AN APPROACH TO CODED STRUCTURED LIGHT TO OBTAIN THREE DIMENSIONAL INFORMATION Joaquim SALVI MAS ISBN: Dipòsit legal: GI

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1 AN APPROACH TO CODED STRUCTURED LIGHT TO OBTAIN THREE DIMENSIONAL INFORMATION Joaquim SALVI MAS ISBN: Dipòsit legal: GI

2 PhD. Thesis UNIVERSITY OF GIRONA Department of Electronics, Informatics and Automation to obtain the degree of: European PhD in Industrial Engineering by: Joaquim Salvi Title of the thesis: An Approach to Coded Structured Light to Obtain Three Dimensional Information Submitted and presented in Girona, december 1997 and february 1998 respectively: Supervisor: Dr. Joan Batlle (Universitat de Girona Spain) Supervisor: Dr. El Mustapha Mouaddib (Université de Picardie Jules Verne France) Referee: Referee: President: Examiner: Examiner: Examiner: Examiner: Professor Bernard Dubuisson (Université de Compiègne France) Dr. Geoff Roberts (University of Wales College Newport Great Britain) Professor Josep Amat (Universitat Politècnica de Catalunya Spain) Professor Juan Jose Villanueva (Universitat Autònoma de Barcelona Spain) Professor Antonio Perez (Universidad Politécnica de Madrid Spain) Professor Emilio Zapata (Universidad de Málaga Spain) Dr. Geoff Roberts (University of Wales College Newport Great Britain)

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61 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 95 Ohw xv mxvwli krz d furvv0surgxfw ehwzhhq wzr yhfwruv fdq eh h{suhvvhg lq d pdwulfldo zd xvlqj wkh dqwlv pphwulf pdwul{1 Frqvlghu wzr yhfwruv R dqg R / wkhq wkh furvv0surgxfw R a R fdq eh h{suhvvhg dv wkh surgxfw riwkh dqwlv pphwulf pdwul{ ri R ghqhg dv dro % e R / dv kdv ehhq suryhg lq 615:1 R ' % + 5 R ' % , 5, ' R a R ' 7 & 6 5 % ' 5 % ' 7 f 5 5 f % 8 + % f 7 % % %5 %+ +% 6 8 ' 8 ' dro % R +615:, Dw wklv srlqw/ wkh ixqgdphqwdo pdwul{ fdq eh frpsxwhg dv wkh uhodwlrq riwkh hslsrodu olqh, 6 ridq lpdjh srlqw 6 dqg lwv fruuhvsrqghqfh srlqw 6 1 Jlyhq d fruuhvsrqghqfh srlqw 6 /ri6/ lw pxvw olh rq olqh, 61Wkhq/ vlqfh/ 6, 6 'f +615;, RR ' nrnnr n ULt E) +615<, Lqidfw615;h{suhvvhvwkhsurgxfwri wzryhfwruv1 Wkhuvwrqhlvwkh yhfwru ghqhg e wkh irfdo srlqw dqg wkh fruuhvsrqghqfh srlqw 6 1 Wkh vhfrqg rqh/, 6 lv ghqhg e wkh furvv0surgxfw ehwzhhq yhfwru e dqg yhfwru 6 "1 Liwklv surgxfw lv htxdo wr f / wkhq wkh wkuhh yhfwruv duh fr0sodqdu1 Rshudwlqj/ 615; fdq eh h{suhvvhg dv/ 6 de o % 3 6 'f +6163, Wkhq/ zh fdq ghqh wkh ixqgdphqwdo pdwul{ 6/ dvwkh % pdwul{/ zklfk uhodwhv wkh hslsrodu olqh, 6 ridq lpdjh srlqw 6 dqg lwv fruuhvsrqghqfh srlqw 6 lq wkh iroorzlqj zd / 6 66 ' f +6164, 6 ' de o % , Zlwkrxw frpsoh{lw wkh uhdghu fdq xqghuvwdqg wkdw dqrwkhu ixqgdphq0 wdo pdwul{ fdq eh h{wudfwhg iurp wkh uhodwlrq ri erwk fdphudv1 6 zloo eh

62 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 96 ghqhg dv wkh ixqgdphqwdo pdwul{ zklfk uhodwhv wkh hslsrodu olqh, 6 ridq remhfw srlqw 6 dqg lwv fruuhvsrqghqfh srlqw 61 6 lv frpsxwhg wkurxjk wkh iroorzlqj htxdwlrqv/, 6 ' e a 6 " +6166,, 6 ' e a ,, 6 ' deo % , 6, 6 ' f +6169, 6 deo % 3 6 ' f +616:, ' f +616;, 6 ' deo % <, Zkhuh lw fdq eh suryhg wkdw 6 ' 6 /vr/ 6 66 ' f +6173, ' f +6174, Wkh uhdghu lv uhihuuhg wr vhfwlrq zkhuh lw lv vhw iruwk dqg suryhg wkdw 6 ' Fkdqjlqj wkh fr0ruglqdwh v vwhp Lq wkh iroorzlqj/ zh lqglfdwh zklfk vlpsolfdwlrqv fdq eh frqvlghuhg lq wkh ghqlwlrq riwkh ixqgdphqwdo pdwul{ lizh dvvxph wkdw zh duh xvlqj wkh qrupdolvhg fdphud prgho dqg/ liwkh zruog uhihuhqfh fr0ruglqdwh v vwhp fr0 lqflghv zlwk wkh fr0ruglqdwh v vwhp rirqh fdphud1 Dv d uvw dssurdfk/ frqvlghu rqo wkh uhodwlrq zlwk erwk fdphud fr0ruglqdwh v vwhpv/ zlwkrxw wdnlqj lqwr dffrxqw wkh lqwulqvlf pdwulfhv ru 1 Wklv idfw zloo vlpsoli wkh htxdwlrqv1 Krzhyhu/ wkh lqwulqvlf pdwulfhv zloo eh xvhg odwhu Zruog fr0ruglqdwh v vwhp {hg dw wkh vhfrqg fdphud/ rshudwlqj zlwk uhvshfw wr wkh uvw fdp0 hud1 Ohw xv hvwdeolvk wkh zruog fr0ruglqdwh v vwhp ` dw wkh vhfrqg fdphud/ zlwk dq ruljlq dqg d fr0ruglqdwh v vwhp f 1 Wkhq/ wkh fr0ruglqdwh v vwhp f riwkh uvw fdphud fdq eh uhodwhg wr wkh vhfrqg rqh e d urwdwlrqdo dqg d

63 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 97 W p P P X X C C K Iljxuh 617= Jhrphwulfdo uhodwlrq rierwk fdphud d{hv dqg d zruog fr0ruglqdwh v vwhp1 Zruog fr0ruglqdwh v vwhp {hg dw wkh uvw fdphud1 wudqvodwlrqdo pryhphqw/ zklfk doorz xv wr h{suhvv wkh ixqgdphqwdo pdwul{ iurp erwk pryhphqwv zlwkrxw frqvlghulqj wkh jhqhudo dqg pdwulfhv1 Frqvlghu wkh jhrphwulfdo uhodwlrq vkrzq lq jxuh 6171 Liwkh zruog fr0ruglqdwh v vwhp ` lv sodfhg dw / zlwk wkh vdph rulhqwd0 wlrq ri f/ wkh wudqvirupdwlrq pdwul{ ri wkh uvw fdphud/ douhdg lqwurgxfhg lq wkh suhylrxv vhfwlrq/ lv jlyhq e / h ' W f +6175, zklfk doorzv xv wr ghqh wkh vhfrqg fr0ruglqdwh v vwhp f /e dpdwul{ ghqhg e d urwdwlrq pdwul{ + dqg d wudqvodwlrq yhfwru / h ' k h + 3 k ' f +6176, Wkhq/ wkh htxdwlrq 6176 fdq eh rewdlqhg iurp jxuh 617 dsso lqj wkh iroorzlqj uhodwlrqv/ Rm ' k 3 Rm +6177, h 3 Rm` ' k 3 h 3 Rm` +6178, h 3 ' k 3 h , h ' h k +617:, hk 3 ' h kk ;,

64 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 98 h ' h k <, Rshudwlqj wkh htxdwlrq 6176 zh rewdlq wkh pdwul{ h h{suhvvhg lq htxd0 wlrq Dv/ h ' , k 3 ' ' ' 3 + W + f ' f f f W + f f ' f + + f 3 f ' f W f +6184, Qh{w/ zh zloo vlpsoli wkh iroorzlqj htxdwlrqv zklfk ghvfuleh wkh hslsrohv/ e ' h e ' h +6185, +6186, Zh fdq uhodwh wkh irfdo srlqw zlwk uhvshfw wr f/ dvwkhsrlqworfdwhg dw d glvwdqfh iurp wkh ruljlq 1 Wkhq/ wkh hslsroh e fdq eh vlpsolhg lq wkh iroorzlqj zd / e ' h ' h ' +6187, Lq wkh vdph zd / xvlqj htxdwlrq 6183 dqg wkh idfw wkdw lv wkh ruljlq ri wkh zruog fr0ruglqdwh v vwhp/ zh rewdlq/ e ' h f ' + + f ' , Wkh hslsrodu olqh, 6 fdq eh vlpsolhg e wkh iroorzlqj htxdwlrq/ dv/, 6 ' de o % 3 6 ' + a ,

65 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 99 3 ' + W ' :, wkhq/ iurp wkh ihdwxuhv ri wkh furvv0surgxfw/ zh nqrz wkdw htxdwlrq 6189 fdq eh h{suhvvhg dv/, 6 ' + E a 6 '+ d o % ;, Dv 6 lv dozd v ghqhg iurp d vfdoh idfwru zh fdq ljqruh wkh vljq/ wkhq/ Dqg wkh rwkhu hslsrodu olqh, 6, 6 ' + d o % <, fdq eh h{suhvvhg e /, 6 ' e a 3 6 ' a +6 ' d o % , wkdw lv ehfdxvh 3 ' E+ 3 ' +/ dv iru dq urwdwlrq pdwul{ + lw lv dozd v wuxh wkdw + 3 ' + 1 Qrz/ zh zdqw wr frqvlghu wkh lqwulqvlf pdwulfhv1 Wkhq/ jlyhq dq lghdo surmhfwlrq 6 dqg 6 lq phwulf xqlwv/ lwv uhdo surmhfwlrq h6 dqg h6 lq sl{hov/ duh jlyhq e wkh iroorzlqj htxdwlrqv/ h6 ' 6 6 ' 3 h6 h6 ' 6 6 ' 3 h , Wkhq/ zh rewdlq wkh iroorzlqj htxdwlrq/ zkhuh/ h6 6 h6 'f +6195, 6 ' 3 + d o % , Wkh iroorzlqj h{sodlqv krz zh kdyh rewdlqhg htxdwlrq Zh ghqh dq hvvhqwldo pdwul{, zklfk grhv qrw frqvlghu wkh lqwulqvlf pdwulfhv olnh wkh rog ixqgdphqwdo pdwul{/ wkhq/, ' + d o % +6197, 6,6 'f +6198, xvlqj wkh htxdwlrqv ghqhg lq 6194 zh rewdlq/ 3 h6, 3 h6 'f +6199,

66 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 9: vlqfh zh nqrz wkdw/ E ' 1 Wkhq zh fdq rewdlq htxdwlrq 619: zklfk lv vlplodu wr 6196 lizh vxevwlwxwh, e htxdwlrq h6 3, 3 h6 'f +619:, Wkh rwkhu ixqgdphqwdo pdwul{ fdq eh fdofxodwhg lq wkh vdph zd / rewdlq0 lqj/ zkhuh/ 'f +619;, 6 ' 3 d o % <, Lqwkhvdphzd /zhfdqsuryhkrzzhkdyhrewdlqhghtxdwlrq619<ghq0 lqj dqrwkhu hvvhqwldo pdwul{, c dv uhodwhg lq wkh iroorzlqj htxdwlrq1 xvlqj 6194 zh rewdlq/, ' d o % + +61:3, 3 h6, 3 h6 'f +61:4, zklfk doorzv xv wr jlyh wkh iroorzlqj htxdwlrq/ zklfk lv vlplodu wr 619< li zh vxevwlwxwh, e 61:3/ h6 3, 3 h6 'f +61:5, Zruog fr0ruglqdwh v vwhp {hg dw wkh uvw fdp0 hud/ rshudwlqj zlwk uhvshfw wr wkh vhfrqg fdp0 hud1 Vrph dxwkruv suhihu wr hvwdeolvk wkh zruog fr0ruglqdwh v vwhp dw wkh uvw fdphud1 Wkhq/ wkh zkroh jhrphwu lv frpsxwhg frqvlghulqj wkdw zh duh sodfhg dw wkh vhfrqg fr0ruglqdwh v vwhp1 Ohw xv hvwdeolvk wkh zruog fr0ruglqdwh v vwhp ` dw wkh uvw fdphud/ zlwk dq ruljlq dqg d fr0ruglqdwh v vwhp f1 Wkhq/ wkh fr0ruglqdwh v vwhp f riwkh vhfrqg fdphud fdq eh uhodwhg zlwk uhvshfw wr wkh uvw rqh e d urwd0 wlrq dqg d wudqvodwlrq1 Wklv uhodwlrq/ dv kdv ehhq h{sodlqhg lq wkh suhylrxv vhfwlrq/ doorzv xv wr h{suhvv wkh ixqgdphqwdo pdwul{ zlwkrxw frqvlghulqj wkh jhqhudo dqg pdwulfhv1 Frqvlghu wkh jhrphwulfdo uhodwlrq vkrzq lq jxuh 6181

67 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 9; W p P P X X C C K Iljxuh 618= Jhrphwulfdo uhodwlrq rierwk fdphud d{hv dqg d zruog fr0ruglqdwh v vwhp1 Zruog fr0ruglqdwh v vwhp {hg dw wkh vhfrqg fdphud1 Ohw xv sodfh wkh zruog fr0ruglqdwh v vwhp ` dw / zlwk wkh vdph rulhq0 wdwlrq riwkh fr0ruglqdwh v vwhp f 1 Wkhq/ wkh wudqvirupdwlrq pdwul{ h ri wkh vhfrqg fdphud lv jlyhq e / h ' W f +61:6, zklfk doorzv xv wr ghqh wkh uvw fr0ruglqdwh v vwhp f/ e dpdwul{ h ghqhg e d urwdwlrq pdwul{ + dqg d wudqvodwlrq yhfwru / h ' h + k 3 k ' f +61:7, Rshudwlqj/ Wkhq/ wkh wzr hslsrohv fdq eh frpsxwhg/ e ' h e ' h h ' :8, ' + + f ' + +61:9, ' h ' W f ' +61::, Wkh hslsrodu olqh, 6 fdq eh vlpsolhg e wkh iroorzlqj htxdwlrq/

68 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ 9<, 6 'de o % 3 6 ' a +6 'd o % :;, dqg wkh rwkhu hslsrodu olqh, 6 e /, 6 ' e a 3 6 ' + a + 6 ' + d o % 6 ' + d o % 6 +61:<, Frqvlghulqj wkh vdph pdwkhpdwlfdo surfhgxuh h{sodlqhg lq htxdwlrqv :5 zh fdq lqfoxgh wkh lqwulqvlf pdwulfhv1 Ilqdoo /d ixqgdphqwdo pdwul{ fdqehrewdlqhgiurphdfkhslsroduolqh/ h6, 6 ' h6 6 h6 'f +61;3, 6 ' 3, 3 +61;4,, ' d o % + +61;5, dqg/ h6, 6 ' h6 6 h6 'f +61;6, 6 ' 3, 3 +61;7,, ' + d o % +61;8, Uhodwlrq ehwzhhq erwk Ixqgdphqwdo Pdwulfhv Wklv vhfwlrq zloo suryh wkdw erwk ixqgdphqwdo pdwulfhv 6 dqg 6 duh uhodwhg e d wudqvsrvh/ wkdw lv/ 6 ' 6 +61;9, 6 ' 6 +61;:, Iluvwo / zh kdyh wr uhphpehu vrph xvhixo ihdwxuhv ri wkh pdwulfldo dojheud= E 3 ' 3 3 E ' E 3 ' E 3 ' 3 d o % ' d o %

69 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ :3 Zh zloo ghprqvwudwh wkh wudqvsrvh uhodwlrq ehwzhhq wkh ixqgdphqwdo pd0 wulfhv rivhfwlrq Wkh uhdghu pd qrwh wkdw wklv ghprqvwudwlrq dovr yhulhv wkh ixqgdphqwdo pdwulfhv ri vhfwlrq ' 3 + d o % 3 +61;;, 6 ' 3 + d o % 3 ' + d o % 3 3 ' +61;<, ' d o % ' 3 d o % + 3 ' 6 +61<3, dqg/ 6 ' 3 d o % <4, 6 ' 3 d o % + 3 ' d o % ' +61<5, ' + 3 d o% 3 ' 3 + d o % 3 ' 6 +61<6, Vlqfh 6 dqg 6 duh dozd v ghqhg iurp d vfdoh idfwru/ zh kdyh ghprq0 vwudwhg wkh uhodwlrq/ dv wkh vljq fdq eh ljqruhg Ihdwxuhv ri Srlqwv dqg Yhfwruv Zh kdyh ghflghg wr uhodwh erwk fr0ruglqdwh v whpv e d urwdwlrq pdwul{ + dqg d wudqvodwlrq yhfwru 1 Wkh vhfrqg v vwhp fdq eh uhodwhg iurp wkh uvw e wkh iroorzlqj htxdwlrq/,@r ' + sor n +61<7, Dq lpdjh srlqw 6 R lv ghqhg dv yhfwru 6 iurp wkh irfdo srlqw dqg wkh srlqw rq wkh lpdjh sodqh 6 R 1 Iru d frqyhqlhqfh/ zh kdyh xvhg 6 dv d srlqw/ dowkrxjk zh kdyh wr ehdu lq plqg wkdw lw lv dfwxdoo d yhfwru1 Dw wklv srlqw zh kdyh wr uhphpehu wzr ihdwxuhv = 6 ' 6 R +61<8, 4, Jlyhq d srlqw lq wkh uvw lpdjh zklfk kdv ehhq {hg dv wkh ruljlq riwkh fr0ruglqdwh v vwhp1 Lwv fruuhvsrqghqfh srlqw lq wkh vhfrqg fr0ruglqdwh v vwhp lv jlyhq rqo e wkh wudqvodwlrq yhfwru 1

70 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ :4 ' + sor n ' + 7 f f f 6 8 n ' +61<9, ',@r sor +61<:, 5, Jlyhq d yhfwru uhodwhg iurp wkh uvw fr0ruglqdwh v vwhp/ lwv wudqviruphg yhfwru iurp wkh vhfrqg fr0ruglqdwh v vwhp lv ghqhg rqo e wkh urwdwlrq pdwul{ +/ dv d yhfwru lv rqo ghqhg e lwv rulhqwdwlrq zlwk uhvshfw wr hdfk d{h/ qrw zlwk uhvshfw wr lwv srvlwlrq lq wkh vsdfh1,@r ' + sor n ' + sor +61<;, Erwk ihdwxuhv kdyh ehhq eurdgo xvhg lq wkh suhylrxv vhfwlrqv lq rughu wr ghgxfh wkh ixqgdphqwdo pdwul{1 616 Ghwhuplqlqj wkh ixqgdphqwdo pdwul{ Wkh sureohp wr frqvlghu lv wkh hvwlpdwlrq ri wkh ixqgdphqwdo pdwul{ iurp d vhw rilpdjh srlqw fruuhvsrqghqfhv i h6 c h6 j1 Zh duh qrw lqwhuhvwhg lq krz wkh fruuhvsrqghqfhv ehwzhhq wzr lpdjhv fdq eh hvwdeolvkhg1 Krzhyhu/ wkh uhdghu pxvw nqrz wkdw wkh ixqgdphqwdo pdwul{ zloo eh fdofxodwhg iurp wkhvh fruuhvsrqghqfhv1 Wkh dffxudf riwkh uhvxowv zloo ghshqg gluhfwo rq wkh dffxudf riwkh whfkqltxh xvhg wr hvwlpdwh wkh pdwul{/ dqg lq d juhdw pdjqlwxgh/ lw dovr ghshqgv rq wkh whfkqltxh xvhg wr ghwhuplqh wkh fruuh0 vsrqghqfhv ehwzhhq erwk lpdjhv1 Wkh fruuhvsrqghqfhv ehwzhhq wzr lpdjhv fdq eh hvwdeolvkhg xvlqj dq riwkh whfkqltxhv ghvfulehg lq ^]kdq <6e`1 Lq idfw/ wkh ghwhuplqdwlrq ri wkh ixqgdphqwdo pdwul{ lv wkh sureohp ri vroylqj htxdwlrq 61<<1 Lq rwkhu zrugv/ lw lv wkh sureohp riqglqj rxw wkh frh!flhqwv ripdwul{ 6 zklfk vroyh wkh iroorzlqj htxdwlrq/ h6 6 h6 'f +61<<, Vhyhudo phwkrgv kdyh ehhq sursrvhg lq uhfhqw hduv1 Wkh uhdghu lv uh0 ihuuhg wr ^Oxrq <6e` wr kdyh dq ryhuylhz ri wkh sureohpv lqyroyhg lq gh0 whuplqlqj wkh ixqgdphqwdo pdwul{1 Wzr phwkrgv kdyh ehhq vwxglhg/ wkh uvw rqh lv edvhg rq wkh lwhudwlyh whfkqltxh riixqfwlrq plqlplvdwlrq sur0 srvhg e Qhzwrq0Udskvrq zklfk kdv ehhq lqwurgxfhg lq fkdswhu wzr/ dqg

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77 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ :; Iljxuh 619= Dq h{dpsoh riwkh hslsrodu jhrphwu prghoohg e wkh ixqgd0 phqwdo pdwul{1 Qrwh wkh hslsrohv dqg wkh hslsrodu olqhv irxqg1 Wkh duhd gholplwhg e wkh fruuhvsrqghqfh srlqwv/ kdyh ehhq pdunhg e d vtxduh1 Iljxuh 61:= D }rrp riwkh vtxduh duhdv riwkh suhylrxv lpdjhv1 Qrwh wkdw wkh fruuhvsrqghqfh srlqwv olh dozd v rq wkh hslsrodu olqhv ghqhg e wkhlu frxsoh srlqwv1

78 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ :< Wkh dojrulwp xvhg wr lqihu wkh ixqgdphqwdo pd0 wul{ Wkh dojrulwp kdv ehhq surjudpphg xvlqj wkh Pdsoh Y Uhohdvh 7 U hqylurq0 phqw1 A zlwk+olqdoj,= A &&&&&&&&&&&&&&&&&&&&&&&&&& A & Rewdlqlqj wkh ixqgdphqwdo pdwul{ A &&&&&&&&&&&&&&&&&&&&&&&&&& A U{=@duud +^^4/3/3`/^3/frv+d,/vlq+d,`/^3/0vlq+d,/frv+d,``,> A U =@duud +^^frv+e,/3/0vlq+e,`/^3/4/3`/^vlq+e,/3/frv+e,``,> A U}=@duud +^^frv+f,/vlq+f,/3`/^0vlq+f,/frv+f,/3`/^3/3/4``,> A W=@duud +^^3/0w}/w `/^w}/3/0w{`/^0w /w{/3``,> U=@pxowlso +U{/pxowlso +U /U},,> A D4=@duud +^^dx4/3/xr4`/^3/dy4/yr4`/^3/3/4``,> A D5=@duud +^^dx5/3/xr5`/^3/dy5/yr5`/^3/3/4``,> A D4l=@lqyhuvh+D4,> D5l=@lqyhuvh+D5,> D5lw=@wudqvsrvh+D5l,> A IL=@pxowlso +D5lw/pxowlso +W/pxowlso +U/D4l,,,> A I=@duud +^^i44/i45/i46`/^i54/i55/i56`/^i64/i65/i66``,> A p5=@yhfwru+^x5/y5/4`,> p4=@yhfwru+^x4/y4/4`,> A p5w=@wudqvsrvh+p5,> A J=@pxowlso +p5w/pxowlso +I/p4,,> A &&&&&&&&&&&&&&&&&&&&&&&&& A & Rewdlqlqj wkh sduwldo ghulydwlyhv A &&&&&&&&&&&&&&&&&&&&&&&&& A gji44=@gl+j/i44,> gji45=@gl+j/i45,> A gji46=@gl+j/i46,> gji54=@gl+j/i54,> A gji55=@gl+j/i55,> gji56=@gl+j/i56,> A gji64=@gl+j/i64,> gji65=@gl+j/i65,> AgJi66=@gl+J/i66,> A & Uhdg wkh fruuhvsrqghqfh srlqwv A uhdgole+uhdggdwd,> A Ps=@uhdggdwd+fruub8/9,> A P=@pdwul{+urzglp+Ps,/7/3,= A iru l iurp 4 e 4 wr urzglp+ps, gr A P^l/4`=@rs+4/rs+l/Ps,,2rs+6/rs+l/Ps,,= A P^l/5`=@rs+5/rs+l/Ps,,2rs+6/rs+l/Ps,,= A P^l/6`=@rs+7/rs+l/Ps,,2rs+9/rs+l/Ps,,= A P^l/7`=@rs+8/rs+l/Ps,,2rs+9/rs+l/Ps,,= A rg= A hydo+p,> A & Lqlwldo ydoxhv ri wkh sdudphwhuv

79 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ ;3 A SL=@Sl> A yd=@314> ye=@31:> yf=@315> yw{=@4333> yw =@0733> yw}=@563> A ydx4=@;8> ydy4=@<3> ydx5=@;8> ydy5=@<3> A yxr4=@463> yyr4=@468> yxr5=@463> yyr5=@468> A yi44=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^4/4`,,> A yi45=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^4/5`,,> A yi46=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^4/6`,,> A yi54=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^5/4`,,> A yi55=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^5/5`,,> A yi56=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^5/6`,,> A yi64=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^6/4`,,> A yi65=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^6/5`,,> A yi66=@vlpsoli +vxev+d@yd/ e@ye/ f@yf/ w{@yw{/ / w}@yw}/ dx4@ydx4/ dy4@ydy4/ dx5@ydx5/ dy5@ydy5/ xr4@yxr4/ yr4@yyr4/ xr5@yxr5/ yr5@yyr5/ IL^6/6`,,> A &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& A & Fdoleudwlqj e wkh Prglhg Qhzwrq Udskvrq A &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& A YJ=@yhfwru+urzglp+P,/3,> M=@pdwul{+urzglp+P,/</3,> A gn=@yhfwru+</3,> YJ5=@yhfwru+urzglp+P,/3,> A MW=@pdwul{+</urzglp+P,/3,> MWM=@pdwul{+</</3,> A LMWM=@pdwul{+</</3,> LMWMMW=@pdwul{+</urzglp+P,/3,> A FY=@pdwul{+63/43/3,> A iru n iurp 4 e 4 wr 48 gr A iru l iurp 4 e 4 wr urzglp+p, gr

80 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ ;4 A yx4=@p^l/4`= yy4=@p^l/5`= yx5=@p^l/6`= yy5=@p^l/7`= A YJ^l`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ J,,= A M^l/4`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji44,,= A M^l/5`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji45,,= A M^l/6`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji46,,= A M^l/7`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji54,,= A M^l/8`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji55,,= A M^l/9`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji56,,= A M^l/:`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji64,,= A M^l/;`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji65,,= A M^l/<`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/i44@yi44/ i45@yi45/ i46@yi46/ i54@yi54/ i55@yi55/ i56@yi56/ i64@yi64/ i65@yi65/ i66@yi66/ gji66,,= A rg> A &mi+{n,m A qyjn=@ pxowlso +wudqvsrvh+yj,/yj,> A &gn A MW =@ wudqvsrvh+m,= MWM =@ pxowlso +MW/M,= A LMWM=@lqyhuvh+MWM,= LMWMMW=@pxowlso +LMWM/MW,= A gn=@hydop+pxowlso +LMWMMW/YJ,,= A &{n A {n=@yhfwru+^yi44/yi45/yi46/yi54/yi55/yi56/yi64/yi65/yi66`,> A & exvfdqw m A m=@3= dfdedu=@3= A iru m iurp 3 e 4 zkloh dfdedu? 4gr A {n5=@hydop+{n 0 5a+0m,-gn,> A & mi+{n 0 5a+0m,-gn,m A iru l iurp 4 e 4 zkloh l?@ urzglp+p, gr A yx4=@p^l/4`= yy4=@p^l/5`= yx5=@p^l/6`= yy5=@p^l/7`= A YJ5^l`=@vlpsoli +vxev+x4@yx4/ y4@yy4/ x5@yx5/ y5@yy5/ i44@{n5^4`/ i45@{n5^5`/ i46@{n5^6`/ i54@{n5^7`/ i55@{n5^8`/ i56@{n5^9`/ i64@{n5^:`/ i65@{n5^;`/ i66@{n5^<`/ J,,= A rg=

81 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ ;5 A qyj5n=@pxowlso +wudqvsrvh+yj5,/yj5,> A &mi+{n05a+0l,-gn,m? mi+{n,m A li qyj5n? qyjn wkhq dfdedu=@4 > A rg= A & {n.4 A m=@m04> A {n5=@hydop+{n 0 5a+0m,-gn,> A yi44=@{n5^4`= yi45=@{n5^5`= yi46=@{n5^6`= yi54=@{n5^7`= yi55=@{n5^8`= A yi56=@{n5^9`= yi64=@{n5^:`= yi65=@{n5^;`= yi66=@{n5^<`= A FY^n/4`=@yi44> FY^n/5`=@yi45> FY^n/6`=@yi46> FY^n/7`=@yi54> A FY^n/8`=@yi55> FY^n/9`=@yi56> FY^n/:`=@yi64> FY^n/;`=@yi65> A FY^n/<`=@yi66> FY^n/43`=@qYJn> A li qyjn? 43a+043, wkhq euhdn> > A rg= A FY+4,> A & Wkh pdwul{ I lv rewdlqhg lq yhfwru FY+4, Wkh dojrulwkp xvhg wr rewdlq wkh hslsrodu olqhv iurp 6 Wkh dojrulwp kdv ehhq surjudpphg xvlqj wkh Pdwode U hqylurqphqw1 fohdu doo> forvh doo> ( Jhqhudwlrq ri wkh fruuhvsrqghqfh srlqwv ( prghoolqj Fdphud 41 Ruljlq ri R zruog fr0ruglqdwh v vwhp D4@v p+*^dx43xr43>3dy4yr43>3343>3334`*,> ;8> <3> 463> 468> D4> hydo+dduw4+4/=,,> hydo+dduw4+5/=,,> hydo+dduw4+6/=,,> hydo+dduw4+7/=,,> ( prghoolqj Fdphud 51 Pryhg iurp R1 v p+*^ > 3 frv+d, vlq+d, 3>3 0vlq+d, frv+d, 3> `*,> v p+*^frv+e, 3 0vlq+e, 3> >vlq+e, 3 frv+e, 3> `*,> v p+*^frv+f, vlq+f, 3 3>0vlq+f, frv+f, 3 3> > `*,> v ppxo+u{/v ppxo+u /U},,> v p+*^4 3 3 w{>3 4 3 w >3 3 4 w}> `*,> v ppxo+w5/u5,> D5@v p+*^dx53xr53>3dy5yr53>3343>3334`*,> v ppxo+d5/uw5,>

82 FKDSWHU 61 WKH HSLSRODU JHRPHWU\ ;6 314> 31:> 315> 4333> 0733> 563> ;8> <3> 463> 468> hydo+dduw5+4/=,,> hydo+dduw5+5/=,,> hydo+dduw5+6/=,,> hydo+dduw5+7/=,,> ( Jhqhudwlqj wkh 6G zruog srlqw yhfwru ^433>0733>5333>4`> ^633>0733>6333>4`> ^833>0733>7333>4`> ^:33>0733>5333>4`> ^<33>0733>6333>4`> ^433>083>7333>4`> ^633>083>5333>4`> ^833>083>6333>4`> ^:33>083>7333>4`> ^<33>083>5333>4`> ^433>83>6333>4`> ^633>83>7333>4`> ^833>83>5333>4`> ^:33>83>6333>4`> ^<33>83>7333>4`> ^433>733>5333>4`> ^633>733>6333>4`> ^833>733>7333>4`> ^:33>733>5333>4`> ^<33>733>6333>4`> ( Rewhqlqj wkh 5G srlqwv lq erwk lpdjh sodqhv1 iru l@4=53/ DUW4-Y+=/l,> S4+4/l,2S4+6/l,> S4+5/l,2S4+6/l,> S4+6/l,2S4+6/l,> DUW5-Y+=/l,> S5+4/l,2S5+6/l,> S5+5/l,2S5+6/l,> S5+6/l,2S5+6/l,> hqg ( Ixqgdphqwdo Pdwul{ jlyhq e Pdsoh1 ^013648<55984< :5:3<<3> :95<77< 13339:5574:3:: 05143<<8;;84> :493: :5:4;`> ( Hslsrodu Jhrphwu ri Fdphud 51 jxuh+4,> krog rq> d{lv+^0845/845/0433/845`,> wlwoh+*fdphud 5*,> iru l@4=53/ op5+4=6/l,@i-s4+4=6/l,> sorw+s5+4/l,/s5+5/l,/*j-*,>

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91 FKDSWHU 71 VWUXFWXUHG OLJKW <5 qhhghg wr fdqfho wkh vxuidfh uh hfwlrq hhfw/ zklfk ghshqgv rq wkh nlqg ri vxuidfhv zkhuh wkh oljkw lv uh hfwhg1 Wklv olplwdwlrq phdqv wkdw wkh sdwwhuq kdv wr eh dovr fodvvlhg dv d vwdwlf sdwwhuq1 Frorxu= Hdfk sdwwhuq srlqw kdv wr eh dvvrfldwhg zlwk d kxh ydoxh1 Lq rughu wr xvh wkh frorxu frqvwdqf surshuw / wkh kxh ydoxhv xvhg kdyh wr eh txlwh glhuhqw iurp hdfk rwkhu1 Wkh pdlq jrdo lv wr jhw dq h!flhqw dqg dffxudwh vhjphqwdwlrq1 Vlqfh wkh v vwhp surmhfwv frorxu rq wkh vfhqh/ lwv xvh lv olplwhg wr d qhx0 wudo frorxu vfhqh/ dv kljko vdwxudwhg frorxu remhfwv fdq surgxfh orrvlqj ri sdwwhuq uhjlrqv lq wkh vhjphqwdwlrq vwhs dqg srvwhulru ghfrglfdwlrq1 Hyhq sdoh frorxuhg remhfwv pd surgxfh d frorxu iuhtxhqf vkliwlqj dv d uhvxow ri wkh lqwulqvlf frorxu ri wkh phd0 vxulqj remhfwv1 Reylrxvo / wkh glvfuhsdqf vxhuhg e wkh frorxu fdswxuhg e wkh fdphud zlwk uhvshfw wr wkh rqh surmhfwhg e wkh sdwwhuq/ udwkhu frpsolfdwhv wkh vhjphqwdwlrq vwhs1 Ixuwkhupruh/ dqrwkhu fodvvlfdwlrq fdq eh sursrvhg/ zklfk fodvvlhv wkh sdwwhuqv iurp lwv vxuidfh ghswk glvfrqwlqxlwlhv ghshqghqfh1 Wkhq/ orrnlqj dw wklv ghshqghqfh/ wkh sdwwhuqv fdq eh fodvvlhg dv= Shulrglfdo= Wkh frglfdwlrq lv shulrglfdoo uhshdwhg dorqj wkh sdwwhuq1 Qrupdoo / wklv whfkqltxh lv xvhg wr uhgxfh wkh qxpehu ri elwv wkdw frgh wkh sdwwhuq/ exw surgxfh d olplwdwlrq ri wkh ghswk glvfrqwlqxlw zklfk fdq qrw eh odujhu wkdq kdoi ri wkh shulrg ohqjwk1 Devroxwh= Hdfk froxpq ru urz ri wkh surmhfwhg sdwwhuq kdv d xqltxh frglfdwlrq1 Vr/ lw grhv qrw kdyh dq ghswk glvfrqwlqxlw ghshqghqfh1 Khuhdiwhu iroorzv d vxuyh ri wkh frghg sdwwhuqv suhvhqwhg lq uhfhqw hduv/ dqdo vlqj iru hdfk rqh lwv dgydqwdjhv dqg glvdgydqwdjhv Srvgdphu0Dowvfkxohu Dowvfkxohu hw do1 ^Dowv ;4` ^Dowv ;:` dqg Srvgdphu hw do1 ^Srvg ;5` sursrvhg d vwdwlf elqdu frglfdwlrq ri d vwulshg sdwwhuq1 Wkh vdph sulqflsoh lv dovr sursrvhg e Pxqg dqg Sruwhu ^Pxqg ;:` dqg Plqrx hw do1 ^Plqr ;4`1 Wkh v vwhp/ vkrzq lq jxuh 718/ lv edvhg rq wkh xwlolvdwlrq ri d sdwwhuq vwuxfwxuhg dv d grw pdwul{ ri?{? elqdu oljkw ehdpv1 Hdfk? froxpq ri wkh sdwwhuq fdq eh lqghshqghqwo frqwuroohg/ vr lw fdq eh oljkwhg ru revfxuhg1 Wkhq/ vhyhudo

92 FKDSWHU 71 VWUXFWXUHG OLJKW <6 Projector Camera z 2 1 y 2 y 1 x 1 1 x Projected Patterns 0 Scene 0 O z 1 Captured Image y w xw z w Iljxuh 718= Wkh whpsrudu frglfdwlrq1 pdvnv fdq eh xvhg wr doorz frglqj dq sdwwhuq grw/ lq d whpsrudo zd / dv d vhtxhqwldo surmhfwlrq ri glhuhqw sdwwhuqv/ dv vkrzq lq jxuh 7191 Wkh qxpehu ri sdwwhuqv wr eh surmhfwhg lv ghwhuplqhg e wkh qxpehu ri froxpqv wr eh frghg1 Eorfnlqj oljkw ehdpv/ d sdwwhuq lpdjh vhtxhqfh fdq eh surmhfwhg zklfk surmhfwv d vhtxhqfh ri f dqg iru hdfk ehdp1 Wkhq/ hdfk srvlwlrq ri wkh phdvxulqj vxuidfh lv whpsrudoo dqg vhtxhqwldoo looxplqdwhg iru wkh glhuhqw ydoxhv ri wkh vdph grw ehdp/ zklfk surgxfhv d frgh wkdw fdq glvwlqjxlvk rqh grw iurp lwv qhljkerxuv1 Lq idfw/ wkh v vwhp zrunv dv iroorzv1 Iluvwo / dq hqwluh grw looxplqdwhg sdwwhuq lv surmhfwhg rq wkh vfhqh1 Wkh fdphud lpdjhv doo wkh grwv uh hfwhg iurp wkh vxuidfhv ri wkh vfhqh/ dqg vwruhv wkhlu srvlwlrqv lq d gdwd edvh1 Lq wkh iroorzlqj vwhsv/ hdfk frghg sdwwhuq lv surmhfwhg dqg wkh v vwhp fdq dvn iru wkh oljkw lqirupdwlrq lq wkh vwruhg srvlwlrqv1 Zkhq doo wkh sdwwhuqv kdyh ehhq surmhfwhg/ hdfk vwruhg srlqw kdv d frgh zklfk doorzv xv wr ghwhuplqh iurp zklfk ehdp froxpq lw kdv ehhq surmhfwhg1 Wkh v vwhp sursrvhg e Srvgdphu hw do1 dqg Dowvfkxohu hw do1 lv olplwhg wr vwdwlf vfhqhv dv lw kdv wr fdswxuh dq lpdjh iurp hdfk surmhfwhg sdwwhuq1 Exw/ dv sursrvhg e Dowvfkxohu hw do1 ^Dowv ;4`/ wkh v vwhp fdq eh lpsuryhg wr eh xvhg lq g qdplf vfhqhv1 Lq wklv fdvh/ doo wkh sdwwhuqv duh surmhfwhg zlwk d glhuhqw iuhtxhqf zdyh dqg? fdphudv duh xvhg/ rqh iru hdfk surmhfwhg sdwwhuq1 Hdfk fdphud vkrxog kdyh dq rswlfdo owhu/ dv hdfk fdphud zloo lpdjh

93 FKDSWHU 71 VWUXFWXUHG OLJKW <7 Reference Dot Pattern Mask = Mask = OO Second Pattern Mask = First Pattern Mask = O Third Pattern Illuminated Dot Obscured Dot Iljxuh 719= Frglqj d?{? pdwul{ ri odvhu ehdp grwv1 rqo rqh sdwwhuq iuhtxhqf 1 Wkhq/ doo wkh sdwwhuqv fdq eh surmhfwhg dw wkh vdph wlph1 Wkh fdphudv vkrxog eh orfdwhg dv forvh dv srvvleoh1 Hyhq vr/ zh frxog dovr qg wkdw vrph srlqwv fdq qrw eh ghfrghg dv wkh duh qrw lpdjhg iurp doo wkh fdphudv1 Wkh lghd/ sursrvhg e Srvgdphu dqg Dowvfkxohu/ kdv ehhq zlgho vwxglhg1 Edvlfdoo / wkh frglfdwlrq dqg wkh vshhg phdvxuhphqw kdyh ehhq lpsuryhg1 Iru h{dpsoh/ Lqrnxfkl hw do1 ^Lqrn ;7` lq 4<;7 sursrvhg fkdqjlqj wkh elqdu frglfdwlrq/ vkrzq lq jxuh 71:/ wr d Jud rqh/ vkrzq lq jxuh 71;/ zklfk lv pruh huuru urexvw1 Odwhu/ lq 4<;9/ Vdwr hw do1 ^Vdwr ;9`/ dqg lq 4<;:/ Vdwr dqg Lqrnxfkl ^Vdwr ;:`/ sursrvhg wr xvh d oltxlg fu vwdo ghylfh/ douhdg vwxglhg e Lqrnxfkl hw do1 ^Lqrn :5` lq 4<:5/ zklfk shuplwv d odujhu qxpehu ri froxpqv wr eh surmhfwhg zlwk d kljk dffxudf 1 Wkh v vwhp dovr lpsuryhv wkh frglqj vshhg/ djdlqvw wkh xvh ri d volgh surmhfwru/ vlqfh wkh OFG fdq eh hohfwurqlfdoo frqwuroohg1 Li dq remhfw kdv d kljk wh{wxudo frqwudvw ru dq kljk uh hfwhg vxuidfh uhjlrqv/ wkhq/ vrph sdwwhuq vhjphqwdwlrq huuruv fdq eh surgxfhg1 Qrupdoo / wklv sureohp fdq eh vroyhg fdswxulqj wkh uvw lpdjh zlwkrxw sdwwhuq surmhf0 wlrq +ru zlwk wkh vdph oljkw surmhfwlrq iru hdfk grw, wr rewdlq d uhihuhqfh oljkw lqwhqvlw 1 Wklv lqwhqvlw jlyhv d g qdplf wkuhvkrog iru hdfk sl{ho1 Vdwr hw do1 ^Vdwr ;9`/ lq 4<;9/ dqg Vdwr dqg Lqrnxfkl ^Vdwr ;:`/ lq 4<;:/ sursrvhg d frpsohphqwdu phwkrg ri vhjphqwdwlrq edvhg rq wkh surmhfwlrq iru hdfk

94 FKDSWHU 71 VWUXFWXUHG OLJKW <8 (HSB) A B C D E F G (LSB) H Iljxuh 71:= ; elwv whpsrudoo elqdu frghg sdwwhuq surmhfwlrq1 (HSB) A B C D E F G (LSB) H Iljxuh 71;= ; elwv whpsrudoo Jud frghg sdwwhuq surmhfwlrq1

95 FKDSWHU 71 VWUXFWXUHG OLJKW <9 CCD camera Semiconductor Laser 12 faces Polygon Mirror Slit Ray Scanning Iljxuh 71<= Wkh Fxelvfrsh v vwhp1 frghg sdwwhuq/ ri lwv srvlwlyh dqg qhjdwlyh uhsuhvhqwdwlrq1 Wkhq/ frpsdulqj wkh lqwhqvlw lpdjh zlwk erwk uhsuhvhqwdwlrqv/ d ehwwhu vhjphqwdwlrq ri wkh surmhfwhg sdwwhuq fdq eh rewdlqhg1 Wkh sureohp ri d oljkw surmhfwru lv vrphwlphv d uhvxow ri khdw luudgldwlrq rqwr wkh vfhqh/ dqg ri lwv elj vl}h dqg zhljkw1 Lq 4<<8/ Kdwwrul hw do1 ^Kdww <8` sursrvhg wr uhsodfh wkh oljkw surmhfwru zlwk d vhpl0frqgxfwru odvhu/ wkdw jlyhv d kljk srzhu looxplqdwlrq zlwk orz khdw luudgldwlrq1 Wkh sursrvhg v vwhp/ qdphg Fxelvfrsh/ lv vkrzq lq jxuh 71< dqg lv frpsrvhg e d FFG fdphud/ d vhpl0frqgxfwru odvhu dqg d vfdqqhg pluuru/ v qfkurqrxvo frqwuroohg1 Wkh pdlq jrdo ri wklv v vwhp lv wr rewdlq vfhqh lpdjhv edvhg rq wkh whpsrudu frglfdwlrq sursrvhg e Srvgdphu hw do1 dqg Dowvfkxohu hw do1 Lq 4<<8/ wkh vdph whpsrudu frglfdwlrq ghvfulehg e Srvgdphu hw do1 dqg Dowvfkxohu hw do1 lq 4<;5 lv djdlq sursrvhg e Pÿoohu ^Pxoo <8`1 Lq 4<<9/ Vdwr ^Vdwr <9` sursrvhg d qhz prylqj prgxodwhg sdwwhuq oljkw dqg vsdwlr0whpsrudo lpdjh surfhvvlqj Fduulkloo0Kxppho Wkh v vwhp sursrvhg e Fduulkloo hw do1 ^Fduu ;8`/ lq 4<;8/ lv edvhg rq jhwwlqj 6G lqirupdwlrq ri dq vfhqh iurp wzr iudph lpdjhv1 Wkh uvw lpdjh lv fdswxuhg zlwk d frqvwdqw looxplqdwlrq surmhfwlrq rq wkh vfhqh1 D olqhdu zhgjh owhu lv xvhg wr surmhfw rq wkh vfhqh d sdwwhuq euljkwo looxplqdwhg rq

96 FKDSWHU 71 VWUXFWXUHG OLJKW <: Iljxuh 7143= Wkh sdwwhuq sursrvhg e Fduulkloo hw do1 rqh vlgh/ dqg kdoi euljkwo rq wkh rwkhu/ lq rughu wr vqds wkh vhfrqg lpdjh1 Wklv sdwwhuq lv vkrzq lq jxuh Iru wkh uvw surmhfwlrq/ lw lv vxssrvhg wkdw wkh looxplqdwlrq lqwhqvlw lv frqvwdqw dorqj wkh %0d{lv dqg wkh +0d{lv ri wkh surmhfwru1 Iru wkh vhfrqg surmhfwlrq/ looxplqdwlrq kdv wr eh d frqvwdqw dorqj wkh 0d{lv1 Wkhq/ iru hdfk fdswxuhg sl{ho/ wkh lqwhqvlw vxewudfwlrq ri wkh wzr lpdjhv/ fdq eh fdofxodwhg1 Wklv glhuhqfh doorzv wr rewdlq wkh froxpq ri wkh surmhfwru iurp zklfk wkh grw kdv ehhq hplwwhg1 Xvlqj d glhuhqfh udwlr iru hdfk sl{ho pdnhv lw hdvlhu wr fdqfho srvvleoh vxuidfh uh hfwlrqv ru kljkoljkwv vlqfh dq looxplqdwlrq udwlr fkdqjh lv dozd v surgxfhg e d fkdqjh lq wkh surmhfwhg looxplqdwlrq1 Xvlqj hohfwur0rswlfv owhuv/ wkh v vwhp fdq surylgh 6G lqirupdwlrq dw kljk vshhg/ exw/ olnh v vwhpv wkdw surmhfw pruh wkdq rqh lpdjh/ lw lv olplwhg wr vwdwlf vfhqhv1 Reylrxvo / dq prylqj remhfw lq wzr frqvhfxwlyh iudphv zrxog surgxfh d fruuhvsrqghqfh huuru1 Fduulkloo hw do1 d!up wkdw wkh v vwhp surylghv dq dffxudwh phdvxuhphqw zlwk sl{hov ri ; elwv ghswk +elwv shu sl{ho,1 Wkh whvw kdv ehhq olplwhg wr 45 elwv ghswk/ dowkrxjk Fduulkloo hw do1 d!up wkdw wkhuh lv d jrrg fruuhodwlrq ehwzhhq wkh vhqvru shufhswlrq dqg uhdolw 1 Lq rughu wr lpsuryh wkh dffxudf phdvxuhphqw zlwkrxw lqfuhdvlqj wkh elw ghswk ri wkh fdswxuhg lpdjh/ d qhz phwkrg edvhg rq d vdzwrrwk sdwwhuq frxogehsursrvhg1 Wzrvdzwrrwksdwwhuqvriglhuhqwshulrgohqjwkduh

97 FKDSWHU 71 VWUXFWXUHG OLJKW <; t 1 (a) t 2 (b) Iljxuh 7144= Wkh xvh ri wkh shulrg ohqjwk wr lpsuryh wkh uhvroxwlrq ri wkh phdvxuhphqw zlwkrxw lqfuhdvlqj wkh qxpehu ri elwv ghswk ri wkh fdswxuhg lpdjh1 Reylrxvo / shulrg sdwwhuqv duh olplwhg wr phdvxuh rqo vxuidfhv zlwk d ghswk glvfrqwlqxlw vpdoohu wkdq lwv shulrg ohqjwk1 vkrzq lq jxuh Reylrxvo / wkh pd{lpxp vxuidfh ghswk glvfrqwlqxlw wr eh phdvxuhg lv olplwhg wr wkh fkrvhq shulrg1 Lq 4<<6/ Kxqj ^Kxqj <6` sursrvhg d juh ohyho vlqxvrlgdo sdwwhuq1 Wkh shulrg ri wkh fdswxuhg sdwwhuq ghshqgv rq wkh ghswk ri wkh vxuidfh zkhuh lw lv uh hfwhg1 Kxqj sursrvhg wr wuldqjxodwh iurp wkh froxpq skdvh ri wkh lpdjhg srlqw1 Iru hdfk sl{ho/ wklv skdvh fdq eh dssur{lpdwho rewdlqhg iurp wkh oljkw lqwhqvlw 1 Krzhyhu/ lw vhhpv wkdw d urexvw 6G uhfrqvwuxfwlrq frxog eh rewdlqhg surmhfwlqj uvw d frqvwdqw looxplqdwhg sdwwhuq dv sursrvh Fduulklo ho do1 Wklv phwkrg/ dv wkh vdzwrrwk rqh/ dovr vxhuv wkh olplwdwlrq ri d shulrglfdo frglfdwlrq Er hu0ndn Lq 4<;:/ Er hu dqg Ndn ^Er h ;:` sursrvhg wr looxplqdwh wkh vfhqh xvlqj d vlqjoh sdwwhuq surmhfwlrq1 Wkh sdwwhuq lv frghg e yhuwlfdo frorxuhg volwv1 Wkh fruuhvsrqghqfh sureohp/ l1h1 jlyhq dq lpdjhg volw/ wr rewdlq iurp zklfk surmhfwru volw lw kdv ehhq hplwwhg/ fdq eh vroyhg dv wkh volw frglfdwlrq xvhg wr exlog wkh sdwwhuq/ lv nqrzq1 Reylrxvo / dv zlwk dq rwkhu v vwhp wkdw surmhfwv frorxu/ lwv xvh lv olplwhg wr suhgrplqdqwo frorxu qhxwudo vxuidfhv/

98 FKDSWHU 71 VWUXFWXUHG OLJKW << Back Wall 1 Target Projection Grid Image Plane Iljxuh 7145= Dq h{dpsoh ri wkh fruuhvsrqghqfh sureohp wkdw kdv wr eh vroyhg ehwzhhq surmhfwhg dqg lpdjhg volwv1 dv kljko vdwxudwhg kxhv frxog surgxfh volw lghqwlfdwlrq huuruv1 Iljxuh 7145 vkrzv rqo d vwulsh sdwwhuq surmhfwlrq xs wr zklfk wkh pdwfk0 lqj sureohp fdq eh frpsolfdwhg ehwzhhq surmhfwhg dqg lpdjhg volwv1 Qrwh wkdw/ volwv surmhfwhg rxw ri wkh vfrsh ri wkh fdphud ru uh hfwhg rq rffoxghg vxuidfhv fdq qrw eh lpdjhg1 Dovr/ wkh volwv lpdjhg e wkh fdphud fdq eh rewdlqhg lq d glhuhqw rughu1 Er hu hw do1 sursrvhg wr frgli wkh sdwwhuq xvlqj wkh wkuhh edvlf frorxu frpsrqhqwv= uhg/ juhhq dqg eoxh1 Wkh sdwwhuq zloo eh pdgh e d vhtxhqfh ri yhuwlfdo volwv frorxuhg zlwk dq ri wkh wkuhh edvlf frpsrqhqwv1 Vhh jxuh Wkh volw fdq dovr eh zklwh1 Rswlrqdoo / ehwzhhq hdfk volw/ d eodfn jds fdq eh sodfhg/ wklv jds fdq eh xvhg dv d volw vhsdudwru1 Qrwh wkdw/ zklwh fdq eh hdvlo rewdlqhg dqg lghqwlhg dv wkh frorxu zklfk kdv dssur{lpdwho wkh vdph uhg/ juhhq dqg eoxh lqwhqvlw ydoxhv1 Li lw lv vxssrvhg wkdw wkh sdwwhuq lv pdgh e q yhuwlfdo volwv/ Er hu hw do1 sursrvhg wr glylgh wklv sdwwhuq lq 6 vxesdwwhuqv/ hdfk rqh pdgh e n yhuwlfdo volwv/ dv? ' 6 &1 Lq rughu wr frgh wkh p sdwwhuqv lq d xqltxh zd / & lv d ydoxh dv odujh dv qhfhvvdu 1 Dv hdfk vxesdwwhuq lv hplwwhg zlwkrxw dq ehjlqqlqj dqg hqglqj frgh/ pxowlsoh pdwfklqjv fdq eh rewdlqhg lq uhfhswlrq1 Dfwxdoo / zh gr qrw nqrz zkhuh d vxesdwwhuq hqgv dqg wkh qh{w ehjlqv/ dqg pruhryhu/ wkh volwv kdyh ehhq uh0rughuhg dv d ixqfwlrq ri wkh phdvxuhg vxuidfh glvfrqwlqxlwlhv1 Dq h{dpsoh ri wkh sdwwhuq ghirupdwlrq fdq eh vkrzq

99 FKDSWHU 71 VWUXFWXUHG OLJKW 433 Red Green Blue Iljxuh 7146= D ghwdlo ri wkh sdwwhuq sursrvhg e Er hu1 lq jxuh 7147/ zkhuh d :5 volw sdwwhuq zdv hplwwhg dqg d 83 volw rqh kdv ehhq uhfhlyhg1 Iru frorxu volw ghwhfwlrq/ Er hu hw do1 sursrvhg d kdugzduh wkdw ghwhfwv uhg/ juhhq dqg eoxh shdnv lq wkh UJE vljqdo jlyhq e wkh fdphud1 Wkxv/ wkh vshflf kdugzduh fdq rewdlq wkh lqgh{ dqg srvlwlrq ri hdfk shdn lq uhdo0 wlph1 Lq idfw/ wkh lqgh{ fdq kdyh d surshu ydoxh iru hdfk glhuhqw frorxu +iru h{dpsoh/ wkh 4/ 5 dqg 6 lqgh{ ydoxhv fdq eh dvvrfldwhg zlwk uhg/ juhhq dqg eoxh frorxuv uhvshfwlyho,1 Frqvhtxhqwo / wkh srvlwlrq fdq eh rewdlqhg iurp wkh fdphud v qfkurqlvp1 Reylrxvo / FDJ ihdwxuh doorzv wkh htxdolvdwlrq ri wkh UJE vljqdov1 Lq rughu wr rewdlq wkh vxesdwwhuqv iurp wkh lqgh{ dqg srvlwlrq surylghg e wkh kdugzduh/ d vriwzduh dojrulwkp lv xvhg1 Lq wkh uvw vwhs/ doo wkh srvvleoh pdwfklqjv ehwzhhq wkh hplwwhg dqg uhfhlyhg vxesdwwhuqv duh irxqg1 Lq wkh vhfrqg rqh/ d uhjlrq jurzlqj dojrulwkp lv xvhg wr uhpryh doo wkh huurqhrxv pdwfklqjv1 Lq wkh wklug rqh/ iru hdfk vxesdwwhuq qrw pdwfkhg/ d khxulvwlf dojrulwkp lv xvhg wr qg lwv ehwwhu pdwfklqj1 Zkhq wkh wklug vwhs lv frpsohwhg/ d gdwd edvh/ zklfk dvvrfldwhv fdswxuhg dqg surmhfwhg vxesdwwhuqv/ kdv ehhq rewdlqhg1 Ilqdoo / d wuldqjxodwlrq surfhvv surylghv wkh 6G vfhqh lqirupdwlrq wkh zhuh orrnlqj iru1 Prqnv hw do1 ^Prqn <5` ^Prqn <6` dvvhuw wkdw wkh pdwfklqj surfhvv sur0 srvhg e Er hu lv qrw rswlpdo/ ehfdxvh li wkh pdwfkhv iru wkh uvw yhuwlfdo volw frqwdlq huuruv/ wkhvh zloo eh sursdjdwhg wkurxjk wkh uhvw ri wkh gdwd1 Prqnv

100 FKDSWHU 71 VWUXFWXUHG OLJKW 434 Projected Pattern Sequence Occlusion Camera Detected Sequence Iljxuh 7147= D srvvleoh uhodwlrq ehwzhhq d surmhfwhg sdwwhuq dqg wkh fdswxuhg rqh1 hw do1 kdyh ghyhorshg d qhz whfkqltxh wkdw holplqdwhv wklv sureohp dqg kdv wkh dgydqwdjh ri ehlqj qrq0lwhudwlyh/ hqfrglqj wkh wrsrorj ri wkh hqwluh vhw ri vwulshv dv d gluhfwhg df folf judsk ^Eudv <3`1 Dv zh vdlg ehiruh/ wkh sdwwhuq sursrvhg e Er hu hw do1/ lv olplwhg wr phd0 vxuh suhgrplqdqwo qhxwudo frorxu vxuidfhv/ dv kljko vdwxudwhg kxhv frxog surgxfh volw lghqwlfdwlrq huuruv1 Hyhq vr/ lw lv vshfldoo uhfrpphqghg lq g qdplf hqylurqphqwv vlqfh rqo rqh surmhfwlrq lv qhhghg Oh Prljqh0Zd{pdq Wkhuh duh d orw ri glhuhqw sdwwhuqv wkdw fdq eh jhqhudwhg edvhg rq wkh julg sdwwhuq frqfhsw1 Vrph h{dpsohv fdq eh vkrzq lq jxuh Zkhq d julg sdwwhuq lv frqvlghuhg/ wkh qxpehu ri furvvlqj srlqwv wr eh surmhfwhg kdv wr eh fkrvhq/ exw wkh olqh wklfnqhvv kdv dovr wr eh fkrvhq/ vlqfh lw ghshqgv gluhfwo rq wkh vprrwkqhvv ri wkh lpdjhg vxuidfh wh{wxuh1 D yhu wklfn olqh zloo jlyh d orz uhvroxwlrq/ dqg/ zlwk d yhu wklq rqh/ zh zloo rewdlq d orw ri glvfrqwlqxlwlhv/ zklfk zloo frpsolfdwh wkh pdwfklqj surfhvv1 Reylrxvo / wkh wklfnqhvv ri wkh olqh kdv wr eh fkrvhq nqrzlqj wkh nlqg ri vfhqhv wr eh phdvxuhg1 Qrwh wkdw wkh sdwwhuqv vkrzq lq jxuh 7148 duh qrw frghg1 Oh Prljqh dqg Zd{pdq ^Prlj ;7` ^Prlj ;8` ^Prlj ;;` sursrvhg wr dgg grwv rq wkh julg/ zklfk fdq eh xvhg dv odqgpdunv wr lqlwldwh wkh ghfrglfdwlrq ru odehoolqj ri wkh surmhfwhg sdwwhuq1 Lq jxuh 7149 vrph julg sdwwhuqv frghg zlwk grwv duh vkrzq1

101 FKDSWHU 71 VWUXFWXUHG OLJKW 435 (a) (b) (c) Iljxuh 7148= Vrph qrw frghg julg sdwwhuqv1 Wkh sdwwhuq uhvroxwlrq lv jlyhq e wkh qxpehu ri furvvlqj srlqwv dqg wkh olqh wklfnqhvv1 (a) (b) (c) Iljxuh 7149= Julg sdwwhuqv sduwldoo frghg e wkh srvlwlrq ri vrph grwv/ zklfk duh xvhg dv odqgpdunv wr lqlwldwh wkh odehoolqj surfhvv1

102 FKDSWHU 71 VWUXFWXUHG OLJKW 436 Wkh frqjxudwlrq xvhg iru wkh v vwhp orfdwhv wkh surmhfwru dw d {hg glvwdqfh iurp wkh fdphud/ dorqj wkh 0d{lv1 Wklv phdqv wkdw yhuwlfdo olqhv duh lpdjhg qhduo zlwkrxw ghirupdwlrq/ nhhslqj lwv qdwxudo sdudooholvp dqg frqwlqxlw / vr wkh zloo eh hdvlo ghwhfwdeoh1 D vtxduh qhljkerxukrrg rs0 hudwru lv frpsxwhg lq hdfk lpdjhg sl{ho wr uhgxfh wkh doehgr ru kljkoljkw hhfw1 Wkh v vwhp xvhv wkh nqrzq orfdwlrq ri wkh yhuwlfdo olqhv dv jxlghv wr vhdufk wkh grwv dqg krul}rqwdo olqh lqwhuvhfwlrqv1 Wkhq/ wkh krul}rqwdo olqhv duh h{soruhg wr mrlq wkhlu glvfrqwlqxlwlhv1 Qrwh wkdw/ li d orw ri glvfrqwlqx0 lwlhv duh irxqg/ lw lv gxh wr wkh idfw wkdw wkh fkrvhq olqh wklfnqhvv lv wrr wklq1 Ilqdoo / iru hdfk odqgpdun grw/ wzr glhuhqw hgjh odehoolqj surfhvvhv/ xvlqj d juhhg dojrulwkp/ duh xvhg1 Rqh surfhvv vwduwv lwv odehoolqj iurp wkh uljkw vlgh/ dqg wkh rwkhu iurp wkh ohiw vlgh ri wkh odqgpdun1 Vr/ vl{ glhuhqw odehoolqjv duh rewdlqhg iurp wkuhh odqgpdun grw sdwwhuqv1 Wkhq/ d phujlqj dojrulwkp lv xvhg wr odeho wkh zkroh sdwwhuq1 Lqlwldoo / rqo wzr odehoohg hgjhv duh frqvlghuhg1 Wkhq/ wkh wu wr odeho wkh qrw odehoohg hgjhv zlwk d orfdo lqwhusrodwlrq1 Dowkrxjk wkh odehoolqj dojrulwkp orrnv olnh udwkhu frpsolfdwhg/ krul}rqwdo olqhv fdq eh kljko eurnhq gxh wr ghswk glvfrqwlqxlwlhv ri wkh phdvxulqj vxuidfhv/ dqg wkh fdq dovr glvdsshdu sduwldoo 1 Vr/ hdvlo pdwfklqj huuruv frxog eh rewdlqhg xvlqj d vlpsohu odehoolqj surfhvv1 Wkh sdwwhuq sursrvhg e Oh Prljqh hw do1 lv vshfldoo lqglfdwhg wr zrun lq g qdplf hqylurqphqwv/ dv d vlqjoh surmhfwlrq lv qhhghg wr rewdlq 6G lqiru0 pdwlrq ri wkh vfhqh1 Exw lw lv wuxh wkdw wkh uhvroxwlrq jlyhq e wkh sdwwhuq lv udwkhu olplwhg/ edvlfdoo iru wzr uhdvrqv= uvwo / yhuwlfdo olqhv gr qrw jlyh dq ghswk lqirupdwlrq vlqfh wkh duh rqo xvhg dv vhdufklqj jxlghv1 Dqg qdoo / wkh pdwfklqj surfhvv pd eh udwkhu vorz lq ghqvlw julgv/ vr/ g qdplf kljk uhvroxwlrq lv qrw shuplwwhg1 Exw wkh xwlolvdwlrq ri wkh sursrvhg sdwwhuq dv d ylvlrq vhqvru iru preloh urerw qdyljdwlrq lq vwuxfwxuhg lqgrru hqylurqphqwv lv kljko uhfrpphqghg1 Lq vxfk hqylurqphqwv/ wkh vxuidfhv gr qrw xvxdoo kdyh kljk frqwudvw wh{wxuhv/ zklfk fdq ghirup wkh sdwwhuq/ dqg wkh vfhqh lv txlwh uhjxodu/ dqg vpdoo glhuhqfhv gr qrw jlyh lqwhuhvwlqj lqirupdwlrq Prulwd0\dnlpd0Vdndwd Lq 4<;; Prulwd hw do1 ^Prul ;;` sursrvhg d elqdu sdwwhuq ri oljkw grwv dv dq 0duud 1 Wkh 0duud kdv wkh douhdg ghqhg frglqj zlqgrz surshuw / dv dq vxesdwwhuq lqwr d zlqgrz h{lvwv rqo rqfh dqg dw rqh sodfh zlwklq d shulrg +iru pruh lqirupdwlrq vhh wkh Yx ovwhnh0rrvwhuolqfn phwkrg,1 Wr vlpsoli wkh fruuhvsrqghqfh sureohp/ Prulwd hw do1 sodfhg wkh fdphud dqg surmhfwru vr wkdw wkh { + dqg { 5 glvwdqfhv ehwzhhq wkhp duh }hur/ dv vkrzq lq jxuh 714:1 Wkhq/ wkh grw lghqwlfdwlrq surfhvv lv txlwh vlpsolhg/

103 FKDSWHU 71 VWUXFWXUHG OLJKW 437 object 1 object 2 object 1 object 2 object 3 object 3 x x Projector y Camera Iljxuh 714:= Wkh v vwhp frqjxudwlrq sursrvhg e Prulwd hw do1 zlwk wkh grw glvrughuv wkdw fdq eh rewdlqhg1 dv wkh grw srvlwlrq rq wkh lpdjh sodqh fdq rqo pryh krul}rqwdoo 1 Lq idfw/ dq 0duud sdwwhuq lv pdgh e d vhw ri flufxodu euljkw/ ru gdun/ grwv/ uhsuhvhqwhg e wkh elqdu qxpehu f/ ru / uhvshfwlyho 1 Iurp wkh 0 duud surshuw / wkh lqglfhv ri doo wkh hohphqwv ri wkh revhuyhg sdwwhuq fdq eh xqltxho ghwhuplqhg uhodwlyh wr wkh surmhfwhg sdwwhuq li qr sdwwhuq glvrughuv h{lvw1 Krzhyhu/ iru frpsoh{ vxuidfhv wkh iroorzlqj glvrughuv fdq eh rewdlqhg= 410 Plvvlqj grwv= Li wzr ru pruh remhfwv duh phdvxuhg/ d grw surmhfwlrq fdqehuh hfwhgrqdqrffoxghgvxuidfh/dqg/lwfdqqrwuhdfkwkhlpdjh sodqh1 Dq h{dpsoh fdq eh vhhq lq jxuh 714: zkhuh wkh srlqwv iurp r2 wr re duh surmhfwhg rq wkh edfn vxuidfh ri wkh remhfw r1 510 Grw glvsodfhphqw= Li wkh ghswk glvwdqfh ehwzhhq wzr remhfwv lv glhu0 hqw/ wkh uh hfwhg grwv zloo eh lpdjhg zlwk d krul}rqwdo glvsodfhphqw ehwzhhq wkhp1 Dv fdq eh vhhq lq jxuh 714:/ wkh grwv uh hfwhg rq remhfw 5 pryh uljkw e rqh grw rq wkh lpdjh sodqh1 610 Grw shupxwdwlrq= Li dq remhfw lv sodfhg lq iurqw ri dqrwkhu/wkh sur0 mhfwhg grwv fdq vzds srvlwlrqv1 Dv vkrzq lq jxuh 714:/ wkh surmhfwhg grwv irup rs wr rh uhdfk wkh lpdjh sodqh lq wkh srvlwlrq ri r2 wr re/ dvwkh kdyh ehhq rffoxghg e remhfw 61 Lq rughu wr rewdlq wkh lpdjh fr0ruglqdwhv ri hdfk grw/ wklv phwkrg kdv wr surmhfw d zkroh looxplqdwhg grw pdwul{1 Wkhq/ d elqdu +euljkw dqg gdun, grw pdwul{ lv surmhfwhg/ vr wkdw hdfk zlqgrz/ zlwk d {hg vl}h/ ghwhuplqhv wkh froxpq lqgh{ iurp zklfk wkh lpdjhg srlqw kdv ehhq surmhfwhg/ vhh jxuh 714;1 Wkh sursrvhg v vwhp lv txlwh vlpsoh/ vr wkdw 6G lqirupdwlrq fdq eh rewdlqhg zlwkrxw d orw ri frpsxwdwlrqdo frvw1 Krzhyhu/ wkh v vwhp lv olplwhg

104 FKDSWHU 71 VWUXFWXUHG OLJKW 438 Illuminated dot Iljxuh 714;= Dq h{dpsoh ri wkh wzr sdwwhuqv surmhfwhg rq wkh phdvxulqj vfhqh e Prulwd1 wr vwdwlf vfhqhv ehfdxvh lw qhhgv wzr surmhfwlrqv1 Dv wkh v vwhp surmhfwv lvrodwhg oljkw grwv/ qrw d orw ri wh{wxudo lqirupdwlrq fdq eh rewdlqhg/ dqg/ li wkh grw vl}h lv uhgxfhg wr jhw pruh uhvroxwlrq/ wkhq/ kljk frqwudvw wh{wxudo vxuidfhv frxog prgli wkh grw vkdsh/ pdnlqj lwv orfdolvdwlrq gl!fxow1 Uhfhqwo / lq 4<<9/ Odyrlh hw do1 ^Odyr <9` kdv sursrvhg d elqdu julg sdwwhuq zlwk d svhxgr0udqgrp grw frglfdwlrq dw hdfk julg yhuwh{1 Wkh grwv duh elqdu frghg/ wkdw lv wkh fdq eh looxplqdwhg ru revfxuhg/ dv wkh P0duud sursrvhg e Prulwd Yx ovwhnh0rrvwhuolqfn D prgho zlwk d g qdplf sdwwhuq/ froxpq frghg/ lv sursrvhg ^Yx o <3`1 Wkh edvlf vwuxfwxuh ri wkh sdwwhuq lv olnh d uhjxodu fkhvv0erdug/ dowhuqdwlqj euljkw dqg gdun vtxduhv1 Wkhq/ wkh sdwwhuq lv prgxodwhg ryhuodsslqj d euljkw ru gdun vsrw dw hyhu vtxduh yhuwh{ +jxuh 714<,/ vr wkdw/ dq vtxduh ri wkh uhjxodu fkhvv0erdug sdwwhuq fduulhv dq dgglwlrqdo lqirupdwlrq elw/ wkdw wrjhwkhu zlwk wkh qhljkerxulqj elwv/ zloo eh xvhg wr frgh hdfk froxpq1 Lq rughu wr lghqwli hdfk grw ri wkh frghg sdwwhuq/ wkh duh uhsuhvhqwhg lq elqdu 1 Wkh grw jhwv wkh ydoxh li lw frphv iurp d euljkw grw1 Rwkhuzlvh/ lw wdnhv wkh f ydoxh/ dvvrfldwhg zlwk gdun1 Dgglwlrqdoo / wkh fkhvv0erdug doorzv qglqj rxw qdwxudoo li wkh frghg grw frphv iurp d euljkw ru gdun vtxduh/ uhsuhvhqwhg e wkh v perov dqg n uhvshfwlyho 1 Wkhq/ irxu glhuhqw frpelqdwlrqv/ vkrzq lq jxuh 7153/ fdq eh rewdlqhg1 Iroorzlqj wkh fkhvv0erdug/ wkh frgh dvvljqphqw lv edvhg rq wzr elqdu vhtxhqfhv/ uhsuhvhqwhg e S & dqg K & ri 96 elwv ohqjwk1 Wkh grwv ri doo wkh &

105 FKDSWHU 71 VWUXFWXUHG OLJKW 439 Iljxuh 714<= D ghwdlo ri wkh sdwwhuq sursrvhg e Yx ovwhnh hw do Iljxuh 7153= Wkh sdwwhuq lv pdgh e irxu glhuhqw frpelqdwlrqv1 Wkh wrs ohiw vtxduh lv uhsuhvhqwhg e wkh v perov 0 dqg./ zklfk uhsuhvhqw d euljkw ru gdun vtxduh uhvshfwlyho 1 Wkh elqdu qxpehuv 3 dqg 4 duh xvhg wr frgh wkh grw dw wkh vtxduh yhuwh{/ zklfk fdq dovr eh gdun ru euljkw uhvshfwlyho 1

106 FKDSWHU 71 VWUXFWXUHG OLJKW 43: c 0 b 1 c 2 b 3 c 4 b 5 c 6 b 7 c 8 b 9 c 10 b 11 c 12 b 13 c 14 c 15 b 0 c 0 b 0 c 1 b 1 c 1 b 2 c 2 b 2 c 3 b 3 c 3 b 4 c 4 b 4 c 5 b 5 c 5 b 6 c 6 b 6 c 7 b 7 c 7 b 8 c 8 b 8 c 9 b 9 c 9 b 10 c 10 b 10 c 11 b 11 c 11 b 12 c 12 c 13 b 14 b 13 c 14 b 12 c 13 b 14 b 15 c 15 b 15 Iljxuh 7154= Wkh frgh dvvljqphqw ghwhuplqhv wkdw dq 5{6 zlqgrz fdq lghq0 wli wkh froxpq lqgh{ Hdfk zlqgrz lv pdgh e d wulsohw ri S ydoxhv dqg dqrwkhu wulsohw ri K 1 Lq wkh h{dpsoh/ iru wkh wzr zlqgrzv/ wkh froxpq lv jlyhq e wkh vdph vhtxhqfh rughu EES cs e cs D c EK ck e ck D 1 froxpq zklfk fruuhvsrqgv wr d n vtxduh w sh duh dvvljqhg wkh elqdu ydoxh S & / zkloh wkrvh ri wkh w shduhdvvljqhgwkhydoxhk & 1D9elwvohqjwkfrgh lv qhhghg wr frgh wkh 96 glhuhqw froxpqv ri wkh sdwwhuq1 Wkhq/ dq zlqgrz ri 5{6 vtxduhv doorzv frglqj dq froxpq lqgh{1 Lq idfw/ dq zlqgrz zlwk 9 vtxduhv vl}h fdq eh xvhg/ exw reylrxvo / d frpsdfw zlqgrz lv ohvv dhfwhg e vxuidfh glvfrqwlqxlwlhv wkdw dq horqjdwhg rqh1 Wklv lv wkh pdlq uhdvrq zk d 5{6 zlqgrz kdv ehhq fkrvhq lqvwhdg ri d 4{91 Hdfk 5{6 zlqgrz kdv d wulsohw ri S & frghv dqg dqrwkhu ri K & / hdvlo gli0 ihuhqwldeoh1 Wkh vruwlqj ri wkhvh frghv jlyhv d 9 elwv ohqjwk qxpehu zklfk frglhv d froxpq lqgh{ ri wkh sdwwhuq1 Dq h{dpsoh iru wkh froxpq & 'lv vkrzq lq jxuh 7154/ zkhuh wkh frgh qxpehu/ zklfk uhsuhvhqwv froxpq 6/ lv jlyhq e wkh vhtxhqfh= EES cs e cs D c EK ck e ck D 1 Wkh frgh dvvljqphqw fdq qrw eh fkrvhq lqghshqghqwo gxh wkh idfw wkdw wkh lghqwlfdwlrq zlqgrzv ryhuods1 Wkhq d nlqg ri uhfxuvlyh frgh jhqhudwlrq vhtxhqfh/ zlwk dq lqlwldo eluwk sro qrp / kdv ehhq xvhg/ zklfk doorzv wkh rewdlqlqj ri d ghvluhg ohqjwk shulrg uhshwlwlrq wr frgh lq d xqltxh zd doo wkh froxpqv ri wkh sdwwhuq1 Wkh sdwwhuq suhvhqwhg kdv edvlfdoo wzr olplwdwlrqv1 Wkh uvw rqh lv edvhg rq wkh gl!fxow wr phdvxuh kljk wh{wxudo vxuidfhv/ zklfk surgxfh sduwldo orvw ri uhjlrqv ri wkh sdwwhuq1 Dqg wkh vhfrqg rqh lv dvvrfldwhg zlwk wkh vxuidfh rulhqwdwlrq1 Li wkhvh duh qrw shushqglfxodu wr wkh rswlfdo d{lv ri wkh surmhfwru/ d ghirupdwlrq ri wkh surmhfwhg sdwwhuq lv suhvhqwhg/ zklfk iurp d ghwhuplqhg dqjoh rulhqwdwlrq/ grhv qrw doorz wkh lghqwlfdwlrq ri wkh sdwwhuq1 Krzhyhu/ wkh sdwwhuq lv zhoo0uhfrpphqghg wr phdvxuh g qdplf vxuidfhv zkhuh rqo rqh surmhfwlrq lv shuplwwhg1 Lq 4<<8/ Sdmgod ^Sdmg <8e` kdv uhlpsohphqwhg wkh vdph sdwwhuq/ h{sodlq0 lqj wkh fdoleudwlrq surfhvv1 Sdmgod kdv sursrvhg/ dv dq lpsuryhphqw/ wr xvh

107 FKDSWHU 71 VWUXFWXUHG OLJKW 43; z λ 1 P Violet λ (x p,z p ) Object Surface Red λ 2 z 0 Lens Camera x White light lamp Iljxuh 7155= Wkh sulqflsoh ri gludfwlqj zklwh oljkw lq rughu wr rewdlq d udlqerz sdwwhuq1 d kh{djrqdo frglfdwlrq lqvwhdg ri d vtxduh rqh1 Lq wklv fdvh/ wkh zlqgrzv vl}h lv uhgxfhg dqg dv d uhvxow/ wkh qxpehu ri qrw lqgh{hg froxpqv gxh wr ghswk glvfrqwlqxlwlhv lv ghfuhdvhg1 Krzhyhu/ wkh lghqwlfdwlrq vwhs lv pruh frpsolfdwhg1 7151: Wdmlpd0Lzdndzd Wkh v vwhp sursrvhg e Wdmlpd ^Wdml <3` lq 4<<3 lv edvhg rq wkh yhuwlfdo volw frglqj whfkqltxh/ zkhuh hdfk volw lv hplwwhg zlwk d glhuhqw zdyhohqjwk1 Wkh surmhfwhg sdwwhuq lv olnh d udlqerz sdwwhuq/ dv wkh zkroh frorxu vshfwuxp/ iurp eoxh xs wr uhg/ lv surmhfwhg1 Wklv fdq eh rewdlqhg gludfwlqj zklwh oljkw dv vkrzq lq jxuh Wkh sursrvhg sdwwhuq lv vkrzq lq jxuh Ghswk fdq eh rewdlqhg xvlqj wkh wuldqjxodwlrq sulqflsoh/ exw uvw wkh volw dqjoh +wkh %R fr0ruglqdwh, zklfk kdv surgxfhg wkh frorxu sl{ho lpdjhg rq wkh lpdjh sodqh/ kdv wr eh nqrzq1 Lq idfw/ wkh volw hplvvlrq dqjoh fdq dovr eh ghwhuplqhg nqrzlqj wkh volw zdyhohqjwk1 Wkhremhfwvlooxplqdwhge wkhudlqerzsdwwhuqduhlpdjhgzlwkdvlqjoh prqrfkurpdwlf fdphud lqvwhdg ri d frorxu fdphud1 Wzr glhuhqw frorxu owhuv sodfhg lq iurqw ri wkh fdphud duh xvhg/ dqg wzr lpdjhv ri wkh vfhqh duh fdswxuhg1 Iru wkh vdph srlqw/ wkh lqwhqvlw uhodwlrq ehwzhhq wkh wzr lpdjhv grhv qrw ghshqg rq wkh looxplqdwlrq/ qru rq wkh frorxu remhfw1 Wdmlpd hw do1

108 FKDSWHU 71 VWUXFWXUHG OLJKW 43< Blue Red Iljxuh 7156= Wkh udlqerz udqjh sdwwhuq surmhfwhg e Wdmlpd hw do1 pdgh e d vhw ri yhuwlfdo volwv zklfk xvh doo wkh frorxu vshfwuxp iurp eoxh xs wr uhg1 kdyh suryhg wkdw wklv lqwhqvlw uhodwlrq ghshqgv gluhfwo rq wkh zdyhohqjwk volw +b,1 Dv wkh v vwhp qhhgv wzr iudphv iru hdfk phdvxuhphqw/ lw lv olplwhg wr vwdwlf vfhqhv/ exw reylrxvo wkh v vwhp fdq phdvxuh g qdplf vfhqhv xvlqj d frorxu fdphud1 Lq 4<<9/ Jhqj ^Jhqj <9`/ vhhplqjo zlwkrxw nqrzlqj wkh zrun douhdg grqh e Wdmlpd hw do1/ sursrvhg wkh vdph udlqerz sdwwhuq lq rughu wr rewdlq 6G lqirupdwlrq iurp wkh phdvxulqj vxuidfh1 Krzhyhu/ wkh lqlwldo lghd sursrvhg e Wdmlpd hw do1 zdv lpsuryhg e Jhqj xvlqj d FFG frorxu fdphud dqg xvlqj d Olqhdu Yduldeoh Zdyhohqjwk Ilowhu +OYZI,1 Wdmlpd*v lghd lpsuryhg e Jhqj fdq eh vkrzq lq jxuh Lq wklv fdvh/ wkh surmhfwru hplwv d zklwh oljkw sodqh/ zklfk/ xvlqj d f olq0 gulfdo ohqv/ jhqhudwhv d frqwlqxrxv idq ri sodqhv1 Iurp wkh qdwxudo ghvljq ri wkh OYZI/ d frqwlqxrxv frorxu vshfwuxp lv rewdlqhg/ vr wkhuh duh qrw wzr oljkw sodqhv surmhfwhg rq wkh vfhqh zlwk wkh vdph zdyhohqjwk1 Reylrxvo / wkh v vwhp uhvroxwlrq ghshqgv rq wkh fdphud ihdwxuhv wr glvwlqjxlvk dprqj glhuhqw frorxuv/ ru glhuhqw zdyhohqjwkv1 Uhfhqwo / Vpxwq dqg Sdmgod ^Vpxw <9` kdyh uhlpsohphqwhg wkh v vwhp sursrvhg e Wdmlpd hw do1 Zlwk uhjdug wr wkh olplwdwlrqv ri wkh udlqerz sdw0 whuq/ wkh vdlg wkdw wkh vxuidfh fdq kdyh dq frorxu/ exw kdv wr eh rsdtxh1 Reylrxvo / qr rwkhu zdyhohqjwk qrw frplqj iurp wkh surmhfwru/ fdq eh hplw0 whg rq wkh vfhqh1 Wkh vfhqh kdv wr eh oljkw frqwuroohg dqg wkh phdvxulqj

109 FKDSWHU 71 VWUXFWXUHG OLJKW 443 y λ i Baseline Camera Scene λ 1 z λ 2 Projector x Cylindrical lens Linear variable wavelength filter Light stripes with different wavelength Iljxuh 7157= Wkh v vwhp sursrvhg e Jhqj1 remhfwv fdq qrw eh xruhvfhqw/ qru skrvskruhvfhqw1 7151; Zxvw0Fdsvrq Lq 4<<4/ Zxvw dqg Fdsvrq ^Zxvw <4` sursrvhg wkh surmhfwlrq ri d vlqxvrlgdo lqwhqvlw sdwwhuq rq wkh phdvxulqj vxuidfhv1 Wkh sursrvhg sdwwhuq lv pdgh e wkh ryhuodsslqj ri wkuhh vlqxvrlgv/ ri q shulrgv dorqj wkh %0d{lv1 Hdfk vlqxvrlg lv dvvrfldwhg zlwk hdfk sulpdu frorxu +uhg/ juhhq dqg eoxh,1 Wkh juhhqv vlqxvrlg lv vkliwhg bf zlwk uhvshfw wr wkh uhg/ dqg wkh eoxh lv vkliwhg bf zlwk uhvshfw wr wkh juhhq/ dv vkrzq lq jxuh Wkh sdwwhuq lv froxpq frghg/ vr doo wkh urzv duh lghqwlfdo/ uhvxowlqj d frorxu yhuwlfdo iulqjh sdwwhuq/ dv vkrzq lq jxuh Lqvwhdg ri rewdlqlqj wkh froxpq lqgh{ e ghfrglqj wkh lpdjhg sdwwhuq/ ZxvwdqgFdsvrqsursrvhgwrrewdlqwkhghswkgluhfwo iurpwkhzdyhskdvh vkliwlqj1 Wklv whfkqltxh lv zlgho xvhg lq Prluh phwkrgv wr phdvxuh frqwlq0 xrxv vxuidfhv ^Uhlg ;9`1 Vrph olplwdwlrqv fdq eh revhuyhg lq wkh phwkrg1 Wkh vfhqh kdv wr eh suhgrplqdqwo frorxu qhxwudo/ lq vslwh ri frorxu surmhfwlrq1 Dv wkh sdwwhuq lv pdgh e shulrglfdo iulqjhv/ lw lv olplwhg wr phdvxuh vxuidfhv zlwkrxw glvfrq0 wlqxlwlhv odujhu wkdq d iulqjh shulrg1 Dffruglqj wr Zxvw dqg Fdsvrq/ fdphud uhvsrqvh ghshqgv rq wkh iuhtxhqf ri wkh hplwwhg iulqjhv/ dqg wkh klvwrjudp htxdolvdwlrq xvhg wr frpshqvdwh iru wkh qrq0olqhdu lqwhqvlw uhvsrqvh dovr

110 FKDSWHU 71 VWUXFWXUHG OLJKW 444 Intensity 255 Red Green Blue 0 Iljxuh 7158= Wkh sulqflsoh ri ryhuodslqj wkuhh vlqxvrlgdo lqwhqvlw sdwwhuqv1 Iljxuh 7159= Wkh shulrglfdo sdwwhuq sursrvhg e Zxvw dqg Fdsvrq/ pdgh e wkh vlqxvrlgdo ryhuodsslqj ri wkh wkuhh sulpdu frorxu frpsrqhqwv1

111 FKDSWHU 71 VWUXFWXUHG OLJKW Coded Order: ( w ij,w ij-1 w i-1j w ij+1 w i+1j ) Coded Word = Iljxuh 715:= Grw frglfdwlrq h{dpsoh xvlqj lwv irxu qhljkerxuv dqg d edvlv htxdo wr 6/ l1h1 rqo wkuhh glhuhqw v perov fdq eh xvhg1 surgxfhv vrph phdvxulqj huuruv1 Lpsurylqj wkhvh dvshfwv wkh v vwhp fdq rewdlq d ehwwhu uhvroxwlrq dqg urexvwqhvv1 7151< Jul!q0Qdudvlpkdq0\hh Jul!q hw do1 ^Juli <5`/ lq 4<<5/ kdyh fduulhg rxw d pdwkhpdwlfdo vwxg derxw zklfk vkrxog eh wkh odujhvw vl}h doorzhg iru d frghg pdwul{ grw sdwwhuq1 Lw lv vxssrvhg wkdw= 410 D grw srvlwlrq lv frghg zlwk lqirupdwlrq hplwwhg e lwvhoi dqg wkh lqirupdwlrq ri lwv irxu qhljkerxuv +Qruwk/ Vrxwk/ Hdvw dqg Zhvw,1 510 Wkhuh fdq qrw eh wzr glhuhqw grw srvlwlrqv zlwk wkh vdph frgh1 610 Wkh lqirupdwlrq lv ghwhuplqhg xvlqj d {hg edvlv/ zklfk ghwhuplqhv wkh v perov xvhg wr frgh wkh pdwul{1 710 Wkh eljjhvw pdwul{/ zklfk jlyhv d ehwwhu uhvroxwlrq/ lv ghvluhg1 Li d edvlv htxdo wr 6 lv grqh/ d srvvleoh grw frglfdwlrq lv vkrzq lq jxuh 715:1 Jul!q hw do1 suryhg wkdw/ jlyhq d edvlv e/ wkh odujhvw pdwul{ + wkh eljjhvw q{p pdwul{, fdq eh rewdlqhg iurp lwv odujhvw krul}rqwdo yhfwru +T6,/ dqg lwv odujhvw yhuwlfdo yhfwru +T6,1 T6lv d yhfwru frpsrvhg e wkh vhtxhqfh ri doo wkh wulsohwv ri qxpehuv wkdw fdq eh exlog zlwkrxw uhshwlwlrq xvlqj d eedvlv1 T6 lv d yhfwru pdgh e wkh vhtxhqfh ri doo wkh sdluv ri qxpehuv wkdw fdq eh rewdlqhg zlwkrxw uhshwlwlrq1 Wkhq/ wkh uvw urz ri wkh pdwul{ lv jlyhq gluhfwo e T6/ s f ' T6 +714, dqg/ wkh rwkhu pdwul{ hohphqwv fdq eh ghwhuplqhg dsso lqj wkh htxdwlrq 715 zkhuh lv wkh urz lqgh{ dqg ydulhv iurp f wr wkh T6ohqjwk/ dqg lv wkh froxpq lqgh{ dqg ydulhv iurp f wr wkh T6ohqjwk1

112 FKDSWHU 71 VWUXFWXUHG OLJKW 446 s ' nees 3 n T6 6J_ K +715, Iru h{dpsoh/ li d edvlv htxdo wr 6 lv vxssrvhg/ wkhq lwv odujhvw yhfwruv duh= T6 ' E , T6 ' E , Vr/ wkh rewdlqhg pdwul{ lv/ Diwhu wkh frghg pdwul{ lv irxqg rxw/ d glhuhqw surmhfwlrq fdq eh dvvr0 fldwhg iru hdfk ydoxh/ wkdw lv/ iru hdfk qxpehu zklfk ehorqjv wr wkh lqwhuydo i ckj1 Iru h{dpsoh/ d frorxuhg grw sdwwhuq fdq eh rewdlqhg li wkh uhg/ juhhq dqg eoxh frorxuv duh dvvrfldwhg wr wkh 4/ 5 dqg 6 qxpehuv uhvshfwlyho / re0 wdlqlqj d sdwwhuq olnh wkh rqh vkrzq lq jxuh 715;1 Wkh uhvroxwlrq ri wkh sdwwhuq fdq eh lqfuhdvhg e vlpso lqfuhdvlqj wkh edvlv ydoxh1 Ghshqglqj rq wkh frorxu glvfulplqdwlqj fdsdelolw ri wkh v v0 whp hpsor hg wr ylvxdolvh wkh vfhqh/ doprvw dq ghjuhh ri uhvroxwlrq fdq eh rewdlqhg1 Lq pdq dssolfdwlrqv/ wkh vfhqh lv qrw exlow e frorxu qhxwudo vxuidfhv1 D vlpsoh uhdvrq frxog eh wkdw wkh lpdjlqj v vwhp xvhg lv rqo deoh wr fdswxuh prqrfkurpdwlf lpdjhv1 Wkhq/ prqrfkurpdwlf oljkw kdv wr eh surmhfwhg rq wkh vfhqh1 Lq wklv fdvh/ hdfk qxpehu ri wkh grw pdwul{ fdq eh fkdqjhg wr jhrphwulf irup1 Dq h{dpsoh lv vkrzq lq jxuh 715<1 Wkhphwkrgsursrvhge Jul!qhwdo1 lvwkhxqltxhphwkrgvwxglhge zklfk/ iurp wkh ghfrglfdwlrq ri wkh sdwwhuq fdswxuhg e wkh fdphud/ iru hdfk

113 FKDSWHU 71 VWUXFWXUHG OLJKW 447 Iljxuh 715;= D srvvleoh frghg grw pdwul{/ rewdlqhg e wkh phwkrg sursrvhg e Jul!q hw do1 D edvlv htxdo wr 6 kdv ehhq vxssrvhg dqg wr hdfk v pero d frorxuhg grw kdv ehhq dvvrfldwhg1 Iljxuh 715<= D srvvleoh jhrphwulf dvvrfldwlrq ri d pdwul{ grw frghg xvlqj d edvlv htxdo wr 81

114 FKDSWHU 71 VWUXFWXUHG OLJKW 448 Iljxuh 7163= Wkh sdwwhuq sursrvhg e Pdux dpd hw do1 pdgh e wkh surmhf0 wlrq ri pxowlsoh volwv zlwk udqgrp fxwv1 lpdjh srlqw E% R2 c+ R2 / wkh surmhfwru srvlwlrq srlqw E% R c+ R iurp zklfk lw kdv ehhq hplwwhg/ fdq eh nqrzq1 Dv vkrzq lq wkh pdwkhpdwlfdo vhfwlrq ghglfdwhg wr vxuidfh phdvxulqj/ lw lv qrw qhfhvvdu wr nqrz erwk surmhfwru fr0ruglqdwhv1 Wkhq/ wkh sdwwhuq fdq eh reylrxvo vlpsolhg wr rewdlq d vlqjoh urz frghg ru froxpq frghg sdwwhuq/ exw zh frxog srvvleo rewdlq d sdwwhuq zklfk xvhv wkh zlqgrzv sursrvhg e Yx ovwhnh hw do1 ^Yx o <3`/ ru wkh frorxuhg volwv sursrvhg e Er hu dqg Ndn ^Er h ;:`1 Lq 4<<9/ Gdylhv hw do1 ^Gdyl <9` uh0lpsohphqwhg wkh frorxuhg grw surmhf0 wlrq v vwhp sursrvhg e Jul!q hw do1 Krzhyhu/ dv dq lpsuryhphqw/ Gdylhv sursrvhv wkh xvh ri d vshfldoo ghyhorshg irupxodwlrq ri wkh Krxjk Wudqvirup lq rughu wr h{wudfw wkh lpdjhg grwv ri wkh surmhfwhg sdwwhuq Pdux dpd0deh Wkh phwkrg ghvfulehg e Pdux dpd hw do1 ^Pdux <6`/ lq 4<<6/ lv edvhg rq wkh surmhfwlrq ri pxowlsoh yhuwlfdo volwv1 Wkh volwv duh frghg iurp wkh srvlwlrq ri vrph udqgrp fxwv/ dv vkrzq lq jxuh Doo wkh udqgrp fxwv duh sodfhg wr rewdlq vkruw olqhv/ vdwlvi lqj wkh frqgl0 wlrq wkdw lwv ohqjwk lv lq wkh lqwhuydo du f (c u f n (o/ zkhuhu f lv d vwdqgdug ohqjwk dqg ( lv jlyhq e d udqgrp qxpehu1 Vhjphqw pdwfklqj lv shuiruphg rqo edvhg rq wkh fruuhvsrqghqfh ri wkh

115 FKDSWHU 71 VWUXFWXUHG OLJKW 449 s' s'' l pattern Epipolar lines image Iljxuh 7164= D pxowlsoh pdwfklqj h{dpsoh1 Lq wklv fdvh wkh hqg srlqwv ri wzr vkruw olqhv/ r dqg r ri wkh sdwwhuq/ pdwfk wkh hqg srlqwv ri d olqh surmhfwhg rq wkh lpdjh sodqh/ dorqj lwv hslsrodu olqhv1 vkruw olqh hqg srlqwv dorqj wkh hslsrodu olqhv1 Dv wkh fxwv duh udqgrpo glvwulexwhg/ pruh wkdq rqh sdwwhuq olqh fdq eh pdwfkhg zlwk d jlyhq lpdjh vhjphqw1 Dq h{dpsoh ri pxowlsoh pdwfklqj lv vkrzq lq jxuh Wkhq/ wkh lpdjhg vhjphqwv duh fodvvlhg lqwr wkuhh jurxsv= 410 Vhjphqwv zlwk qr frpshwlwruv/ dv wkh kdyh rqo rqh pdwfklqj1 510 Vhjphqwv wkdw fdq eh vlpso lghqwlhg xvlqj dgmdfhqf uhodwlrqv ehwzhhq lwvhoi dqg lwv qhljkerxuv1 Lq wklv fdvh/ wkh pdwfklqj fdq qrw eh grqh gxh wr wkh qrlvh rq wkh lpdjh ru gxh wr d vxuidfh ghswk glvfrqwlqxlw / zklfk kdv fkdqjhg wkh olqh ohqjwk1 610 Rwkhuzlvh1 Pdux dpd hw do1 frqvlghu wkdw wkh hslsrodu olqhv fdq dozd v eh krul}rq0 wdoo frpsxwhg/ vr wkdw rqo wkh %0d{lv kdv wr eh h{dplqhg wr qg rxw doo wkh olqhv rq wkh sdwwhuq zklfk pdwfk zlwk wkh lpdjhg vhjphqw1 Wklv lv qrw dozd v wuxh/ dv hslsrodu olqhv ghshqg rq wkh surmhfwru srvlwlrq dqg rulhqwd0 wlrq/ zlwk uhvshfw wr wkh fdphud d{lv/ dqg Pdux dpd hw do1 gr qrw lpsrvh dq uhvwulfwlrq1 Exw/ lw lv wuxh wkdw wkh lpdjh fdq dozd v eh wudqviruphg wr jhw krul}rqwdo hslsrodu olqhv/ dv wkh vdlg lq wkhlu zrun1 Lq rughu wr uhpryh huurqhrxv pdwfklqj/ wkh lqirupdwlrq ri qhljkerxu vhjphqwv lv wdnhq xs1 Ilqdoo / zlwk wkh dlp wr rewdlq wkh fruuhvsrqghqfh ri doo wkh vhjphqwv iurp jurxsv 5 dqg 6/ d uhjlrq jurzlqj dojrulwkp pdwfklqj iurp dgmdfhqf frqvwudlqwv lv xvhg1 Wr lpsuryh wkh v vwhp/ zh frxog wklqn ri xvlqj d sdwwhuq zlwk dq lqwho0 oljhqw fxw glvwulexwlrq zklfk pdwfkhv wkh vdph lpdjhg vhjphqw/ dorqj lwv hslsrodu olqhv +lq rughu wr qrw rewdlq pruh wkdq rqh pdwfklqj,1 Vr/ d elmhf0 wlrq ehwzhhq fdswxuhg lpdjh dqg surmhfwhg sdwwhuq lv ghwhuplqhg1 Exw/ dv

116 FKDSWHU 71 VWUXFWXUHG OLJKW 44: Pdux dpd hw do1 vdlg/ li wkh dgmdfhqf frqvwudlqwv duh xvhg/ wkh pdwfklqj fdq eh grqh xvlqj d uhjlrq jurzlqj dojrulwkp1 Krzhyhu/ vxuidfh ghswk glv0 frqwlqxlw ru qrlvh sureohpv lq wkh lpdjh frxog surylgh vhjphqwv zklfk gr qrw kdyh d pdwfklqj olqh1 Lq wklv fdvh/ d uhjlrq jurzlqj dojrulwkp kdv wr eh xvhg wr pdwfk wkhp1 Wkh phwkrg lv vxlwdeoh iru phdvxulqj 6G remhfwv zlwk uhodwlyho vprrwk vxuidfhv1 Iru remhfwv zlwk d orw ri glvfrqwlqxlwlhv dqg zlwk kljko wh{wxuhg vxuidfhv/ wkh phwkrg zloo kdyh vrph gl!fxowlhv1 Reylrxvo / olqh glvfrqwlqx0 lwlhv surgxfhg lq wkh fdswxuhg vhjphqwv frpsolfdwh wkh pdwfklqj surfhvv1 Krzhyhu/ wkh sdwwhuq lv shuihfwo xvhg wr phdvxuh g qdplf vfhqhv/ dv rqo rqh surmhfwlrq lv uhtxluhg Lwr0Lvkll Lq 4<<8/ Lwr dqg Lvkll ^Lwr <8` sursrvhg d wkuhh0ohyho fkhfnhuerdug sdwwhuq1 Hdfk 5G sdwwhuq srlqw ru qrgh kdv d vtxduh irup dqg lw lv vxuurxqghg e irxu surmhfwhg vtxduhv zklfk fdq eh frghg xvlqj rqo wkuhh glhuhqw juh ohyhov1 Wkh juh ohyhov xvhg duh= revfxuhg E? e?r + ' 2DD/ kdoi looxpl0 qdwhg E? e?r + ' 2H dqg looxplqdwhg E? e?r + ' f/ zklfk kdyh ehhq frghg dv 2/ dqg f uhvshfwlyho 1 Lwr hw do1 ghqhg d vxefrgh ri d qrgh dv wkh forfnzlvh frpelqdwlrq ri wkh frghv ri wkh irxu dgmdfhqw qrghv1 Vhh jxuh Wkh dvvhuw wkdw wkh txdqwlw ri frghv lv odujh hqrxjk wr dyrlg idovh pdwfklqjv ehwzhhq wzr vsdwldoo frghg sdwwhuqv1 Dowkrxjk sdwwhuq jhqhud0 wlrq zlwkrxw uhshdwhg dsshdudqfh ri wkh vdph ihdwxuh frgh ydoxhv lv d ixuwkhu uhvhdufk vxemhfw/ lw lv qrw d sureohp ehfdxvh wkh hslsrodu frqvwudlqw holp0 lqdwhv frqixvlrq1 Lwr hw do1 d!up wkdw wkh phwkrg surylghv kljk vsdwldo uhvroxwlrq dqg pdnhv lw srvvleoh wr wdnh kljko dffxudwh phdvxuhphqwv ri vwdeoh dqg prylqj remhfwv1 Lqghhg/ d xqltxh sdwwhuq surmhfwlrq lv qhhghg wr lqihu 6G vfhqh lqirupdwlrq1 Krzhyhu/ lw vhhpv wkdw wkh phdvxulqj ri kljko vdwxudwhg vxuidfhv pd frpsolfdwh wkh vhjphqwdwlrq ri wkh sdwwhuq/ dv lw frxog eh gl!fxow wr glvwlqjxlvk wkh wkuhh glhuhqw juh ohyhov Fkhq0Kxqj0Fkldqj0Zx Lq 4<<:/ Fkhq hw do1 ^Fkhq <:` sursrvhg wkh surmhfwlrq ri d sdwwhuq pdgh e frorxuhg vwulshv1 Wkh dssurdfk lv prvw vlplodu wr wkh rqh sursrvhg e Er hu hw do1 ^Er h ;:`1 Krzhyhu/ Fkhq sursrvhg wr frgh hdfk volw lqghshq0 ghqwo iurp wkh rwkhuv1 Iluvwo / Fkhq jhqhudwhv d vhtxhqfh ri frorxuhg volwv c 2 c c c? 1 Wkhq/ lq rughu wr lqfuhdvh wkh lqwhqvlw yduldwlrq ehwzhhq dgmdfhqw volwv/ d eodfn volw lv lqvhuwhg ehwzhhq wkhp/ rewdlqlqj wkh vhtxhqfh E cc 2 cc c c c? 1 Hdfk volw lv frgh zlwkrxw uhshwlwlrq ydu lqj lwv

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