ACCURACY ENHANCEMENT OF VISION METROLOGY THROUGH AUTOMATIC TARGET PLANE DETERMINATION

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1 CCURCY ENHNCEENT OF VSON ETROLOGY THROUGH UTOTC TRGET PLNE DETERNTON J.O. Otpk *, C.S. Frr titut o Photogrmmtr & Rmot Sig, Thil Uivrit o Vi, Guhutr 7-9/E, 040 Vi, utri jo@ip.tuwi..t Dprtmt o Gomti, Uivrit o lour, Vitori 00, utrli.rr@uiml.u.u Commiio V, WG V/ Kwor: Viio trolog, Trgt, Sur, utomtio, lgorithm, Priio, Clo Rg Photogrmmtr STRCT: igitl lo-rg photogrmmtr, ommol rrr to viio mtrolog, irulr trgt r ot u or high priio pplitio. Th mot ommo trgt tp u oit o rtro-rltiv mtril, whih provi high otrt img with lh photogrph. Th murmt o img oorit o igli trgt otiu to tor limitig th hivl ur o high-priio viio mtrolog tm. thmtil lgorithm r u to trmi th tr o img trgt i D p. Th D troi r th u i trigultio pro to lult th trgt poitio i D p. Thi omputtiol pro um tht th trgt rprt prt poit i p. Howvr, i prti trgt-thik trgt-imtr vrl t thi umptio, lig to th itroutio o tmti rror to iorrt lultio o D poitio. Th ppr prt th vlopmt o trgt pl trmitio pro, whih will rv to utomtill orrt or th rror. Thi will lo l to high uri withi th ul jutmt vi improv mthmtil mol.. NTRODUCTON Now, viio mtrolog (V) i rgulrl u i lrgl iutril muturig priio girig. Th liilit o th viio- opt, omi with w vlopmt uh high-rolutio igitl mr w omputtiol mol, h m igitl lo-rg photogrmmtr highl-utomt, high-priio thrimiol (D) oorit murmt tholog. V trtgi mplo trigultio to trmi D ojt poit oorit. To hiv ur to w prt pr millio, pil trgt r u to mrk poit o itrt. Vriou ivtigtio hv how tht irulr trgt livr th mot tiig rult rgrig ur utomt troi rogitio murtio. For uh trgt, rtrorltiv mtril i wil u u o-i illumitio o th trgt rtur m tim mor light th orml ttur ur. Thi rult i high otrt img, whih r k rquirmt or high priio i igitl lo-rg photogrmmtr. Th prptiv proprti o irulr trgt r uh tht irl viw rom irtio othr th orml to th trgt ur will ppr llip or i grl oi tio, iit i Figur. Proli hproli urv ppr ol i th irl touh or itrt th vihig pl (th pl prlll to th img pl, whih ilu th projtio tr). u o th tpill mll iz o trgt mplo th limit il o viw o th murig vi, it i ulikl tht th irulr trgt will ppr proli or hproli urv. Thror, ol lliptil img r oir i th ollowig. Figur. Prptiv viw o irl. V tm u troiig lgorithm to omput th tr o h llip, th troi omig th tul orvtio or th trigultio pro. Howvr, it i wll kow tht th tr o irl o ot projt oto th tr o th llip, whih thu itrou tmti rror i trigultio pro. Thr r two ro wh thi rror i uivrll igor i to V tm. Firt, th t i mll, pill i o mll trgt (Dol, 996; h t. l, 997). So, to t thr h o prtil mtho to utomtill trmi th trgt pl, whih i i rquirmt or th orrtio o thi rror. Thi ppr prt utomti trgt pl trmitio pro whih i pplil to V twork uig irulr trgt. will poit out, ultr-pri urv houl it rom th vlop pro u th tmti triit rror orrt, whih will rult i highr otil ur. Howvr, v mium to high-priio pplitio mplo th trgt pl iormtio to utomtill ompt or trgt thik i th o * Corrpoig uthor

2 ur iptio, or mpl i th murmt o t rltor or moul ompot. Th trgt pl trmitio pro w implmt vlut i utrli, photogrmmtri otwr pkg or o-li V (Frr & Emuo, 000; Photomtri, 004) TRGET PLNE DETERNTON Th propo trgt pl trmitio pro uivi ito two tg. Firt th llip prmtr o th irulr trgt r omput i h img. th t tg th tul lmt o th irulr trgt (trgt pl orml riu) r trmi uig th omput llip iormtio th trior orittio (EO) o th img. Coirig mthmtil rigor, thi tg houl prorm ii th ul jutmt i ojt poit th EO o th img r orrlt (withi th ul). Howvr, thi t m glt u th triit rror h ol vr mll t o th prmtr o th ul jutmt. H, it i jutii to omput th trgt lmt ol o wh th ul i r ovrg. Th th il itrtio r omput oirig th triit orrtio. th ollowig, kowlg o lt-qur ormultio i ul jutmt i um thror ol th umtl orvtio qutio or th jutmt mol r riv. 0 Figur : Tpil trgt img i V it itit img. it tur out, th umultiv Gui itriutio (CGD) i il utio (Figur ) or th ig trgt utio, whih llow riptio o trgt with th ormtio itit pltu. Figur : Cumultiv Gui itriutio (CGD).. Ellip Prmtr Dtrmitio D Gui Ditriutio Fittig Th trmitio o th llip prmtr i lit prolm i trgt r tpill ol w pil i imtr ( Figur ). Stt-o-th-rt V tm ol trmi th tr o th img trgt, motl vi th wll-kow itit-wight troiig pproh: m ij g ij i j 0 ij () m 0 g i j ij Hr, 0, 0 r th troi oorit, ij, ij r th pil oorit g ij r th gr vlu withi wiow o imio m. t houl mtio, tht rul thrholig pro to prorm or th tul troiig, to rmov iturig kgrou oi. Equtio poit out lrl tht muh pil iormtio poil i u to omput th trgt tr. Thi oirtio i lo out or i th trmitio pro or th llip prmtr. Th CGD i i Ω( ) G( ) πσ ( µ ) σ r ( µ ) σ whr G() i th Gui itriutio, σ i th orrpoig tr vitio µ th pttio. Sutitutig ( ) i Equtio l to th D utio how i Figur 4. Th t tp i to utitut impliit llip qutio, whih rult i th ought-tr D utio T. o i () i o Ε (4) Τ(, β,,,,,, σ, µ 0 Ω Ε (5) ) ( ) β Equtio ri trormtio, th u o whih withi th impliit llip qutio 4 llow th itrprttio o th tr o th llip th rig o th mi mjor i. () Th i o uig th D Gui itriutio to i th tr o grvit o D ojt ou i litrtur quit ot. Howvr, viul li o th Gui itriutio (ll urv) itit img o rl trgt (Figur ) prov tht th Gui itriutio it wll to mll trgt ol. iggr trgt hv itit pltu, whih ot ri th Gui itriutio. Figur 4: Trgt utio riv rom th CGD.

3 Formul 5 ri, or th jutmt u, th t-it qutio whr i l tor (Ω ol provi vlu tw 0 ) β i kgrou oi. mollig th kgrou, th thrholig pro or th itit-wight troiig voi. Figur 5 6 or ttr urtig o th prmtr o th trgt utio T; th how grph uig irt prmtr t or T. Epill otworth i th lt prmtr σ (0. 0.), whih i th hrp o th trgt igl. For omplt, it houl mtio tht horizotl tio o T r llip. T σ G( E) T E G( E) σ T Ω( E) T β (8) (9). Trgt Pl jutmt Orvig th mpliit Ellip Prmtr Figur 5: Grph o T(55, 0, 0, 0, 4, 4, 0, 0.). Kgr (98) h how tht ol two irt irl i p with th m riu projt oto th m llip withi th img. H, two img o th trgt hv to it to rolv thi miguit. Thi i o o or i rolutio o uh miguit i umtl rquirmt withi photogrmmtr. O th othr h, u o th mll imtr o th llip, it lmt (mi mjor mi mior, rig) ol trmi with low ur. Coqutl ll llip img o o trgt hv to u to hiv th hight poil ur o th trgt pl. Thror V or il prrquiit i trgt r grll img multipl tim (>4). Th propo trgt pl jutmt i prorm or h trgt t th tim o orvig th impliit llip prmtr o ll img with kow EO. To prorm thi, th mthmtil otio tw th irulr trgt i ojt p th llip prmtr i img p h to riv. Figur 6: Grph o T(00, 0, 0, 4, 4,, 0, 0.). Th utio T tur out to il trgt utio to prorm t-it jutmt whr th gr vlu o th pil r tk orvtio th prmtr o T ukow., thi timtio pro i o-lir thror prtil rivtiv o T with rpt to h prmtr r rquir. Si th rivtio r tright orwr, ol th il qutio r prt hr. Th prtil rivtiv with rpt to th llip prmtr (Equtio 6-8) oti ol th Gui itriutio G itl i th itgrl withi th CGD Ω th rivtio l h othr out. T o i σ G( Ε) T i o σ G( Ε) T σ G( E) T σ G( E) (6) (7) Figur 7: Viw o whih touh irulr trgt. oliqu o i i (Figur 7) whih touh th irulr trgt th p o th o i poitio t th projtio tr o th img. Th th o i itrt with th img pl. th rultig tio igur prt i th m mthmtil orm impliit llip qutio th prolm i olv. Tht w, th llip prmtr r rprt utio, whih p o th irl prmtr jutmt o iirt orvtio prorm. th ojt p, th o ri ( oα iα ) ( C) X C λ r λ (0)

4 whr C i th projtio tr, r ritrr orthogol vtor withi th irl pl, i th mipoit o th irl r th irl riu. Uig th wll kow oplrit qutio R R R ( X C) R ( X C) th o trorm ito img p ( oα iα ) R ( C) () λ r R λ () Th itrtio o Equtio with th img pl i impl. Th pl i i z -. H, λ oti rom λ () ( r oα r iα C) R th oorit o th itrtio igur ollow R ( r oα r iα C) R v R ( r oα r iα C) R v (4) R ( r oα r iα C) R v R ( r oα r iα C) R v Equtio 4 trorm o tht th prmtr α i limit, th impliit orm o th llip qutio (5) i ou. Th rivtio i lgth ol th il orm o th impliit prmtr i prt hr: 0 (5) Thu, riptio o th impliit llip prmtr pt o th irl prmtr i ou. For th trgt pl jutmt, liritio with rpt to th irl prmtr (, r, ) i rquir. Th ho prmtritio o th irulr trgt mipoit, riu r irl pl vtor oit o 0 lmt. Howvr, irl i D grll ri 6 prmtr, i.. mipoit, riu two rottio gl. H, th lt prmtritio h 4 gr o rom whih hv to limit withi th jutmt. O poiilit i to itrou otrit. Thi w implmt i th vlop pro i utrli. Thr, th lgth o th vtor w i to th orthogolit o w ur. Th il otrit prvt rom rottig withi th pl o th irl. Si th orvtio or thi jutmt wr rt prviou jutmt, th prvioul omput ovri iormtio iorport wll. Tt hv how tht thi i olut rquirmt or th omputtio o urt trgt pl i th impliit llip prmtr hv irt l irt uri (or itrouig ull vri/ovri mtri, ikhil t l. 996). Fill, it houl mtio tht th irt jutmt livr pliit llip prmtr whr th trgt pl jutmt tk impliit llip prmtr. Th rquir ovrio o th prmtr o th ovri mtri i how i th ppi.. QULTY NLYSS OF THE TRGET PLNE DETERNTON PROCESS r m r m m r m r m m r m m whr th ollowig utitutio hv u: (6) For th qulit li o th vlop trgt pl trmitio pro ojt with pril kow ur hp w urv. Th tt il w pl o lirtio tl whih h mhi-lvll ur. Th tl w kil m vill oig utrli Limit t tor i lour. Th mi im o th tt il w to ivtigt th trgt iz t th ur o trmiig th trgt orml. Th trgt o th tt il wr rrg i 4 4 gri, our irt trgt iz wr u (, 5, mm). Thu, th tt il oit o 64 iptio trgt om itiol tm-rquir trgt (Figur 8). m R R R R m R R R R m R R R R R R ( C) R R ( C) R R ( C) R R ( C) R R ( C) R R ( C) R R (Μ C) R R (Μ C) R R ( C) R R ( C) R R ( C) R R ( C) ( r m ) (7) Figur 8: Tt il o mhi-lvll ur.

5 pt, th iggr th trgt iz th mor urtl th trgt orml trmi (Tl ). Whr th rult o th irt thr trgt l r titor, th trgt orml o th mllt trgt r uoutl ot goo. Th trgt oti ol vr limit lliptil iormtio (Figur 9) thror it i quit impriv how urtl th trgt orml till trmi. oorit. Suh imult tt il rult i prt i th ollowig. Th lt tt il rprt iu-hp ur with th horizotl tt o 5 m (Figur 0). 6 img wr rtiiill grt uig tpil V mr ( o 0 mm, rolutio o pil). Thi rult i vrg trgt imtr o pproimtl pil withi th img. vrg Trgt Dimtr [pil] vrg gl Error [gr] St. Error o gl [gr] Tl : Trgt orml ttiti prt ito th our trgt group Figur 0: D viw o iu-hp ur iluig trgt orml. Figur 9: Trgt img o th mllt trgt group iluig th omput llip V i ot u i ur iptio, whr poit o th ur r rquir. Howvr, with th ug o trgt th omput D oorit r lw poitio ov th ought-tr ur. With th kowlg o th trgt orml th orrpoig poit o th ur omput irtl. Thi i lr vtg or prtil pplitio. Uig tpil trgt thik o 0. mm it timt gl rror o 5 gr rult i horizotl ot o ol 0 µm (vrtil ot l th µm). Thi how lrl tht th hivl ur o th trgt orml v or mll trgt i goo ough to ompt or trgt thik. To ivtigt th triit rror, r twork jutmt uig itit-wight trgt troi w prorm. trwr, th omput ojt oorit wr trorm ito th origil (rror-r) oorit rr rm. Th rultig poitiol irpi r illutrt i Figur lit i Tl. vrg [mm] iml [mm] Dirpi (trormtio) Ojt poit igm (ul jutmt) Tl : Numril rult o ul jutmt th irpi withi th origil ojt oorit. 4. THE ELLPSE CENTRE ECCENTRCTY ND TS DSTORTON EFFECTS ON THE UNDLE DJUSTENT Erlir ivtigtio (Dol, 996; h t l., 997) hv tui th impt o th triit rror o ul jutmt. t w rport tht i r twork jutmt with or without imultou mr lirtio, th triit rror u mortl iz img trgt i lmot ull ompt or hg i th trior orittio prmtr ( th priipl it) without tig th othr timt prmtr (h t l., 999). Ntwork imultio prorm th uthor hv how goo grmt with rlir iig, pill wh mploig tt il with littl vritio i th trgt orml. Howvr, tt il with igiit rg o trgt orittio with mium to ig-iz trgt how igiit itortio withi th trigult ojt poit Figur : Dirp vtor tw jut ojt oorit origil oorit. From th rult, itrtig oluio rw. Firt, th triit rror tmtill itort th ojt poit oorit, thi ig viil i Figur. Th mout o

6 itortio lrl th murmt ur o V. Th u o high qulit igitl quipmt llow th hivmt o tpil trigultio uri o :00.000, whih i out 0.05 mm i thi. Howvr, th rl ur o th prt twork i out 0.5 mm or th ojt poit ( Tl ). Fill, grou t or prtil pplitio orv. Si th jutmt prmtr ompt or th triit rror, th ul jutmt timt th ur o th ojt oorit too optimitill ( tor 0 i thi ), whih m l to miitrprttio, g i ormtio murmt. Kgr (98) h t l. (999) hv vlop two irt orrtio ormul or th llip tr triit. Uig Equtio 6 7, th prolm olv vi thir pproh. Firt th impliit llip prmtr o th img trgt irl r omput. Thi llow trmitio o th llip tr oorit (Equtio ). Uig th img p trgt tr th llip tr, th ough-tr orrtio vtor lult. Th qulit o th thr orrtio ormul w umrill prov th uthor. 5. DSCUSSON ND CONCLUSONS Th prt trgt pl trmitio lgorithm i ull utomt pro whih i uitl to V tm whih mplo irulr trgt. Th pro h implmt vlut withi th utrli otwr tm. how hr, th lgorithm grt urt trgt pl iormtio, whih will rv prtil pplitio. Th it r th orrtio o trgt thik i th o ur iptio th grl ir ur i ultrpri urv, i th orvtio qutio o th ul jutmt ri mor rigoroul. To t, o h lw h to i ompromi tw ig (high troiig ur) mll trgt (mll triit rror). Th propo mtho rolv thi prolm llow u o ig trgt without th impt o triit rror. Furthr rrh o rl high-priio twork houl urthr how tht th ur o th ojt poit ir oirig th triit rror. Si th improv ur i ot viil rom itrl mur withi th ul jutmt ( ri i Stio 4) ultr-pri rr (hkpoit) oorit o ojt poit r to vri th improv ur. REFERENCES h, S.J., Wrk, H.-J. Kotowki, R., 999. Stmti Gomtri mg urmt Error o Cirulr Ojt Trgt: thmtil Formultio Corrtio, Photogrmmtri Ror, 6(9), h, S. J. Kotowki, R., 997. Gomtri img murmt rror o irulr ojt trgt. Optil -D urmt Thiqu V (E.. Gru H. Khm). Hrrt Wihm Vrlg, Hilrg. 494 pg: Dol, J., 996. lu o lrg trgt o th rult o photogrmmtri ul jutmt. trtiol rhiv o Photogrmmtr Rmot Sig, (5): 9. Frr, C.S., 997. utomtio i Digitl Clo-Rg Photogrmmtr, t Tr Tm Survor Cor, Frr J (), Proig o th t Tr Tm Survor Cor, : Nwtl, NSW: titut o Survor, utrli. Frr, C.S. Sho, J., 997. mg urtio Strtg or utomt Viio trolog, Optil D urmt Thiqu V, Hilrg, Grm: Wihm Vrlg, Frr, C. S. Emuo, K.L., 000. Dig implmttio o omputtiol proig tm or o-li igitl lo rg photogrmmtr. SPRS Jourl o Photogrmmtr Rmot Sig, 55(): Kgr H., 98, ültrigultio mit iirkt ohtt Kriztr. Gowihtlih ittlug Ht 9, titut ür Photogrmmtri r Thih Uivrität Wi. Kru, K., 996, Photogrmmtri, : Vrirt tho u wug, Fr. Dummlr Vrlg. ikhil, Ewr. krm, F. (996) Orvtio Lt Squr, EP- Du-Doll. Photomtri, 004, W it: ( 5 pril 004). PPENDX th ollowig th ovrio tw pliit llip prmtr th impliit orm ( grl polomil o th o gr, Equtio 5) i giv. Th prmtri orm o th llip qutio ri o i oα (8) i o oα whr, r th tr oorit, i th rig o th mi-mjor i, r th mi mjor mi mior o th llip. Th orrpoig ovrio to th impliit orm ollow o i o i i o (9)

7 (0) Th rvr ovrio i giv 4 4 () rt () o o o o i i i i () Si th vri-ovri mtri Σ o th impliit prmtr i or th trgt pl trmitio, rror propgtio u to trorm th giv vriovri mtri o th pliit prmtr Σ E T E E E F Σ F Σ (4) whr F E i i F E (5)