Recursive 3D Model Reconstruction Based on Kalman Filtering

Transcription

1 SMB-E Recursve 3D Model Reconsrucon Based on Kalman Flerng Yng-Kn YU Kn-Hong WONG and Mchael Mng-Yuen HANG Absrac A recursve o-sep mehod o recover srucure and moon from mage sequences based on Kalman flerng s descrbed n hs paper. he algorhm consss of o major seps. he frs sep s an exended Kalman fler for he esmaon of he objec s pose. he second sep s a se of exended Kalman flers one for each model pon for he refnemen of he posons of he model feaures n he 3D space. hese o seps alernae from frames o frames. he nal model converges o he fnal srucure as he mage sequence s scanned sequenally. he performance of he algorhm s demonsraed h boh synhec daa and real orld objecs. Analycal and emprcal comparsons are made among our approach he nerleaved bundle adjusmen mehod and he Kalman flerng based recursve algorhm by Aarbayejan and Penland. Our approach ouperformed he oher o algorhms n erms of compuaon speed hou loss n he qualy of model reconsrucon. Index erms: 3D srucure acquson Srucure from moon Kalman flerng Mulmeda processng I. INRODUION HE research ork presened n hs paper falls no he caegory of srucure from moon n he feld of compuer vson. he goal of hese knds of researches s o reconsruc a 3D srucure and s pose from a sequence of 2D mages. A subse of he problems s o perform he recovery of srucure and pose n a sequenal manner. hs s also knon as recursve or casual srucure from moon. here are many real orld applcaons for he casual model reconsrucons. One novel applcaon s ha he pose of he camera n a move scene recovered can be used o produce augmened realy vdeo n hch synhec objecs can be mxed h real orld characers. Anoher applcaon s o use hese algorhms o produce 3D moves. In ha he 3D scene s reconsruced from he frames of Manuscrp receved July hs ork as suppored by he Research Gran ouncl of Hong Kong Specal Admnsrave Regon. Projec No. UHK4389/99E) Y.K.Yu and K.H.Wong are h he Deparmen of ompuer Scence and Engneerng he hnese Unversy of Hong Kong Hong Kong. e-mal: ykyu@cse.cuhk.edu.hk khong@cse.cuhk.edu.hk ). M.M.Y.hang s h he Deparmen of Informaon Engneerng he hnese Unversy of Hong Kong Hong Kong. e-mal: mchang@e.cuhk.edu.hk).

2 SMB-E he moves sequenally. he veers are alloed o change he vepons of he scenes as he move s played. here are varous echnques o deal h he 3D reconsrucon problem. One of he mos popular approaches s he use of eppolar geomery. Wh he knon correspondences beeen he o ves a consran beeen hese ves can be se up. he camera moon can be recovered from he Fundamenal marx up o a scale facor f he camera s fully calbraed. he srucure of he 3D model can be found be solvng a se of equaons. In a smlar sense he echnque has been exended o hree ves or more [7]. Facoraon [5] [6] s anoher common approach o ackle he problem of srucure from moon. he ork n [5] demonsraes he approach under he assumpon of orhographc projecon. he facoraon mehod has been exended o handle he reconsrucon of mulple ndependen movng objecs [6]. Bundle adjusmen s also an effecve mehod [9]. I mnmes he re-projecon error beeen he esmaed model and he mage measuremens. he mnmaon procedure can be done n bach eher by he ell-knon Neon s or Levenberg-Marquard eraon. A branch of s he nerleaved bundle adjusmen as descrbed n [2] and [9]. I breaks up he mnmaon problem no o seps so as o reduce he se of he Jacoban nvolved resulng n speedng up he algorhm. he mehods menoned prevously ackle he problem n a bach n hch he srucure and moon are opmed for all he mages a one me. here are soluons ha recover he srucure and moon n a sequenal ay. Mos of hem are based on Kalman flerng. he ork n [3] fnds he pose of he objec based on a knon AD model from sereo mages n real-me. he resuls are appled for vsual servong of robo manpulaors. Some researchers adop eraed exended Kalman fler IEKF) for updang he srucure n Eucldean [4] or projecve frameork []. he pose and he srucure of he objec are recovered alernaely by a RANSA-based equaon solvng echnque and he IEKF. homas and Olenss apply sandard Kalman flerng o fuse he recen srucure esmaes found by Horn s algorhm usng he mos recen mage par h he prevous srucure esmaes a each me-sep [2]. he seres of mehods n [0] [] [3] [4] recover boh he srucure and moon n a recursve manner. he ork by Broda e al [4] s he ancesor of hs seres of researches. hey apply a sngle IEKF o recover he srucure and pose of he objec. Aarbayejan and Penland descrbe a mehod n [] ha makes sgnfcan mprovemens over [4]. Exenson s made o recover he focal lengh of he camera n addon o he pose and srucure. he ponse srucure s represened by one parameer per pon such ha he compuaon s overdeermned a every frame hen he number of feaures s larger han 7 resulng n a beer convergence and sably of he fler. he mos recen

3 SMB-E ork of recursve srucure recovery s by huso e al [0]. Smlar echnques n srucure from moon have also been appled o smulaneous localaon and map-buldng for robo navgaons [6]. he o-sep Kalman fler based algorhm presened n hs paper s nspred by he mehods of nerleaved bundle adjusmen as descrbed n [9]. he man advanage of our o-sep approach s ha e acheve a lnear me and space complexy n erms of he avalable model feaures. hs saves a lo of compuaon hen he number of feaures needed o be handled s large hch s que common for he reconsrucon of objecs h full deals. In addon our mplemenaon can handle he srucure from moon problem h changeable se of feaure pons. he full 360 o ve of an objec can be reconsruced hch s demonsraed n he expermen. he res of hs paper s organed as follos. he modelng of our problem s frs nroduced n Secon II. In secon III he overve of he o-sep algorhm s descrbed. In secon IV and V he formulaons of he EKF for pose esmaon and srucure updang are presened. In secon VI he handlng of he changeable se of feaure pons n our mplemenaon s dscussed. In secon VII here s an analycal comparson among our Kalman fler based approach he nerleaved bundle adjusmen mehod [2] and he recursve algorhm by Aarbayejan and Penland []. In secon VIII some expermens h real and synhec daa are performed. he resuls from he hree approaches menoned are analyed. II. PROBLEM MODELING Fgure. he geomerc model of he sysem O O O O Fgure descrbes he geomery of he model reconsrucon sysem. [ x y ] and [ x y ] denoe he coordnaes of he pon h respec o he objec and he camera coordnae frame respecvely. A pon on

4 SMB-E he mage plane s denoed by p u v ]. he relaonshp beeen he objec frame and he camera frame s as follos: [ O R + ) + ) R s a 3x3 roaon marx and s a 3x ranslaon vecor. s a 3x ranslaon vecor ha brngs he objec n he objec frame o he camera frame. I s a consan n he model recovery process. amera used n he sysem s calbraed. I has a fxed focal lengh f. he camera model s full perspecve. he problem of srucure from moon n our sysem s o recover he coordnaes of model pon O n he objec coordnae frame and he pose of he objec.e. he roaon R and ranslaon h respec o he ves a each me-sep. III. OVERVIEW OF HE ALGORIHM he model reconsrucon sysem s dvded no hree pars: feaure exracon and rackng model nalaon srucure and pose updang. o make he presenaon of he algorhm easy o undersand e frs assume ha all he feaures are observable from he frs o he las frame n he mage sequence. he deals of he exra reamens needed o handle he changeable se of feaure pons are dscussed n secon VI. A. Feaure exracon and rackng he KL racker descrbed n [8] s used o exrac feaure pons and rack hem from mages o mages. In our ork s assumed ha he problem of rackng has been solved and pon maches from KL are relable enough for model reconsrucon. B. Model nalaon he model nalaon s acheved by assumng ha he projecon of he frs mage n he sequence s orhographc. Perspecve projecon s assumed for mage formaon process n he remanng frames. he orhographc projecon s expressed mahemacally as: u f v n x y 2) n s he dsance beeen he objec and camera cener. I s a parameer gven by he user of he sysem and can be approxmaed easly. o oban he nal model feaures n he frs mage are back-projeced from he mage plane o he camera coordnae frame accordng o equaon 2). he resulng nal srucure s a planar model

5 SMB-E locaed a a dsance n from he camera.. Srucure and pose updang Fgure 2. he flochar of our o-sep Kalman fler based algorhm. he nal model and he second mage are fed no he frs sep for pose esmaon. An EKF s adoped. he pose of he objec h respec o he second mage s esmaed. he nely recovered pose and he npu mage are passed o he second sep of he algorhm for srucure updang. he second sep consss of a se of N EKFs. Each fler corresponds o one coordnae pon n he reconsruced 3D model. Wh he observaons and he pose recovered for he curren mage frame he coordnaes of each feaure pon are updaed accordngly. he algorhm alernaes beeen he sep and 2 unl all mages n he sequence are used. IV. SRUURE UPDAING he follong s he formulaon of he EKF for srucure updang. For N model pons N EKFs are needed for he srucure updae. For smplcy e consder only one pon n he model denoed by here s he me-sep of he model pon h respec o he objec coordnae frame. are he posons of pon afer he predcon and updae respecvely. We frs defne he dynamc model of a 3D pon. he sae ranson and observaon equaon for a model pon can be ren as: + γ ε h ) + v γ and ν are he ero mean Gaussan nose h covarance Q and R respecvely. ε s he real measuremen from he mage sequence. h ) s he projecon funcon of he sysem:

6 SMB-E y x f h ) s obaned from equaon ) by subsung O by. he EKF frs provdes an opmal esmae of he sae a he nex sample me n accordance h he follong equaons: Q + Λ Λ hey are knon as he predcon equaons. Λ s he 3x3 covarance marx of. Here a nose covarance Q of γ s added. In normal suaons only he enry corresponds o he coordnaes of he 3D pon s se o non-ero. he reason s ha he nal guess of he srucure s a planar objec. Folloed by he sae predcon he fler mproves he prevous esmae usng he measuremens acqured: )) Λ + Λ Λ + h W h W ε ) + Λ Λ R h h h W hey are knon as he updae equaons. W s he 3x2 Kalman gan marx of he fler. R s he measuremen nose covarance marx. I s a unng parameer and s se accordng o he qualy of he mages. I can also be acqured durng he process of camera calbraon. h s he Jacoban of he non-lnear projecon funcon h ) evaluaed a. In hs ay he coordnaes of he model pons can be updaed accordngly. V. POSE ESIMAION he dynamc model ha descrbes he moon of he objec s as follos. s he sae of he sysem and s defned as: [ ] γ γ β β α α y y x x x y and are he ranslaons of he objec along he x y and he axes respecvely. y x are her correspondng veloces. γ β α are he Ya Pch and Roll angles. her correspondng angular veloces are γ β α. s denoes he duraon over he sample perod. Over he sample perod he veloces are assumed consan. he sae ranson and observaon equaon for he model are:

7 SMB-E A γ s s dag A v g ) + ε γ and ν are he ero mean Gaussan nose h covarance Q and R respecvely. A s a 2x2 block knon as he sae ranson marx. ε s a mx column vecor represenng he mage measuremens for m seleced feaure pons. ) g s he projecon funcon: n n n n y x y x y x f g ) Smlar o ) h s obaned from he equaon ) by subsung O by. he roaon marx R and ranslaon marx are evaluaed h he parameers of he column vecor. In our sysem a fxed number of feaure pons e.g. 50 n our expermen) exraced by he racker are passed o he EKF for pose esmaon. he model pons are chosen based on ho much hey are updaed n he sep of srucure refnemen. hose pons ha are seady and have a hgh endency o reman a he same 3D coordnaes are used. he reason s ha less updae on a pon mples ha he pon s n an accurae poson. Here are he four core Kalman fler equaons for pose esmaon. he predcon equaons for calculang he opmal esmaes are: Q A AP P A + he updae equaons for he correcons of esmaes are: )) + P g K P P g K ε ) + R g P g g P K and are he saes of afer he predcon and updae respecvely. P and P are 2x2 marces ha correspond o he covarances of and. K s he 2x2m Kalman gan marx. g s he Jacoban of he nonlnear observaon equaon ) g evaluaed a. In hs ay he pose of he model o he nex frame s esmaed.

8 SMB-E VI. HANDLING HE HANGEABLE SE OF FEAURE POINS he se of acve feaure pons s changng due o occluson and dsoccluson. Exra reamens are needed n each sep of he model reconsrucon process. In feaure rackng he hole mage sequence s dvded no a number of secons. For each secon a number of frames near he end of ha secon are overlapped h he frames a he begnnng of he succeedng secon. he KL racker n [8] h feaure replacemen mechansm s appled o each secon ndependenly. ung he mage sequence no secons forces he racker o release obsolee feaures afer a fne me lm. I s mporan because rong pon correspondences arse hou hs reamen. Ne model pons n he srucure are naled hen ne pon feaures appear n he mage sequence. hs s obaned by assumng he projecon of ha pon on s frs appeared mage frame s orhographc. he nal poson expressed n he camera coordnae frame s compued accordng o equaon 2). he coordnaes are hen ransformed back o he objec coordnae frame by equaon ). Afer he nalaon of he 3D poson a ne EKF s se up for updang s poson. In addon hs ne pon s added o he pool ready o be seleced for pose esmaon. No modfcaon s needed n he EKF for pose esmaon. When a pon feaure vanshes from he mage sequence he fler ha corresponds o he pon s removed. he 3D poson of ha feaure ll no longer be updaed. he ndex of ha feaure s also marked nvald for pose esmaon snce no relaed measuremens n fuure me-seps can be used for fndng he pose of he objec. he reamens for handlng changeable feaure se are smple n our algorhm compared o he procedure n [0]. No sub-flers are requred n our approach. VII. ANALYIAL OMPARISON WIH OHER ALGORIHMS A. he nerleaved bundle adjusmen mehod ) ompuaon effcency he man advanage of our Kalman fler based recursve approach s he gan n speed and scalably. An exra ve of he objec can be handled naurally by calculang he predcon and updae equaons for boh he pose and srucure only for ha ne measuremen. Hoever he nerleaved bundle adjusmen mehod needs o re-compue from he frs frame o he laes frame for a several eraons. Applcaon lke 3D move as descrbed n he nroducon requres our recursve approach unless he flm s pre-processed usng a hgh performance compuer.

9 SMB-E ) onvergence of soluons Anoher advanage of our Kalman fler based mehod s ha has a beer convergence rae n handlng long sequences h large objec moon say a oal of 90 degrees roaon along one of he axes. onsder he roaon of he objec beeen he frs and he las frame. In he frs pass and he frs eraon of he nerleaved bundle adjusmen mehod he nal model s used o esmae he pose of he objec h respec he las frame. hs resuls n a large pose esmaon error and evenually leads he compuaon n he second pass of he nerleaved bundle adjusmen o dverge. For our recursve approach he model s updaed ncremenally from frames o frames he mos up-o-dae model s used for pose esmaon. he problem of usng an naccurae model o compue he pose s elmnaed. B. he EKF by Aarbayejan and Penland ) Algorhm omplexy he major dfference beeen our approach and he EKF n [] s ha he srucure refnemen and pose esmaon s broken don no o seps and each correspondence pon n he srucure s decoupled. In our approach here are one 2x sae vecor for pose esmaon plus N 3x sae vecors for srucure updang here N s he oal number of avalable feaures. hs respecvely resuls n one 2x2 and N 3x3 sae covarance marces. Snce he number of measuremens nvolved n he pose esmaon sep s fxed boh he sorage and compuaon complexy are ON). For he EKF descrbed n [] he pose and srucure are encoded n a sngle sae vecor. he se of he sae covarance marces s N+7)xN+7). he sorage and compuaon complexy are ON 2 ) and ON 3 ) respecvely. Our modfcaon s acually a radeoff beeen speed and accuracy. Hoever expermenal resuls sho ha he loss n accuracy s lle and accepable n real applcaons. Moreover he reducon n complexy s useful for real-me robocs applcaon snce he compuaon resources n mcroconrollers are gh. Also our algorhm s ready o be mplemened on dsrbued mcro-processng sysem. he se of N EKFs used for srucure updang can be run n parallel n a se of N mcro-processors n a roboc sysem o speed up he compuaon. 2) he problem of scalng Anoher advanage of our algorhm s ha he exac model can be reconsruced gven he algnmen of ranslaon beeen he objec coordnae frame and camera coordnae frame. he EKF by Aarbayejan and Penland s subjec o scalng problem even s gven. hs s due o he naure of he srucure model adoped n he fler. A

10 SMB-E small devaon n he esmaon of he Z coordnaes of he pon feaures causes a sgnfcan change n he scale of he objec. he problem can be fxed by gvng he EKF he real 3D coordnaes of one of he feaure pons and seng her correspondng enres n he sae covarance marx ero. VIII. EPERIMENS AND RESULS A. Expermens h synhec daa he frs se of expermens as conduced h synhec daa. A synhec objec h 300 random feaure pons n 3D hn a cube of volume of 0.3m 3 cenered a a place 0.33m aay from he veng camera as generaed. he camera has a focal lengh of 6mm. I mposes a 2D ero mean Gaussan nose h sandard devaon 0. pxels on he mage capured. he objec as movng h a seady moon a a rae of [ ] degrees and [ ] meers for [Ya Pch Ro] and [x y ] respecvely. Random nose of 0.0 degrees as added o each roaon angle and a nose of meers as added o each of he ranslaon parameer. 300 frames ere generaed for each es and a oal of en ndependen ess ere carred ou. Our Kalman fler algorhm he nerleaved bundle adjusmen mehod [2] and he EKF by Aarbayejan and Penland [] ere esed h he daa and her resuls ere compared. Fgure 3-5 sho he resuls. he sold lne doed lne and he dash lne are for our Kalman flerng approach he nerleaved bundle adjusmen mehod and he EKF by Aarbayejan and Penland respecvely. he mplemenaons of he hree algorhms are n Malab h a Penum III GH machne. Fgure 3 demonsraes he convergence of 3D model error versus PU me. Here he model error s defned as he percenage of mean-square-error of he 3D coordnaes n he objec coordnae frame. In our approach he 3D model converges quckly o he soluon hn he frs en frames of he sequence. he average error s 0.69%. For he nerleaved bundle adjusmen mehod he accuracy of he resulng model falls o 0.33% afer 50 eraons. Bu for far comparson e should concenrae on he resuls afer he frs eraon. In hs case he average error s 0.74% hch s smlar o our approach. he resul s reasonable snce our recursve algorhm canno opme he srucure error of he model for all he mages n he sequence smulaneously or opme he error for scannng he sequence more han once resulng n a larger fnal error han he bach processng approach. hs s one of he characerscs of all recursve reconsrucon algorhms. he plo of 3D model error of he EKF by Aarbayejan and Penland s no ncluded here. he reason s ha he

11 SMB-E model recovered by her algorhm s subjec o scalng problem as descrbed n secon VII B 2). Wha can be concluded s ha our Kalman flerng approach can fnd an accurae esmae of he srucure n a shorer perod of me han he nerleaved bundle adjusmen mehod. Fgure 3. he 3D model error versus PU me n seconds) elapsed for he o approaches. Fgure 4. A graph shong he relaonshp beeen he PU me and he mage resdual error among he hree algorhms. Fgure 5. A graph shong he me needed o reconsruc a model hen exra frames are added o he mage sequence. Noe ha he nerleaved bundle adjusmen algorhm s se o run 20 eraons n he model reconsrucon process. Fgure 4 shos he me for he hree algorhms o opme he mage resdual error of he back-projeced model. By careful analyss our algorhm mnmes he resdual error o a lo level n he shores me among he hree algorhms. Our approach fnshes he processng of he 300-frame sequence n 33 seconds. he EKF by

12 SMB-E Aarbayejan and Penland and he nerleaved bundle adjusmen mehod complee a 786 and 436 seconds respecvely. he fgure also ndcaes ha our approach falls o an error smlar o he EKF by Aarbayejan and Penland hch reveals ha here s no sgnfcan loss n he srucure acquson accuracy even he fler s decoupled. Fgure 5 shos he me needed o reconsruc a model hen exra frames ere added sequenally o he mage sequence. he frs sep n hs plo as o reconsruc a model h he frs 0 frames. he succeedng 40 frames ere sequenally fed o he algorhm as he ne measuremens of he scene. Our approach ouperformed he oher o algorhms. I akes only 0.5 seconds o updae he srucure of he scene for every exra frame added o he mage sequence. he EKF by Aarbayejan and Penland akes abou 3 seconds hle he nerleaved bundle adjusmen mehod needs a leas 0 seconds o do he same ask. B. Expermens h real scene Expermens usng real scene mages ere performed. o es mage sequences one for he reconsrucon of a paper box and one for a house model ere used n he expermen. he objecs ere pu on a roang urnable. Images ere aken h a commercal eb camera. he lenghs of he paper box and he house sequence are 200 and 80 frames respecvely. Our recursve model reconsrucon algorhm as appled o acqure he 3D models. Afer ha he re-frame of he objecs as bul and exure from he approprae mages n he sequence as mapped o he recovered srucure. he resulan objecs ere oupu n he form of VRML fles. Fgure 6 shos he resuls of he expermen. We have successfully reconsruced he 360 o ve of he paper box model from s 2D mages. he oal number of pon feaures presen n he model s abou 500. he qualy s good n general. Hoever you may noce ha here s a presence of oulyng model feaures n he recovered srucure resulng n flas n some pars of he model. he oulyng model feaures are manly due o pon msmaches ha arse from he process of feaure rackng by he KL racker. For he recovered house model he oal number of model feaures n he scene s abou 000. More geomerc deals are revealed n hs case. hs demonsraes ha our algorhm s able o handle complex scene reconsrucon hn a reasonable me lm.

13 SMB-E I. ONLUSIONS A o-sep Kalman fler based algorhm s proposed and mplemened. Our algorhm acheves lnear me and space complexy n erms of he number of avalable pon feaures. Our algorhm needs respecvely less han oneforh and one-hrd he me of he EKF by Aarbayejan and Penland and he nerleaved bundle adjusmen mehod o process a sequence h 300 pon feaures per frame. Besdes an elegan mehod s proposed o handle he changeable se of pon feaures. he mehod s appled o reconsruc he full 360 o ve of a paper box n he real daa expermen. he major lmaon of our model reconsrucon sysem s caused by he feaure racker and he exure mappng mehod. Feaure rackng and exure mappng play a sgnfcan role n he reconsrucon of 3D models from he real mages. One possble mprovemen o our sysem s o make a fler on he op of he orgnal KL racker o elmnae he oulyng pon feaures n neghborng mages h he fundamenal marx [5]. Oher mprovemens lke ncorporang a robus mechansm for choosng he exure from mages can be made o mprove he qualy of model reconsrucon.. AKNOWLEDGMEN he ork descrbed n hs paper as suppored by a gran from he Research Gran ouncl of Hong Kong Specal Admnsrave Regon. Projec No. UHK4389/99E) REFERENES [] P.A. Beardsley A.Zsserman and D.W.Murray Sequenal updang of projecng and affne srucure from moon Inl. Journal of ompuer Vson 23 pp [2] M.M.Y.hang and K.H.Wong Model and pose acquson usng exended Loe s mehod IEEE rans. on Mulmeda acceped) [3] V.Lppello B.Sclano and L.Vllan Objecs moon esmaon va BSP ree modelng and Kalman flerng of sereo mages Proc. of he IEEE Inl. onf. on Robocs and Auomaon Washngon D pp [4].G.Harrs and J.M.Pke. 3D posonal negraon from mage sequence Image and Vson ompung Vol 6 No [5].omas and.kanade Shape and moon from mage sreams under orhography: A facoraon mehod Inl. Journal of ompuer Vson 92)

14 SMB-E [6] J.osera and.kanade A Mulbody Facoraon mehod for ndependenly movng objecs Inl. Journal of ompuer Vson 293) [7] R. Harley and A Zsserman Mulple Ve Geomery n ompuer Vson ambrdge Unversy Press [8].omas and.kanade Deecon and rackng of Pon Feaures arnege Mellon Unversy echncal Repor MU- S-9-32 Aprl 99. [9] B.rggs P.McLauchlan R.Harley and A.Fgbbon Bundle adjusmen A modern synhess In proc. of he Inl. Workshop on Vsual Algorhm: heory and Pracce. pp orfu Greece 999. [0] A.huso P.Favaro H.Jn and S.Soao Srucure from moon casually negraed over me IEEE rans. on PAMI vol24 No [] A.Aarbayejan and A.P.Penland Recursve esmaon of moon srucure and focal lengh IEEE rans. on PAMI vol 7 no 6 June 995. [2] J. Ingo homas and J.Olenss Recursve mul-frame srucure from moon ncorporang moon error Proc. DARPA Image Undersandng Workshop 992. [3] J.Weng N.Ahuja and.s.huang Opmal moon and srucure esmaon IEEE rans. on PAMI vol 5 no. 9 Sepember 993. [4].J.Broda S.handrasekhar and R.hellappa Recursve 3-D moon esmaon from monocular amge sequence IEEE rans. on Aerospace and Elecronc Sysems vol 26 no. 4 July 990. [5] S. Gbson J. ook. L. J. Hoard R. J. Hubbold and D. Oram. Accurae camera calbraon for off-lne vdeo-based augmened realy. In IEEE and AM ISMAR 2002 Sep Darmsad Germany. [6] A.J.Davson and D.W.Murray Smulaneous localaon and map-buldng usng acve vson IEEE rans. on PAMI Vol.24 No.7 July Mr. Yng-Kn Yu receved a B.Eng h frs class honours n ompuer Engneerng from he hnese Unversy of Hong Kong n He s no a graduae suden n he ompuer Scence and Engneerng Deparmen n he same unversy. He has been aarded he Sr Edard Youde Memoral Felloshp ce for hs academc achevemens. Hs research neress are compuer vson augmened realy and genec algorhms. Hs conac address s: he ompuer Scence and Engneerng Dep. he hnese Unversy of Hong Kong Shan Hong Kong. Emal: ykyu@cse.cuhk.edu.hk Prof. Kn-Hong Wong receved a B.Sc. n Elecroncs and ompuer Engneerng from he Unversy of Brmngham n 982 and a Ph.D. from he Engneerng Dep. of he Unversy of ambrdge U.K. n 986. He as a roucher research fello

15 SMB-E a he Unversy of ambrdge from 985 o 986. Prof. Wong joned he ompuer Scence Dep. of UHK n 988 and s no an Assocae Professor. Hs research neress are 3D compuer vson vrual realy mage processng paern recognon mcrocompuer applcaons and compuer musc. Hs conac address s: he ompuer Scence and Engneerng Dep. he hnese Unversy of Hong Kong Shan Hong Kong. Emal: khong@cse.cuhk.edu.hk Prof. Mchael Mng-Yuen hang receved he B.Sc. n elecrcal engneerng from Imperal ollege London Unversy and he PhD degree n elecrcal engneerng from Unversy of ambrdge n 988. He hen joned he Deparmen of Informaon Engneerng he hnese Unversy of Hong Kong and s no an Assocae Professor. Hs curren research neres s n characer recognon scenfc vsualaon and nellgen nsrumenal conrol. Hs conac address s: he Informaon Engneerng Dep. he hnese Unversy of Hong Kong Shan Hong Kong. Emal: mchang@e.cuhk.edu.hk Fgure 6. he resuls of model reconsrucon. Frs column: he frs and he 00 h mage of he paper box sequence. Second column: he reconsruced 3D paper box model veed n orona. One ve h exure mappng he op one) and s reframes he boom one). hrd column: he frs and he las 80 h ) mage of he house model sequence. Forh column: he reconsruced 3D house model. One ve h exure mappng he op one) and s re-frames he boom one). More resuls can be found a hp://.cse.cuhk.edu.hk/~khong/demo/