Spectral Analysis for Sampling Image-Based Rendering Data. Abstract

Transcription

1 Spa Anay o Sampng Imag-Ba nng Daa Cha Zhang an Tuhan Chn Ea & Compu Engnng Cang Mon Uny Pbugh PA 151 Ema: {zhang uhan}@anw.mu.u Aba Imag-ba nng (IB) ha bom a y a ah aa n n ya. Th pa anay pobm o IB ha no bn ompy o. In h pap w pn a nw mho o paamz h pobm whh appab o gna-pupo IB pa anay. W no ha any pnop unon gna by gh ay m//a om h ob ua. W nou h ua pnop unon (SPF) whh pn h gh ay ang om h ob ua. Gn ha aan aong a gh ay o no hang un h gh ay bok SPF u h mnon o h ogna pnop unon o 6D. W a hn ab o map o anom h SPF o IB pnaon apu aong any ama aoy. Aumng om pop on h SPF w an anayz h pop o IB o gn n uh a n wh amban o non-amban ua an n wh o whou ouon an o n ampng ag uh a gh/onn moa. W n ha n mo a n hough h SPF may b banm h quny pum o IB no ban-m. W how ha non-amban on ph aaon an ouon an a boan h pum wh h a wo bng mo gnan. SPF n o n wh known gomy. Whn h gomy unknown pa anay pob. W how ha wh h unang wnow anay an om onuon oban wh SPF h pum panon au by non-amban on an ouon an b quanay ma n whn h n gomy no py known. Gn h pum o IB w ao uy how o amp IB aa mo ny. Ou anay ba on h gnaz po ampng hoy wh abay gomy. W how ha h ampng ny an b up o w o ha whn w u angua ampng. Th aanag an aanag o gnaz po ampng o IB a ao u. Kywo: pnop unon mag-ba nng gh onn moa pum anay.. Cona Auho: Po. Tuhan Chn Dpamn o Ea an Compu Engnng Cang Mon Uny 5 Fob Anu Pbugh PA 151. T: (41) Fa: (41) Ema: uhan@mu.u. Wok uppo n pa by NSF CAEE Awa an Inua Thnoogy ah Inu.. Subm o IEEE Tan. on Cu an Sym o Vo Thnoogy: Spa Iu on Imag-ba Mong nng an Anmaon Sp. 1. an ubm n Sp.. Th na a ubm n Ap

2 I. Inouon Imag-ba nng (IB) ha aa a o o anon ny. Popo by Aon an Bgn [1] a a 7D pnop unon IB mo a D ynam n by ong h gh ay a y pa oaon owa y pob on o any ang o wa-ngh an a any m. By mong h m an h wangh mnon MMan an Bhop [] n pnop mong a gnang a onnuou 5D pnop unon om a o amp. Th onp o gh by oy an Hanahan [] an umgaph by Go a. [4] y paamz h pnop unon no a 4D unon un h onan ha h ob n pa. Shum an H [5] popo onn moa wh h numb o mnon o h pnop unon a uh o h by ng h w momn n a. Th pnp o h gh [] an b by a a oow. In pa aan o no hang aong a n un h gh ay bok. Th gh ay a hu paamz by h non wh wo pan n abay poon. On o h pan n wh oona ( u ) an h oh wh oona ( ). In Fgu 1 w how an amp wh h wo pan h ama pan an h oa pan a paa. Th h mo wy u up. An amp gh ay hown an n a ( u ). Th oona a hn z o ha a n numb o gh ay a o. In pa w pu a D aay o ama on h ama pan whh ha h am oa pan. Th mag apu om a D mag aay a hown n Fgu. To a a nw w o h ob w u p h w no gh ay whh a hn aua by npoang ng naby gh ay n h mag aay. Th nw w hn gna by ambng h p ay ogh. Conn moa [5] uh ha boh h ama an h w a on a pan. Th n apu by mounng a ama a h n o a bam an hoong mag a gua na a h bam oa a hown n Fgu. Th gh ay a hn n by h ama poon o h bam oaon ang an h p oaon ( u ). Th paamzaon quan o hang many ama oang aoun a ommon n an akng mag aong h angn on hu h nam onn moa. Th onn moa an b n wh gh ay npoaon oo. IB ha many aanag o h aona mo-ba nng. Whn nough mag a apu IB qu y o n no goma nomaon abou h n o aay n. Th y aa u o h uy o onu goma mo o ob n a a-wo n. Th nng p o IB nay popoona o h mag z bu no h n ompy whh mak IB y uab o nng a n wh omp gomy. Nh on a hug numb o mag ha o b akn n o o ao aang o ghong ung h nng. I ho my mpoan o know how many mag a nough o apu a n ba on h pum anay o h pnop unon. ny Cha a. [6] popo a mho o uy h quny pum o gh. Aumng amban ua an no ouon hy how ha any mag akn a poon ( ) an b mapp o h mag apu - -

3 a poon ( ). A ky onuon ha h pa uppo o a gh gna boun by h mnmum an mamum ph o ob n h n ony no ma how ompa h n. Thy am ha by knowng h boun o h uppo h mamum ampng ny an b ah by ompang op o h pa uppo n h quny oman. Thy uh popo h Sampng Cu whh g h aonhp bwn h numb o mag o b akn an h knowg abou h n gomy (numb o b ha pn h ph ). Th anay po a ay goo -o appomaon o h pum anay o IB. How h pnny on mappng mag apu a abay poon o on poon (a n h a om ( ) o ) pn om bng app o mo ompa n uh a non-amban ua n wh ouon an oh IB mho uh a onn moa. Du o h ompy o h pobm w a ha bn popo o nhan h wok n [6]. In [7] Chan an Shum popo o w h pnop ampng pobm a a mumnona ampng pobm. Thy how ha ph aaon au h pnop unon o pa n h quny oman. Th am mag mappng n [6] app n h pap an hu ba h am aanag. Mahan-Ma an V [8] n h wok o n wh unona ua. Thy h gh ay on an o n a on-o-on mappng om h ob ua o h ama pan. Th on-o-on mappng a whn no ouon ou. Thy how ha n whn h no ouon a ban-m gna pa on a unona ua w no u n a ban-m gh pum. Th maon o h anay ha hy no on gna n wh ouon o non-amban ua. gh wa h ony IB mho ha wa on. Thy ao popo a goma anay o a ampng o gh. Ouon wa u y no gnan an paa u w awn om h anay. Anoh nng wok wa on by n an Shum [9]. Thy pom ampng anay on boh gh an onn moa wh a-pa hoy un onan-ph aumpon. Th boun a om h ap o gomy an ba on h goa ha no puou a hou b gna ung h nng ( a h auay qumn). Ahough h wpon o h anay y nng h onanph aumpon on oo ong o b h a wo. In h pap w popo a nw mho o paamz h pnop unon o IB pum anay. Sma o [6] w ao wok n h Fou anom oman. How na o mappng mag apu a abay poon o on poon w map h IB pnaon ono h o-a ua pnop unon (SPF a n n Son II). Th aow u o o o ou non-amban n a w a oh IB apung mho uh a onn moa. Fo non-amban ua w how ha whn h ua mon/on hang owy aong n on h Fou anom o h n ao pan by a m amoun. W hn how ha whn h n ha ph aaon h pum w b boan u o h nonnay bwn h SPF an h IB pnaon. W ao how ha ouon au a mouaon bwn ay n h n whh gna aona quny omponn. Among h h ou w n ha ph aaon an ouon a on muh ong n pum pang. Fo anayzng h pum o n wh unknown gomy w appy h unang wnow anay [6] an om o h - -

4 abo onuon. W a ab o quanay ma h pum pa u o non-amban ua an ouon. Gn h pum w appy gnaz po ampng hoy wh abay gomy o IB. W how ha non-angua o qunun/hagona ampng an u h ampng a by a ao o hoay. Th p h na o ompy o boh aa apung an nng. Epmn an ommn a gn a h n o h pap. Th pap oganz a oow. In Son II w pn h nw mho o paamzaon. Son III g amp on n n amp wh gh. W anayz h gh pum o n wh unknown gomy n Son IV. Son V by how h anay o onn moa. W b h nonangua ampng o IB n Son VI. Conuon an uu wok a gn n Son VII. II. Paamzaon Mho Imag-ba nng a n by MMan an Bhop n [] o gna a onnuou pnaon o h pnop unon gn a o amp (omp o nomp) om ha unon. To anayz h pum o IB mpoan o ha a o ook a how pnop unon gna. Obouy any gh ay n h pa ha a ou. I an b h m om om gh ou (.g. h Sun) o by om ob ua. I h ob anpan aon ao no. h n ua o a h gh ou an ob b S. W an away a a gh ay n h pa bak o a pon on S. Aum h aan o no hang aong a n un h gh ay bok h 7D pnop unon an b paamz o 6D nung m (1D) wangh (1D) pon on h ua S (D) an azmuh an aon ang (D) h gh ay m. W nam h 6D unon a h ua pnop unon (SPF). SPF ba o aonhp o h ua gh popo n [1][11]. A mno n ha SPF mo gna han ua gh bau nu h m an wangh nomaon. Woo a. [11] ou on h pnaon nng an ompon o ua gh wh w u SPF o ampng anay. Wong pnop umnaon unon [1] an n aan [1] a ao ma o SPF n h n ha hy o mo n gh ay aan om am ua pon. How h wok u n un n umnaon ( wpon) wh w on n un n wpon ( umnaon). Th ampng o aan [1] npnn o h n gomy bau h wpon an h oponn bwn gh ay om h am ua pon known (away a h am p poon). In ona o IB ampng anay w n om gomy nomaon n o o know h gh ay oponn uh a h onan ph aumpon ma n [6]. Th aumpon ha h aan o no hang aong a n un h gh ay bok wy aop n many IB pnaon [][5]. Un h aumpon h gh ay omng ou om h on hu o h n an ao b paamz ba on h ama ua (h ua wh h ama oa) whh h n o IB pnaon. Sn gh ay a om h ob ua an n a apung ama h an ono mappng om h SPF o h IB pnaon. Suh a mappng pn on boh h n gomy an h ama ua bu no h ua popy uh a BDF. I w ha om knowg abou - 4 -

5 h n n oh wo w know om popy abou h SPF a popy an b o h IB pnaon. Mo mpoany h mappng o no qu h n o ha no ouon o amban ua whh y aa o IB pa anay. Whou o o gnay w u h D wo a amp houghou h pap o onn. Th onuon awn n h pap a ay o n o h D wo. In h D wo ua o ob/gh ou b wh u. Ignong m an wangh h SPF D: on mnon o bng a pon on a u h oh o uang h on o h gh ay m//a. An amp n hown () n Fgu 4. Th ua an b pn by h S ( y) o wh an b h a ngh b y y () h n o n ob. Fo a an ob n SPF a: () ( ) on h u (1) y y () wh < h on o h gh ay. h aan o h gh ay ha an b a bak o h ua pon mn by. No ha h abo unon o no appa o b a wh wha pop on u o auang ghng uh a ua noma BDF. W nn o o o bau on oo ompa w y o mo how h gh ay a gna n aon o h a ha uh a mo o no away o a n. Tho w ony on h uan ghng n (1) an aum ha w ha om knowg abou h SPF. I w a ab o mo h ghng y w h oowng anay an appy a auang h ghng ba on h known mo. amban h aumpon w ou mak o h n n ha bn uy u n h au. In m o SPF amban popy g h oowng aonhp: ( ) an Fou anom : ( ) ( ) wh h Fou anom o ( ) ( ) h Fou anom o () () δ 1. In h a wo pu amban ob a a. Hghy ua (k a mo) nqun oo. In mo a gh ay om h am pon on h ob ua n o b ma an ha ow hang wh p o h ang. I ho aonab o aum ha an b appoma by a banm gna. Tha : wh B ( ) ( ) I ( ) B () I h nao unon whh n a: I B ( ) 1 < B ohw. (4) 1 Sy pakng a a an pon on h ua ( ) n o b una on bau w an ony ob gh ay ha om ou o h ob. Tho aong anno b a a unon no an b ban-m. How w aum ha h wnowng aa nggb

6 an B n h banwh. Ou ban-mn aumpon an b onn o h ban-mn o h ua BDF wh h gna-pong amwok o n nng ny pn by amamooh an Hanahan [14]. Fo pon on a ua h ougong gh an b b a h onouon o h nomng gh an h ua BDF. I h nomng gh a (hu h nomng gh an b on a a a unon wh p o h ang) whn h BDF ban-m h ougong gh w b banm. In o o apu h pnop unon o ua pnop unon ng IB appoah agn ama on a pah/ua an ak mag o h n. Fo amp ama a pa on a pan n gh an on a n onn moa. In h D wo D gh ha ama on a n wh D onn moa ha ama on a. In gna h ama an b pu aong an abay u a hown n Fgu 4. h () () ama pah b S ( y) o wh h a ngh. Aum ha h ama pah u y y nab an h opa a o ou ama a na o h noma o h ama pah. Tha a a ngh h opa a ha on ( y '() '() ) wh '() an y '() a h o a. Dno h on o h opa a wh ang hn an( ) ' y ' () (). Th mag p an b n by h ang bwn h apu gh ay an h opa a a pn by n Fgu 4. Dno h aan o h gh ay apu a a ngh ang a ( ). Th goa o pa anay o h p IB pnaon o n h Fou anom o ( ) no a ( ) o ha w an mn h mnmum numb o mag w ha o apu. Gn h knowg w ha on h SPF ( ) an Fou anom ( ) h agy o aoa ( ) wh ( ) an hop ha w an pn ( ) n m o. In h n wo on w w how amp wh w an appy h abo agy o gh an onn moa. Bo mong on o h n on nay o ompa ou wok o h wok by Mahan-Ma an V n [8]. Bng npnny op hy ha om ma a. Fo amp boh o hm y o n a mappng bwn h apu gh an h gh ay om h ob ua. How ou appoah mo gna han ha n [8]. W mpoy h onp o ua pnop unon whh aow u o pom. Th nu gh an onn moa. In aon ouon an non-amban ua an b b anayz whn ou amwok. Anoh wok ha mgh b a hap om u (SFT) [15]. Boh SFT an ou appoah a abou anomng om pa popy om a an ob ua o h apu mag. How IB pa anay gnany n om hap-om u. F h goa o SFT o onu h n gomy om u nomaon wh w y o n h Fou pum o h IB pnaon gn h gomy. Son SFT on o gomy om a ng mag (ahough an b n o mup w) wh w a wh many mag. Th SFT ony on u pum (.g. a b anay on gna IB pnaon a ong a w an pn n m o - 6 -

7 oopy o homogny) wh w on boh u an gh ay aan hang aong n on nung non-amban ua an ouon. III. Anay o gh A hown n Fgu 5 D gh paamz by wo paa n n by an py. Th n h ama n wh h n h oa n. Th an bwn h wo n whh h oa ngh o h ama. I ay o how ha a gh ay n by pa ( ) a h oowng agba quaon: y (5) No ha h oa n n oay wh p o wh h ama. a oow. Fo h am gh ay Th aonhp bwn gh ( ) an h SPF m//a om a ua pon mu b apu a h oponng ang. Tha : an ( ) o 1 an (6) wh an an 1 h o w. Th abo quaon auay h mappng bwn a p angua poon an mag oona. Suh a mappng an b naz a: (7) Th abo nazaon w nou 4.% mamum o h FOV o h ama 4º. In pa h appomaon n Equaon (7) an b pa by a mp p -aangmn. Anoh onan ha h gh ay ( ) an b a bak o a o pon on h ob ua who a ngh an b oban hough ong: () () y y y Whn mup ob n h n o om ob ou hm Equaon (8) may ha mup anw. W ha o gu ou whh o pon h o o h ama. Th o pon w ou a h oh. Th may mak n wh ouon ha o anayz. How o mp n h oab an w w how amp a n h on. A. Sn a a onan ph Th mp n w an ha o gh on a a onan ph. Th ua an b b by: () () y y W an o Equaon (8) whou onnng abou ouon: (8) (9) - 7 -

8 - 8 - (1) Th gh pum an b a: (11) W an ha h pum o h gh a onan ph a oa on o h SPF pum wh om onan ao n magnu an om h n pha. Th oaon ang mn by h n ph an h oa ngh. I h ob ua amban w ha δ a n Equaon (). Tho δ (1) Th a n n h pa whh h am onuon a ha n [6]. Whn h ob ua non-amban bu h SPF ban-m w ha I a n Equaon (). Conquny B I (1) Th pum ao bu h m ha a n wh B ppnua o h pum (o B hozonay) bau o h nao unon. Th abo anay ua n Fgu 6. A n a onan ph ha wo nuo (n quny) pa on a u a hown n Fgu 6 (a). Fgu 6 (b) h ppoa mag (EPI) whn h n amban. Fgu 6 () Fou anom. Th pum ha a pak bau h u on h n ob pu nuo. I baay on a n wh om ma hozona an a wnowng aa ha u o h unaon o h ang o an. W gno h wnowng aa n ou anay o mpy. Fgu 6 () how h EPI o a non-amban a a h am ph. I an b n ha bau o h non-amban popy Fou anom n Fgu 6 () pan owa h noma on o h n. B. Sn on a n W n uy a n on a n. W w h ua quaon a:

9 - 9 - () () n o y y y (14) wh < an ang ha known. Aumng no ouon w an o Equaon (8) a: n o n o y y (15) To guaan ha whn ah apu mag h paam onnuou φ anno b abay. I w an ha onan ha n o >. Th gh pum : y y n o n o n o (16) Unounay n o a n a mp a a n Equaon (16) oo omp o o. H w on a a wh Equaon (16) an b uh mp. h n b amban.. a n Equaon (). W ha: () y y y n o n o n o n o n o n o (17) I w ha a nuo pa a h u.g. () n. I Fou anom : [ ] 1 δ δ (18) Du o ymmy u on h magnu o whn > an >. γ an γ u o h m FOV. Pug no Equaon (17) an w ha: [ ] ohw n o n o whn n n o n o 1 γ γ γ δ γ γ y (19)

10 Fgu 7 (a) how a n on a n wh / 6. A ng nuo pa on h n a u. Fgu 7 (b) h EPI o h gh an Fgu 7 () Fou anom. No ha ou anay mah y w wh h amp. Fo amp h pum non-zo ony bwn an gon h pum ay whn na. Th pum boun o hho. In h non-zo u o h mnmum an mamum ph o h n a wa b n Son III-A. On hng w may no n h amp ha ompa wh h ogna SPF (whh u a nuo) a n a mp a a n an au h IB pum o pa a o. Conng h a ha gh ay om a an ua pon n o hang owy n h a wo w may onu ha h pum pang n a wo n many au by gua hap nung h oung whh w w u n h n ubon. Th a wo paa onaon. F h gomy o h n may b y u o oban. Whn h gomy unknown w may appoma h n gomy wh pw onan ph a u n Son IV. Foowng h unang wnow anay h w may oban -o appomaon o h pum n h n non-amban. Son gn h n gomy omm an anaya pon aoang h pum o SPF an ha o IB pnaon may no. To o o uh n numa mho may b app. Fo amp by pang ( ) wh h n Fou anom o ( ) Equaon (16) ou b o numay. C. Ouon bwn ob Whn ouon happn IB pa anay bom y u u o h onnuy a h ouon bounay. In a any ouon w mpy au h IB pum o b ban-unm. In h ubon w anayz ou n un an aumpon an g om ngh on h omaon o h pum o uh n. Wh SPF ong o ou n man nng h o o pon among mup ouon o Equaon (8). W aum ha ob o no ou hm. Mahan-Ma an V [8] on h no-ouon onon o unona ua. Smay n ou noaon no ouon qu: y ma '() ' < () wh y '() an '() a o a. Equaon () mpy man ha h op o h ua hou no b ga han ha o any pob gh ay apu. Th aumpon how ha o uy. W a h a an amp wh ouon an b o un ou paamzaon. In h manm n pa muua ouon a on mo gnan han -ouon an ou ob an omm b ompo no ma ob o ha h ouon bom muua. Whn ob o no ou hm h pum an b oban hough pouy mnon mho a h a no ouon. h numb o ob n h n b N. ( ) N 1 b h N W am muua ouon mo gnan han -ouon bau h om on au a hap bounay/g n h EPI wh -ouon on o no h ua noma hang owy

11 gh an ( ) N 1 ob a: b h Fou anom. W ao n a hou gh o ah ( ) 1 whn gh ay an b a bak o ob ( ) N 1 (1) ohw Th Fou anom a no a SI ( ) N 1 oban by ng ( ) 1 on ob ua.. No ha h hou pum an b W a now ay o n h pum o h ou n. Sn Fou anom na h oa pum mpy h um o nua ob pum. I an ob no ou w an u a pum o h oa on. Ohw ob b ou by M oh ob ( M < N 1 ). Dno h M oung ob hou gh a ( ) M 1 gh an b wn a: wh o ( ) o M 1 [ ] ( ) ( ) 1 ( ). Th onbuon ob ha o h oa () h ou gh o ob. I Fou anom : o ( ) ( ) ( ) SI ( ) wh an o onouon ( ) [ ] [ ( ) SI ( )] δ () δ M 1 δ h Fou anom o onan 1. Fom Equaon () w an ha h pum o an ou ob unou pum moua by a h oung ob hou pum. Th mouaon w bng om aona omponn o h oa pum. Fgu 8 (a) how an amp amban n ha ha h ob. Eah ob a a onan ph an ha wo nuo pa a u. Tho om wha w ha n ubon A no ouon on o ( ) an SI ( ) boh on a n who op wh h ph o h ob. Sn ob a ga ph a ou by o ob w w no aona moua omponn aong ag op n. Moo h aona moua omponn w b aong ma op oponng o h o ob. Th ay hown n Fgu 8 (). IV. Anay o Sn wh Unknown Gomy Th ua pnop unon n on h n gomy. I may au h munanng ha h abo anay no appab whn h n gomy n unknown. In h on w how how uh n an b anayz wh h unang wnow anay [6] an h onuon oban abo. W know ha pob o appoma a omp n wh mup onan ph ay. In [6] Cha a. aop uh aumpon an ga a unang wnow anay o non-amban n. Thy how ha h no ouon h pum uppo o ah ay ook k a naow p. Th oa pum mpy h um o h pum o a h ay. A a o appomaon h oa pum w b

12 bwn wo op on mn by h mnmum ph mn an h oh mn by h mamum ph ma. Th awn n Fgu 9 (a). Whou o o gnay w aum n h pap ha h pum many boun by h ouon o h ama an h un o h u a 1 o ha < <. I angua ampng app a mnmum ampng a h pum pa a n Fgu 9 (b). Th oponng mamum ampng an ao popo o u ma wh pn h oa ngh. Th auho o [6] mn 1 ( 1 1 ) ma mn ma op a h b ph o n h n whh an b ay oban 1 hough Fgu 9 (b). I h n non-amban a ha h unang wnow anay a p ha o ah ay h pum uppo bom a a p. Th au h ogna an-k pum o b pan. I h SPF ban-m aong h gh banwh panon ao m a hown n Fgu 1 (a). Th o gon an o h a pum uppo au by h non-amban ua. A ona maon o h amoun o panon B on ah aong h hozona a mn ba on h uon a Equaon (1). Tho wh angua ampng h b way o ompa h pum a Fgu 1 (b) an h ampng a o non-amban n ha o b na. Nh h o non- amban popy on u o ob n h pum bau ypay h gh ay om h am ua pon hang aan y owy. W n how an amp wh w ha o ak mo mag n o o n oy bau o h non-amban popy. W n wo ph (Fgu 11 (a) an (b)) - on amban an h oh a puy ua. Manwh w aum ha w ha a 6-b ph map o h n. Aong o h ampng u popo n [6] h numb o mag qu o nng h n u w ha an aua ph map. W oun ha a a an ampng a w a ab o onu h amban n y w a n Fgu 11 (). How w u h am ampng a o h ua h onuon y ba (Fgu 11 ()). Th man ha w n o amp mo mag o onu h a ua. Th unang wnow anay an b app o mo omp n ouon ha o b on. Whn h n hay ou a ay w b bok by o ay whh au a pum mouaon a n Equaon (). In wo a h mao oung ob a a mn whh gna aona moua omponn aong h op mn wh h oa ngh. Th oponng pum gn n Fgu 1 (a). Th o uppo h aona moua omponn. I w appy h angua ampng agy h pum an b ompa a n Fgu 1 (b). No ha w ha o na h mnmum ampng a by a ao o. O h mamum ampng an Manwh om Fgu 1 (b) w ha h opma nng ph bom 1 ma. ( 1 1 ) mn ma mn na o op. In gna - 1 -

13 whn h mao oung ob a a an o h pum hown n Fgu 1 (). A h mo ompa angua ampng h pum hown n Fgu 1 (). Th mnmum ampng a an h mn ma opma nng ph boh pn on o. W g an amp o y h abo anay. In Fgu 1 (a) w how an OpnG n ompo o ub. Th ub ay on a D gua g an ha a o o ouon. Th n paam a: oa ngh 18 mnmum ph 6 an mamum ph 18. A h nng a on hough pho bna npoaon. W amp h n wh h appoah n [6].. ma.146. Fgu 1 (b) an () how h n n wh nng ph an op ( 1 1 ) mn ma mn py. W oun ha h n n wh op appa b han h oh wh mn. How boh mag appa bu. In Fgu 1 () an () w na h ampng a by a ao o. Fgu 1 () n a op wh Fgu 1 () n a mn. I obou ha () muh b han () an () ao b han (b). Th a ha () muh b han () po ha h aona moua omponn ha o b on ung h ampng an nng. I h aona moua omponn ou b gno nng a op wou ha a a gna a goo u a (). Tha om Fgu 1 (b) h wa no o aa u o h ouon op wou b on o h b nng ph. V. Anay on Conn Moa D onn moa apu by oang a ama aong a a hown n Fgu 14. h au b. W n onn moa by wo ang an. pn h ang bwn h gh ay an h ama opa a; no wh h ama on h. Fo onn moa w u poa S o oona na o angua oona. Th ob ua a pn a ( ) Th gh ay n n by pa ( ) : n (4) n( ) Equaon (4) ay omp w wan o o o an om an φ. Po ha n pa h FOV o h ama on m w () () n. Bau o h up o onn moa h ob n h n mu b ou h apung w ha <. Tho w an ao n ( ). Equaon (4) hu mp a: ( ) (5). Whn h FOV abou 4 g.. / 9. Makng n ha % mamum o. No ha n onn moa w ha h am nazaon o a n gh (Equaon (7))

14 W ao ha mp aonhp: (6) Sma o h anay n gh gh ay hou b a bak o a o pon on h ob ua who a ngh an b oban hough ong: () () (7) Equaon (7) n ga may o Equaon (8). Tho uon on gh an b boow y. In h on w ony g a mp amp by onng a n a onan ph. A onan ph onn moa n b a: () () (8) wh h ph o h n. W an ay o Equaon (7): (9) Th onn moa pum an b a: 1 1 () Agan h pum a oa on o ha o SPF pu om magnu hang an pha h. I h n amban o δ w uh ha: 1 1 δ (1) Th pum on a n ha ha op. Sn > h op away han 45 g. Fgu 15 (a) how an amp n a onan ph wh wo nuo pa a u. In Fgu 15 (b) h oona an a a n a o h op o no map o h u au. How h pum n Fgu 15 () obouy aong a n. I h a bwn an h am h n w ah mamum op whn h ph o h n bom nn.

15 VI. Non-angua Sampng o IB Chan an Shum w h auho who az ha h pnop ampng pobm baay a mumnona ampng pobm [7]. I w known ha h angua ampng agy no nay opma o mumnona gna [17]. Ina h gnaz po ampng hoy wh abay gomy hou b app. W h a o h hoy o [17][18]. In [7] h auho mnon ha ao pob o mn h mnmum ampng n o h qunun an hagona ampng a. W ha pom om pmn on non-angua ampng o IB. W w by go o ou pmn an g om ommn. Mumnona gna an b amp on a a n h paa oman whh a o h paon o h Fou anom on anoh a n h quny oman. Fo h gh pum ak non-amban an no ouon n a an amp. Th pum an b ompa a n Fgu 16 (a) whh mp qunun/hagona ampng. Wh h ampng agy h ampng ny an b mpo by a ao o ompa o angua ampng n Fgu 9 (b) whh man w ony n 5% o h amp. Obouy h onuon a an-k. In hoy w may b ab o onu h ogna IB gna whou ong any nomaon. In pa how w anno gn an a onuon whou anon ban. W hoo o u h ampng ny o h a o onuon. To g a a ompaon bwn h qunun/hagona ampng (QS) an h angua ampng (S) w hm ha h am ampng ny. Th S pum hown n Fgu 9 (b) wh h QS pum hown n Fgu 16 (b). W gn onuon o QS wh h gn appoah [19][]. Fo S w u h bna npoaon. Pa o [16] o a pon on h QS an onuon gn. W how om pmna u on h wo n ampng appoah. In o o ha u ono on h n an h ama w hoo wo n n om D mo wh u. Th n a hown n Fgu 17 wh n (a) an (b) a nam Duk an Conan py. Sn w ou on D gh n h pap w ak h n hozona n o onu h EPI. Fgu 17 (a1) an (b1) a napho o h n; (a) an (b) a h EPI; (a) an (b) a h Fou anom o h EPI. Ahough ouon an b ob n h n w gno hm n ou anay n h aona moua omponn au by ouon a no gnan n h wo amp. Fom h Fou anom o h n n Fgu 17 w an n h oponng ampng a o ompa h pum o Fgu 9 (b) an Fgu 16 (b). On houan anom mag a hn n o ah n wh h onuon. Th mag a ao ynhz hough h D mo nng ngn. Th n bwn h ynhz mag an h n mag u o mau h quay o h ampng po. In ou pmn PSN u o mau uh n. Th u a hown n Tab I. W ob ha o mooh n a Duk h mag quay o S an bna npoaon auay b han ha o QS an oponng onuon. Whn n ha mo hgh quny omponn a n Conan h a appoah ghy b han h om on. Th abo amn gnay a an an b u by ookng a how S an QS pa h pum. In Fgu 9 (b) o S wo nghbong paon ha a hug mpy pa n bwn whn h quny ow

16 bu hy amo ouh whn h quny hgh. A a ompaon n Fgu 16 (b) o QS h pa n bwn kp a a onan. Tho S mo uab o n ha ha pan ow quny omponn an o no ha oo muh hgh quny omponn. Th on u o a wo n. En o h Conan n h mpomn by ung QS mno whh anno uy h na ompy. Sn QS nonn wh how h mag a akn h qu -ampng may nou o. Th nng p anoh onn. Da n [16] h onuon o QS ha o o ou m mo bna npoaon han ha o S. Tho w onu ha angua ampng pab o non-angua ampng o mag-ba nng. VII. Conuon an Fuu Wok In h pap w pn a nw appoah o anayzng h IB pum. W n h ua pnop unon hn how ha any IB pnaon an b u w an n h gh ay mappng om h SPF o h IB pnaon. W how amp wh h mappng an b on o gh an onn moa. Non-amban popy n ph aaon an ouon nauay no ou appoah an w w ab o anayz h o hm a ong a an aumpon a a. W b ha h appoah gay mpo h unanng o IB pa anay. A w aay how n h pap h pum o h IB pnaon y ky o b ban-unm. Th am u wa ao awn n [8]. Th may a o h onuon ha IB ampng mpob. On h oh han uh a non-amban popy ph aaon an ouon a bng n pang o h pum a howng away y ma ban an n many a h amoun o pa pab. In pa h o appomaon (pum boun by h op mn by h mnmum ph an h mamum ph) n [6] o g goo u. Whn h n a hghy o h ouon a y hay w how n on III ha h mnmum ampng a ha o b na up o a an amoun. SPF w b uu n h uh unanng o a numb o IB ah pobm. Fo amp n h mappng bwn SPF an h IB pnaon mn by boh h n gomy an h ama pah h an opma pah ha w hou u o apung a an n? I h ama pah pmn an w know ha h SPF ha goo pop uh a ban-mn mak n o apu mag nonunomy uh ha h ampng on h SPF o o unom. Wok n pog ookng no h oppoun. Aknowgmn Th wok uppo n pa by NSF Ca Awa an Inua Thnoogy ah Inu. W wou ao k o hank h w who ga u nauab ommn an hp u o mpo h quay o h pap

17 n [1] E. H. Aon an J.. Bgn Th pnop unon an h mn o ay on Compuaona Mo o Vua Pong Chap 1 E by Mha any an J. Anhony Mohon. Th MIT P Cambg Ma []. MMan an G. Bhop Pnop mong: an mag-ba nng ym Compu Gaph (SIGGAPH 95) pp Aug [] M. oy an P. Hanahan gh nng Compu Gaph (SIGGAPH 96) pp. 1 Aug [4] S. J. Go. Gzzzuk. Szk an M. F. Cohn Th umgaph Compu Gaph (SIGGAPH 96) pp Aug [5] H.Y. Shum an.-w. H. nng wh onn moa Compu Gaph (SIGGAPH 99) pp.99-6 Aug [6] J.X. Cha X. Tong S.C. Chan an H. Y. Shum Pnop ampng Compu Gaph (SIGGAPH ) pp.7-18 Juy. [7] S. C. Chan an H. Y. Shum A Spa Anay o gh F nng ICIP. [8] D. Mahan-Ma an M. V Sampng Thoy o Imag-Ba nng Ma h EPF Ap. 1. [9] Z. C. n an H. Y. Shum On h Numb o Samp N n gh F nng wh Conan- Dph Aumpon Po. CVP. [1] G. S. P. M S. ubn an D. Ponon azy Dompon o Sua gh F o Pompu Goba Iumnaon nng Thnqu 98 (Po. Euogaph Wokhop on nng) pp Spng [11] D. N. Woo D. I. Azuma K. Ang B. Cu T. Duhamp D. H. San an W. Suz Sua gh F o D Phoogaphy SIGGAPH pp Juy. [1] T.-T. Wong C. W. Fu P.-A. Hng an C.-S. ung Th Pnop Iumnaon Funon IEEE Tan. on Muma pp Vo. 4 No. Sp.. [1] Z.-C. n T.-T. Wong an H.-Y. Shum ghng wh h Iaan F: pnaon Sampng an onuon Innaona Jouna o Compu Von pp Vo. 49 No. - Sp.-O.. [14]. amamooh P. Hanahan A Sgna-Pong Famwok o In nng SIGGAPH 1 pp Aug. 1. [15] D. A. Foyh an J. Pon Compu Von: A Mon Appoah Pn Ha. 1 on (Augu 14. [16] C. Zhang an T. Chn Gnaz Pnop Sampng Cang Mon Uny Thna po AMP1-6. [17] D.E. Dugon an.m. Mau Mumnona Dga Sgna Pong Pn-ha gna pong [18] P. P. Vayanahan Mua Sym an F Bank Pn-ha gna pong 199. [19] P. P. Vayanahan an T. Q. Nguyn Egn: A Nw Appoah o a-squa FI F Dgn an Appaon Inung Nyqu F IEEE Tan. on CAS pp. 11- Jan [] T. Chn Un Egn Appoah: wh Appaon o Spa/Spaa Fng IEEE ISCAS Chago May

18 Tab Tab I n mag qua o n ampng mho an onuon Duk Conan S bna npoaon 6.1 B 1.67 B QS onuon gn by h gn appoah 6.6 B.1 B Fgu gh ay Cama pan ( ) u (u ) Foa pan z Ob Fgu 1 On paamzaon o h gh. M u 1 1 Fgu A amp gh mag aay: u pa

19 Cama pah Cama oa Bam u Fgu Conn moa apung. S y Cama pah ( y) O () y y () Ob 1 S ( y) 1 O 1 () y y1() S ( y) O () y y () Ob Fgu 4 D ua pnop unon an gna IB apung. y Ob 1 S ( y) 1 O 1 () y y1() S ( y) O () y y () - Ob Fgu 5 Th gh paamzaon

20 y Ob a onan ph (a) (b) () () () Fgu 6 amban an non-amban n a onan ph. (a) A n a onan ph. (b) Th EPI o h gh whn h n amban. () Th Fou anom o (b). () Th EPI o h gh whn h n non-amban. () Th Fou anom o (). - -

21 y Ob on a n (a) (b) () Fgu 7 A pana n wh a nuo pa a u. (a) Th n on a n. (b) Th EPI o h gh. () Th Fou anom o (b). y Ob 1 Ob Ob 1 (a) (b) () Fgu 8 A h-ay n wh nuo pa a u. (a) Th ob on n onan ph. (b) Th EPI o h gh. () Th Fou anom o (b)

22 ma Opma nng ph mn by: op B (a) mn (b) Fgu 9 Fquny pon o a no ouon EPI an h opma ampng n [6]. (a) Fquny uppo o a n wh no ouon an amban mo. (b) Th Opma ompang an h onuon n [6]. ma B mn Opma nng ph mn by: op (a) mn (b) Fgu 1 Opma ampng whn h n non-amban. (a) Th pum pan om h amban a. (b) Opma ompang o h pum o angua ampng. - -

23 (a) (b) () Fgu 11 An amp o how h mnmum ampng a o non-amban ua. (a) A amban ph. (b) A puy ph. () A a an ampng a w a ab o onu h n y w o h amban ph. () A h am ampng a h onuon y ba o h ua. () ma Opma nng ph mn by: mn B mn (a) (b) o () () Fgu 1 Opma ampng whn h a ouon. (a) Th mo ona maon o h pum whn h ob a mn au h mao ouon (b) Th opma angua ampng agy o ompang (a). () Th pum gn ha h ob a o h man ou o ouon. () Th opma angua ampng agy o ompang (). - -

24 (a) (b) () () () Fgu 1 An amp o how h mnmum ampng a un hay ouon. (a) Th hay ou n. (b) U h mnmum ampng a n [6] n wh op (b) bu n wh mn. () U w h ampng a n (b) n wh op n wh mn.. () Sam a. () Sam a () bu - 4 -

25 S ( ) O () () Fgu 14 Th onn moa paamzaon. Ob a onan ph Cama aaoy (a) (b) () Fgu 15 A onan ph onn moa n wh nuo pa a u. (a) A n a onan ph. (b) Th EPI o h onn moa whn h n amban. () Th Fou anom o (b)

26 B (a) (b) Fgu 16 Qunun/hagona ampng o IB. (a) Th mo ompang paapp ampng. (b) Th qunun/hagona ampng ha ha h am ampng a a h opma angua ampng. (a1) (a) (a) (b1) (b) (b) Fgu 17 Th ng n EPI an h Fou anom. (a) Th n Duk. (b) Th n Conan