified ono a horizonal plane by a digial resampling wih auomaic mosaicking. wo real CCD image sequence have been processed and recified wih encouraging numerical resuls (secion 7). 2. SUVEYING WIH A SIMPLIFIED MMS As well-known, he 3D surveying of every poin placed wihin a road can be done by means of he MMS sensors hanks o he below hree seps of coordinae ransformaions:. oaion and ranslaion from a given mapping frame o he GPS/INS frame, by means of he posiion and aiude measured by GPS/INS pos-processing echniques. 2. oaion and ranslaion from he GPS/INS-frame o each CCD frame, by means of he posiion and aiude parameers suiably measured in he MMS calibraion. 3. everse projecion (space resecion) from, a leas, wo differen CCD frames o he poin posiion, by means of digial phoogrammeric echniques. Inside of his echnology of surveying, our research group has developed an original analyical model o deermine he

2 exernal orienaion of he CCD frames, i.e. o simulaneously solve he seps. and 2.. I exends he usual direc mehod (e.g. El-Sheimy, 996) GPS/INS measuremens based, since he CCD posiion and aiude is also achievable by an indirec mehod. In fac, his radiional phoogrammeric process makes use of an image sequence also for he orienaion and no only for he 3D-surveying, well displayed from he aerial riangulaion procedure. Moreover his MMS configuraion has low coss since, in principle, GPS/INS sensors are no required. In order o fix he ideas, in our researches we have ried o envelop and assess a simplified low-cos monoscopic MMS wih only one CCD camera, a GPS receiver, an odomeer, bu wihou INS sensors. his choice has some operaive drawbacks o overcome by proper analyical echniques. In his sense: he requiremen of sacks of conrol poins along he roue can be avoided if 3D digial map poins are available; he influence of he precision of such poins on he image orienaion accuracy can be handled wih a mixed model of esimaion and predicion (Dermanis, 990); he no opimal esimaion by classical (saic) analyical models can be replaced by a Kalman filer pseudodynamic model for a compuaionally efficien process. 3. COPLANAIY CONDIION FO A SIMPLIFIED MMS hroughou his secion, i is explained how he so-called coplanariy condiion, involving homologous poins of wo consecuive images, is exremely precious o acually carry ou he surveying wih a monoscopic low-cos MMS wihou INS. Figure. Firs and second image of a monoscopic sequence. Le consider a firs image acquired a he insan and a second one acquired a he (+) one, as hose fronally acquired wih a poining ahead-down camera in our experimens and repored in Figure. he following equaion saes he coplanariy condiion beween he wo 3D segmens joining each sho poin wih he corresponding image poin (see e.g. Crosilla and Visinini (998) for he analyical proof): χ + q + = 0 () Equaion () gahers ogeher, in is wo erms, he image coordinaes wih he orienaion parameers, in fac: χ+ = [ x+ x x+ y x + y+ x y+ y y + x y ] is one row (for each couple of homologous poins) of a nine column marix, wih x, y,x +, y + normalized image coordinaes ono he CCD consecuive frames; q + is a nine row vecor obained by sacking he rows (and ransposing) of he marix Q + involving he exernal orienaion image parameers as: Q + x, y = + 0 H+ + H N+ N H E + x +, y H + E N+ + N E+ E 0 where and + = [ E N H ] are he CCD roaion marices, while r and r [ N H ] + = E are he coordinaes of he CCD posiions, each one in he wo respecive sho insans. I should be now clear as equaion () is fundamenal for a monoscopic MMS wihou INS: i conains eiher image coordinaes or orienaion parameers of successive frames of an image sequence. By means of (), i is indeed possible o solve: Exernal orienaion problem : if r, are known (ha is he firs image is oriened) and x, y,x +, y + are measured, he exernal orienaion r +, + of he second image can be esimaed, simply by considering enough homologous poins in he equaion (). Epipolar maching problem : if insead r,, r +, + are known (ha is boh images are oriened) and x, y are chosen, a relaionship (epipolar line) joining ogeher he image coordinaes x +, y + of he homologous poin can be achieved saring again from equaion () and suiably exploiing i o auomaically find such a poin. In more deail, o esimae he exernal orienaion parameers E +, N +, H +, ω +, φ +, κ + of he second image, i is no difficul o rerieve some homologous poins o direcly apply he equaion (), may be raher a problem o auomaically find hem! From he geomerical poin of view, he coplanariy condiion allows he relaive orienaion wih respec o he already exernally oriened firs image. his is exacly he same conribuion given from he INS gyros and acceleromeers, if used wihou GPS geomerical consrains. Also for our orienaion, he accuracy decreases for he drif effec as long as we use images wihou any conrol poin consrain. For he epipolar maching problem insead, equaion () has o be rewrien for a couple of homologous poins using pixel values relaing o he emplae and pach window cenres ( and P) involved in such a problem. In his way, i becomes a P k, : sraigh-line equaion of (epipolar) consrain on [ ] P h P D h P = k P + ( Nxc Dyc + C) N Nλ (2) = x ( q ) + y ( q ) ( q N ) 3 D = x ( q + ) 4 + y ( q + ) 5 ( q + ) 6 C = x ( q + ) 7 + y ( q + ) 8 ( q + ) 9 x x0 c c = normalized coordinaes of he pixel frame origin along x-direcion; yc = y0 c normalized coordinaes of he pixel frame origin along y-direcion; λ = 25,4 c r image scale-facor [/pixel], where r is he image sensor equivalen resoluion [dpi]. I mus be sressed ha, working wih a simplified MMS, a reliable area based image maching procedure is pracically mandaory. In fac, a lo of homologous poins have o be deeced on successive images and used for phoogrammeric and no inerial relaive (exernal) orienaion. Once he user has chosen a poin in he firs image, he auomaic poin deecion of he homologous poin P in he second image is hen essenial o acually achieve his alernaive orienaion, wihou increase o much he user job for he poin collimaion.

3 4. DYNAMIC ANALYSIS OF AN IMAGE SEQUENCE BY KALMAN FILES MODELS Explained in he previous secion he basic geomery of a monoscopic image sequence, here he algorihmic soluions of he orienaion and maching problems are described. As main concep, he unknowns of hese problems consiue sae vecors of specific Kalman filer models (Visinini, 200c), describing heir geomerical evoluion insead of he emporal one, as usually done in processing dynamic phenomena. In addiion, since he orienaion of each image pracically solves he problem of is recificaion by a homography, as will be explained in secion 6, he Kalman filer soluion of he orienaion parameers implicily regards he homographic ones. 4. Kalman filer orienaion of an image sequence o obain he exernal orienaion parameers of he second CCD image acquired a (+) ime: x + = [ E+ N+ H+ ω+ φ+ κ+ ] considered as a sae vecor, a Kalman filer model has been applied (Visinini, 200c). Since he MMS moion has a regular rajecory (in local sense) wih an irregular course (in global sense), a ransiion marix Φ describing approximaely he evoluion of x can be suiably obained. he filer sae equaions are in fac achieved by applying cubic spline funcions on he Eas, Norh and Heigh coordinae of poins in a carography approximaely describing he MMS roue (Crosilla and Visinini, 998). he linearized form of he sae equaion is hen: δ x + = Φδx + µ + wih µ + N ( 0, Θ + ) (3) hree kinds of linearized observaions are exploied:. Image coordinaes l of couples of homologous poins (e.g. he road lane corners) visible in successive images submied o he coplanariy condiion (), here rewrien as: { x l } C x + D 0 h δ (4) +, + + v = 2. Image y 2 and absolue X coordinaes of visible 3D map poins submied o he well-known collineariy condiion: { x X} C 2 x + E2s v 2 g +, + δ + + (5) 3. CCD frame coordinaes m obained by kinemaic GPS gps measures and aking ino accoun known eccenriciy a ccd gps and roaion ccd beween CCD and GPS frames: { + } + C3δx v 3 r gps m x + + (6) h x l, g x, X m equaions values compued { } { } { } +, +, x + wih an approximaed value x + ; C D, C2, E2, C3, parial derivaives marices of he equaions wih respec o he unknowns x + and s; s prediced coordinae incremens of 3D-map poins, saring from he sochasic values X of he digial mapping. Gahering equaions (4), (5) and (6) ogeher, he following observaion sysem can be wrien: h = y rgps b + = Cδ x + + Es + Dv (7) { x +, l} g{ x + X} m{ x } b + 2, + C C = C2 C3 0 E = E 2 0 v D 0 D = v = 0 I v2 v3 Finally, he Kalman filer ieraive soluion of sae (3) and observaion (7) equaions gives ou he predicion of he image exernal orienaion parameers as: ~ ~ + = Φx + K + b + x (8) Q ) δ x = Θ ΦQx Φ = Q ) x+ Qb = DQ D EQ E CQ v + XX + ) + δx+ + = Qδx C Q + b + K ) Kalman gain marix Discerning his analyical orienaion model, i can be defined as an indirec & direc mehod since i explois for he goal eiher indirecly image coordinaes or direcly GPS orienaion parameers. From he phoogrammeric poin of view, he available 3D map poins submied o he collineariy condiion (5) only opporunely fix he daum of he opical model consiued by he image sequence. his las is mainly buil hanks o coplanariy condiion (4) and, using a lo of homologous (whaever) poins, he resuling opical model has a srong geomerical inernal (relaive) auo-consisency. Furhermore, he exploiing of road poins near o he MMS and far from he vanishing poin warrans a very high 3D-accuracy. Concerning insead absolue accuracy, a fine benefi is assured from he mixed model (Dermanis, 990) applied for he unknowns in he equaions (5) and (7). I allows simulaneously he orienaion esimaion and he predicion of 3D-coordinaes saring from sochasic values sored in map. In such a way, also for exernal orienaion, he high scale of MMS images is well exploied, enforcing he opical model ono more precise 3D poin posiions, keeping ino accoun he GPS consrain (6). 4.2 Kalman filer maching in an image sequence o exploi he coplanariy-epipolariy condiion for he maching problem also if he exernal orienaion parameers are no available in equaion (2), a Kalman filer approach has been again pursued (Visinini, 200a). In his way, we ake advanage of he epipolariy conribuion in whaever condiion, even o auomaically find homologous poins o exernally orien he second (no oriened) image! ha is mahemaically possible inroducing in equaion (2) he approximaed orienaion values compued by he cubic spline funcions, as jus described in subsecion 4.2. Anyway, for he pseudo-dynamic soluion of he maching problem, he incremenal sae unknowns are alernaively: κ = δk = k k wih κ N(0, Σk ) η = δh = h h wih η N(0, Σ ) k = [ a b c] h = [ d e f ] C h

4 wih a, b, c, d, e, f, affine ransformaion parameers from he emplae o he pach window cenered on he homologous poins and P. he incremenal sae unknown is hen a hree row vecor κ swiching in η (and again in κ) during he ieraions and conaining hree of he six coefficiens of he affine geomeric window ransformaion. he maximum likelihood condiion on every pixel grey-values of he emplae and pach windows yields o he following linearized alernae sysems of observaion equaions: wih: r 0, r b = Aπ + Eη + v (9.) b = Aπ + Fκ + v (9.2) [ r0 + rg ( ai + bj+ c,di + ej f )] p, k h b = f ( i, j) + +, π = δp = p p wih π N(0, Σ ) p = [ r ] 0 r : radiomeric ransformaion parameers on greyvalues from he emplae o he pach window; A, E, F: parial derivaive marices of he grey dispariy respec o he p, h and k maching unknowns. As menioned before, he epipolar line obained from equaion (2) can be more or less correc depending from he orienaion values accuracy of r +, +, and also, wihin he same image couple, can be ruhful for a poin and unruhful for anoher one. For such reason, he equaion (2) has o be handled in sochasic way, exploiing i as a sae equaion, so o ake ino accoun possible errors in he sraigh-line coefficiens. he following alernae sae equaions in he η,κ vecor space have been suiably obained, wih very simple ransiion marices: D η = I κ + ν η wih ν η ~ N (0, Σ ) (0.) N νη N κ = I η + ν κ wih ν κ ~ N (0, Σ ) (0.2) D νκ he Kalman filer ieraive soluion of he sae (0.) and observaion (9.) equaions gives now: [ A Q A] ˆ p = p + πˆ = p + b A Qb b (.) ~ h = h + ~ η = h + G η[ b Aπˆ ] (.2) 2 Q ) D Q Q = Q ) η = νη + 2 κ h N Qb = Qv + EQ ) ηe G η = Q) ηe Qb Kalman gain Every sep done for vecor η can be exacly redone o predic vecor κ and esimae again vecor π by exploiing now equaions (0.2) and (9.2) wih soluions analogous o (). Once his new predicion is carried ou, an updaed value of he firs unknown becomes available for a second predicion ~ η of η (or ~ κ of κ). Such recursive predicions will be hus repeaed p as long as he soluion convergence is saisfied. he pach cenre P hence alernaively ranslaes along rows or columns only (as a saircase series), bu saying in he epipolar line surroundings, unil he final posiion is reached. he saisfying numerical resuls in maching CCD image sequences acquired by our simplified MMS are described in Visinini (200b). 5. FLOW CHA OF HE DYNAMIC ANALYSIS OF AN IMAGE SEQUENCE In he flow char of he dynamic analysis () of a sequence of n CCD images, le consider now having o orien he (s+)-h image, operaion possible once he previous s-h image has been already oriened. he spline orienaion values of he ransiion marix in (3) are now beer of hose compued via a mapping, since he firs s sho poins have been exacly evaluaed ye. In his way, he cubic spline inerpolaion will beer inerpolae he remaining n-(s+) poins he more (s+) leans o n. Following he flow char repored in Figure 2, once a firs poin (emplae cener) has been manually seleced in he s-h image:. he Kalman filer maching compues by () he h, k and p unknowns, namely auomaically exracs he homologous poin (pach cener) in (s+)-h image. 2. he Kalman filer orienaion uses he so found couple of homologous poins as coplanariy observaion and compues by (8) he x + unknown exernal orienaion. MACHING POBLEM OIENAION POBLEM homologous Iniial value Prediced value Iniial value Prediced value poin for κ,η for κ,η for r +, + for r +, + s poin by epipolar line maching of spline values relaive orienaion x P,y by spline values s poin P by poin 2nd poin by epipolar line maching of s poin relaive orienaion x P,y P by s poin sol. 2nd poin soluion by 2 poins 3rd poin by epipolar line maching of 2nd poin relaive orienaion x P,y P by 2nd poin sol. 3rd poin soluion by 3 poins 4h poin by epipolar line maching of 3rd poin relaive orienaion x P,y P by 3nd poin sol. 4h poin soluion by 4 poins Figure 2. Flow char for he maching and orienaion problems. Seps. and 2. are repeaed for a second, a hird, and so on poin, bu each ime wih beer improved orienaion approximaed values x + as well as a new poin is inroduced. In his way, each ime he Kalman filer esimaions and predicions eiher for he maching problem or orienaion one will be numerically more sable (for his reason he green coloring grows in Figure 2). Moreover, inroducing a new poin, he soluions will require each ime a smalles number of ieraions, since he sochasic conribuion of he sae equaions becomes bigges wih respec o he observaion ones. Of course, when he search of homologous poins among s-h and (s+)-h images and he exernal orienaion of he (s+)-h image have been solved, he dynamic analysis involves he following (s+2)-h image and is homologous poins, and so on unil o orien he las n-h image. Summarizing, he maching and orienaion pseudo-dynamic problems are sricly correlaed ogeher and can be here preferred he comprehensive expression of maching for he orienaion as he global aim of he dynamic analysis. emembering ha image orienaion means, de faco, image

5 homographic recificaion, he global dynamic analysis here described involves all he sequence issues. In spie of his, he exernal orienaion of he whole MMS image sequence makes clearly possible o compue he r i posiion of each poin of our ineres. Using precise known map poins and/or GPS daa ensure bes accurae exernal orienaion r, and off course bes accurae coordinae r i, given by: pix i r Si ri r = + (2) Equaion (2) considers a reverse projecion from, a leas, wo differen images, bu in his form i considers pixel coordinaes pix r i of one image and a poin-varying image scale value S i : in ruh, his value is only implicily compued during he phoogrammeric space resecion compuaions. 6. ECIFICAION OF IMAGE SEQUENCES hroughou he previous secions he concep of he Kalman filer orienaion of monoscopic images has been shown: now he paper philosophy of he digial recificaion of such fronal images is finally delineaed. As firs general consideraion, his 2D or 2,5D raser represenaion is characerized by a fully auomaion in is producion and such a reason makes his kind of oupu more popular hen a 3D vecor represenaion. o obain a phoo-mosaic of images orho-projeced or recified, one has o know (for each image): he image exernal orienaion, aained as shown up o now; he surface reconsrucion, i.e. he Digial Surface Model (DSM) for complex geomery requiring differenial recificaion (orhophoo) or jus he plane displacemen for simples case (recificaion). In any case, geomerical informaion abou he surface where remap (exurizing) he images has o be known and hese daa have o be acquired in some way by means of, in order of complexiy, opographic, phoogrammeric or (oday grealy emerging) laser scanning surveying. A par mehodological and pracical reasoning abou inegraion of survey echniques, here he alone MMS phoogrammeric echnology and he image projecion ono he road surface are only considered, sending for example o Visinini (2003) for he projecion over he façades of he buildings facing he road. In his conex, he geomery of he road surface can be modelled wih DSMs of differen levels of deail and accuracy, anyway keeping in mind ha such a DSM has o be defined in he same (mapping) reference frame of he MMS image sequence. In oher words, he relaive congruence among CCD image and road surface has o be fixed, ha is a sor of relaive orienaion beween he image plane and he road surface. Equaion (2) can be applied o measure a cerain number of 3D poins allowing building he road DSM in form of a riangular Irregular Nework (IN) more or less deailed wih verexes in such a poins. However, he qualiaive shape of a DSM of a road is generally a quasi horizonal plane. In any case, he projecion over his DSM is formally a mosaicked orhophoo. Some simplifying hypohesis can be however done, as ha he road surface is composed by wo planes slaning of some from he axis owards he borders, so defining a riangular secion according o he consrucive requiremens. his is he shape for recilinear road rac, varying in he clohoid up o a unique ransversal inclinaion in a bend rac. In his way, he image projecion is simplified as a recificaion ono hese planes. In oncella and Forlani (2006) he furher simplificaion of a road surface as a unique plane is no recommended since his can inroduce up o decimeric errors. As definiive working hypohesis, in his paper we consider o recify each monoscopic image of he sequence over a small plane consiued from he par of he road acquired jus in fron of he MMS, being or no his plane ransversally slaning. he road is hen a sor of mosaic of finie planes. Neverheless, i mus be recalled as he raser represenaion of a road survey is anyway done ono a horizonal plane. his means, as ulimae working assumpion, ha i is sufficien o share each image projecion over differen planes, e.g. one for he righ rack and one for he lef one. o finally perform such projecion-recificaion a homographic ransformaion is applied beween wo planes (Harley and Zisserman, 2000): in roboic vision lieraure i is known as inverse perspecive mapping (Mallo e al., 99) and i is applied for boh racks since he goal is no a precise surveying bu he obsacle deecion insead (e.g. Berozzi and Broggi, 998). Our fronal images of he road acquired by a poining ahead-down camera are hen resampled according o: a x b y c E = u x + v y + a x b y c N = (3) u x + v y + where he eigh parameers of he homography are expressed as combinaions of he six parameers of he image exernal orienaion as follows: a = ( H E ) c 3 wih: 33 b = c 33 = E ( H E ) c 33 H a = 2 c b = 2 33 c H 22 N c = N 2 H 33 u v = = ( H N ) c c = cos φ = cos ω = sin ω = ( ) cos φ = cos ω = sin ω = sin φ = sin ω = cos ω + sin ω cos ω cos φ cos φ sin ω + cos ω sin φ sin φ sin φ sin φ

6 hanks o hese relaionships, each exernally oriened MMS images can be direcly recified ono horizonal planes composing he road surface, wih he H value defined in ruh as he elevaion of he CCD wih respec o he road plane, moreover pracically consan during he MMS surveying. his mehod has been implemened in a Malab language program, exploiing in paricular he funcions makeform and imransform of he Image Processing oolbox. Once solved he analyical problem by equaion (3), he recificaion of he image lower pars is so accomplished by a digial resampling wih auomaic mosaicking. From he numerical poin of view, he analyical parameers of equaion (3) are suiably convered in oher ones for he resampling, since he i,j pixel coordinae sysem is a clockwise and poining down frame. 7. NUMEICAL APPLICAION Here are repored firs numerical applicaions of he mehod proposed in his paper, considering image sequences dynamically acquired wih a Fuji FinePix F700 CCD camera (2.832x2.28 pixel, 35 mm equivalen focal lengh) in he parking area of he Sadio Friuli in Udine (Figures 3). Such wide area is composed from grids of opposie parking seas wih significan conrary slopes, visible in he lanes in Figure 3 a lef. In his way, such area well simulaes a recilinear way if roued orhogonally o he parking seas, where he parking spliing lane sands for he cenral (axial) lane of a cerain road. Figure 3. Lef, he area of he es, only roughly horizonal; righ, an irregulariy of he asphaling in elevaion and in slope. Figure 4. From he hird o he eighh image of a monoscopic sequence acquired by a recilinear rajecory. Unforunaely, he road pavemen presens an imperfecion due o a sep edge of some millimeres in he asphaling in he righ rac (Figure 3 a righ). he levelling apparaus shows how he pavemen does no slan owards he righ exernal border bu in he opposie lef direcion. his means an unconvenional ransversal secion jus in he rack roued by our simplified MMS, whose consequence in he image recificaion will be shown aferwards. Anyway, his free area allowed o compleing wihou resrain also a second curved MMS rajecory in he same framework. he firs experimen involves eigh fronal poining down images acquired wih a mean inerval of 5 m during a recilinear surveying roue from a heigh of abou 2,35 m wih respec o he road surface. Images from he hird o he eigh compose Figure 4, while he firs wo images are displayed in Figure. In able 5 he six exernal orienaion parameers are repored wih E, N, H locally referred, while able 6 repors he eigh homographic parameers resuling form equaions (3). image E [m] N [m] H [m] ω [g] φ [g] κ [g] 6,986-3,053 2,380 72,772,800-4,79 2 6,838,8 2,36 72,356-0,45-4, ,776 6,767 2,396 73,283 2,534-5, ,828,793 2,374 7,68 2,90-6, ,84 6,65 2,362 72,788 3,09-5, ,88 2,65 2,358 72,50 2,77-5, ,906 26,670 2,345 70,850 3,696-6, ,92 3,74 2,357 7,56 3,53-5,92 able 5. Exernal orienaion parameers of he image sequence. a image [m/pix] b [m/pix] c [m] a 2 [m/pix] b 2 [m/pix] c 2 [m] u [/pix] v [/pix] 2,39e-03-5,03e-03 6,82-2,e-04 3,07e-03-3,22 6,54e-05-7,40e ,23e-03-4,85e-03 6,85 3,05e-05-5,22e-04,82 4,92e-05-7,29e ,54e-03-4,94e-03 6,54 5,52e-04-4,30e-03 6,53 8,8e-05-7,55e ,4e-03-4,54e-03 6,58,00e-03-7,35e-03,5 8,53e-05-6,92e ,50e-03-4,86e-03 6,54,43e-03 -,5e-02 6,3 8,5e-05-7,40e ,43e-03-4,8e-03 6,58,70e-03 -,50e-02 2,4 7,82e-05-7,30e ,38e-03-4,55e-03 6,60 2,28e-03 -,74e-02 26,4 8,50e-05-6,83e ,4e-03-4,69e-03 6,65 2,62e-04-2,5e-03 3,5 8,4e-05-7,03e-04 able 6. Homographic parameers of he same image sequence. I can be numerically noiced how, for heir definiion and dimensionaliy, c, c 2 coefficiens have a magniude order many imes higher ha he ohers; furhermore all he c values are pracically consan as E are, while c 2 coefficiens grow according o increasing values of N. he images have been herefore recified ono wo planes, one for each rac, assuming a 2,5 ransversal slope owards he exernal. In ruh, he MMS rajecory was pracically cenred on he righ porion of he parking area, neverheless a small par of hen depics also he lef side. By means of he inverse perspecive mapping he recangular images become rapeze shapes on he road, recovering he rue surface geomery, e.g. he orhogonaliy among he lanes (Figure 7): he proposed mehod correcness is hence qualiaively proved. If we observe again Figure 7, i can be seen also he good congruence of he resuling auomaic mosaicking, of course beer for he par near o he MMS and worse for he far ones involving he vanishing poin. he misakes in he digial reconsrucion near o he cenral lane are due o he sep edge irregulariy previously remarked: his is essenially he well-known planimeric effec of a heigh error in he modeling of he surface o be remap.

7 Figure 7. Mosaic of he second, hird and fourh recified image. he final global mosaic is repored in Figure 8, wih images lowes par depicing he car covered from he image before: he recified areas are highlighed in Figure 6 by yellow do lines. Figure 9. From he firs o he eighh image of a monoscopic sequence acquired by a curved rajecory. Figure 8. Mosaic of eigh recified images. he second experimen regards insead a curved rajecory, having roued a righ-lef bend over he same area (Figure 9). Figure 0. Mosaic of sixeen recified images.

8 Figure 0 is he alogeher mosaic of he sixeen recified images, showing again a good geomerical congruence (a par he shadow of he illuminaion pole consiuing a meridian angularly reporing he ime beween he acquisiion of he firs image sequence and he second one!). Summarizing he road surveying obained in hese firs numerical experimenaions, we can sae is general likelihood, posponing o nex fuure he necessary saisical evaluaions abou he achieved values for accuracy and reliabiliy, sharing he effecs resuling from he homographic parameers o hose due o he road surface modeling. 8. CONCLUSIONS his paper proposes an original mehod for a mosaic digial represenaion of a road by a Kalman filer based recificaion of monoscopic images acquired wih a poining ahead-down camera wih a low-cos MMS. o his goal, he image sequence is oriened mainly exploiing image coordinaes submied o classical phoogrammeric equaions as he coplanariy and collineariy condiions. In addiion, a maching procedure applying anoher Kalman filer is exploied o improve he auomaion of he relaive orienaion among he successive images. Exploiing only poins in he lower par of he images, i.e. near o he MMS, a high-scale opical model is achieved. he image recificaion requires eiher image orienaion parameers or geomerical informaion abou he surface o be projeced: for he second aim, i is sufficien o share he road pavemen in finie planes, one for he righ rac and one forh he lef rac for each image. egarding insead he image orienaion, he six exernal parameers univocally deermine he corresponding eigh homographic ones. he numerical experimens in he processing of real CCD image sequences wih a Malab rouine implemening his mehod are qualiaively saisfying, alhough quaniaive analyses have o be carried ou as soon as possible. As possible developmen of his research, he Kalman filer sae vecor could be direcly consiues from he eigh homographic parameers, bu he derivaion of he corresponding sae equaions from he image sho coordinaes and aiude angles, no rivial from he analyical poin of view. In paricular geomerical condiions, e.g. a perfec plane surface where he sho direcion is more consrained or can vary only in azimuhal sense, as happens for indusrial applicaions and in roboic vision. In his case, some homographic parameers remain consans or i is easier o analyically derive he predicion of heir evoluion. EFEENCES Berozzi, M., Broggi, A., 998. GOLD: a parallel real-ime sereo vision sysem for generic obsacle and lane deecion. IEEE ransacions on Image Processing, 7 (), pp Crosilla, F., Visinini, D., 998. Exernal orienaion of a mobile sensor sysem for carographic updaing via dynamic vision of digial map poins. Bolleino di Geodesia e Scienze Affini,, Isiuo Geografico Miliare, Firenze, pp Dermanis, A., 990. Modeling and soluion alernaives in phoogrammery. In: Proceedings of he ISPS ICWGIII/VI uorial Mahemaical aspecs of daa analysis, hodes, Greece, pp El-Sheimy, N., 996. he developmen of VISA - A Mobile Survey Sysem for GIS applicaions. PhD hesis, Universiy of Calgary, Dep. of Geomaics Engineering, Canada, 79 pp. El-Sheimy, N., (ed.), 200. Proceedings of he 3rd Inernaional Workshop on Mobile Mapping echnology, Cairo, Egyp (on CD). Harley,., Zisserman, A., Muliple view geomery in compuer vision. Cambridge Universiy Press, Cambridge, 496 pp. Li,., Murai, S., (eds.), 999. Proceedings of he 2nd Inernaional Workshop on Mobile Mapping echnology, Bangkok, Asian Insiue of echnology, Pahumhani. hailand. Mallo, H.A., Bülhoff, H. H., Lile, J.J., Bohrer, S., 99. Inverse perspecive mapping simplifies opical flow compuaion and obsacle deecion. Biological Cyberneics, 64, pp Ohio Sae Universiy (ed.), Mobile Mapping Symposium. Proceedings of he s Inernaional Workshop on Mobile Mapping echnology, Columbus, Ohio, American Sociey of Phoogrammery & emoe Sensing, 274 pp. oncella,., Forlani, G., Auomaic lane parameers exracion in Mobile Mapping sequences. In: Proceedings of he ISPS Commission V Symposium, Dresden, Germany, IAPS&SIS, vol. XXXVI, 5, 6 pp. (on CD). ao, V., (ed.), Proceedings of he 4h Inernaional Symposium on Mobile Mapping echnology, Kunming, China, (on CD). ao, V., Li, J., Advances in Mobile Mapping echnology. ISPS Book Series, vol. 4, aylor & Francis, London, 9 pp. Visinini, D., 200a. A Kalman filer based maching for a MMS image sequence. In: Proc. of he 3rd Inernaional Symposium on Mobile Mapping echnology, Cairo, Egyp, 4 pages (on CD). Visinini, D., 200b. esing a dynamic algorihm for image maching in a CCD sequence acquired by a low cos MMS. In: Proceedings of he Ialy-Canada Workshop on 3D digial imaging and modeling applicaions, Padua, Ialy, 8 pp. (on CD). Visinini, D., 200c. A simplified mobile mapping sysem for 3D-measuremens via image sequence dynamic analysis. In: Proceedings of he 5h Opical 3-D measuremen echniques Conference, Vienna, Ausria, pp Visinini, D., High-efficiency building surveys by dynamic and saic digial images oriened wih mixed models. In: Proc. of he ISPS WG V/4 and IC WG III Workshop on Vision echniques for digial archiecural and archaeological archives, Ancona, Ialy, IAPS&SIS, vol. XXXIV, 5/W2, pp ACKNOWLEDGEMENS his work was carried ou wihin he research aciviies suppored by he INEEG IIIA Ialy-Slovenia projec Cadasral map updaing and regional echnical map inegraion for he GIS of he regional agencies by esing advanced and innovaive survey echniques.