EE 584 MACHINE VISION

Transcription

1 MTU 584 Lctu Not by A.AydnALATAN 584 MACHIN VISION Photomtc Sto Radomty BRDF Rflctanc Ma Rcovng Sufac Ontaton MTU 584 Lctu Not by A.AydnALATAN Photomtc Sto It obl to cov th ontaton of ufac atch fom a numb of mag takn und dffnt lghtnng condton Although th mthod ml to mlmnt, t u contol of lghtnng Undtandng th mthod u dtald analy of bghtn

2 MTU 584 Lctu Not by A.AydnALATAN Imag Bghtn Imag of a 3-D objct dnd on Sha Rflctanc ot Dtbuton of lght ouc Und dffnt lghtnng, om dg havng tong contat n on mag, may not b vbl n anoth Radomty th cnc of adaton maumnt and t ncay to comltly undtand mag fomaton Bghtn dtmnd by th amount of ngy an magng ytm cv unt aant aa MTU 584 Lctu Not by A.AydnALATAN Radomty : Dfnton Sold angl of a con : Aa cut out by a con on a unt h Hmh Aa cut out by A Ω aa π Ω π adanc con A Ω? tadanc Angl Aco Ω A dacoθ dω A

3 MTU 584 Lctu Not by A.AydnALATAN Radomty : Dfnton Radant flux: ow oagatd a lght adaton W Iadanc : amount of lght fallng on a unt ufac W/m Radanc : amount of lght adatng fom a unt ufac towad a old angl W/m tadan [ufac mut b ndcula to th angl dcton] Radant xtanc adoty : amount of lght adatng fom a unt ufac W/m Radant ntnty: amount of lght adatng towad a old angl W/tadan Radant ntnty of lght ouc : I Radant flux, Φ I Ω I A coθ / Iadanc, Φ / A I coθ / MTU 584 Lctu Not by A.AydnALATAN Imag Fomaton /4 Am to fnd th laton btwn th adanc at an objct ont cn adanc and th coondng ont n th mag mag adanc δ I d α δ O f -z 3

4 MTU 584 Lctu Not by A.AydnALATAN Imag Fomaton /4 Ray ang thu th cnt of ln a not dflctd Sold angl of con on both d of th ln a ual to ach oth d δ O δ I α f -z Ω δ I coα, Ω δ O co o f / coα z / coα Ω Ω δ O coα o δ I co z f MTU 584 Lctu Not by A.AydnALATAN Imag Fomaton 3/4 Sold angl fo th ln fom th objct atch : π d coα Ω l 4 α z / co δ I d α f -z δ O Pow of lght, δp, fom objct atch, ang thu ln : π d 3 δp LδO Ωl co LδO co α co L : ufac adanc 4 z Fnally, th adanc,, on th mag atch : δp δo π d 3 π d 4 L co α co L co α δi δi 4 z 4 f 4

5 MTU 584 Lctu Not by A.AydnALATAN Imag Fomaton 4/4 L π d 4 4 f co α δ I d α f -z δ O Imag adanc ootonal to cn adanc by ua of ffctv f-numb, f/d Th ato ctcal whl takng hot wth a cama, f th cn l llumnatd 4 th ow of con of th angl btwn otcal ax and th ay ang thu th otcal ax In mot ca, th ffct not that v, nc th angl uually mall MTU 584 Lctu Not by A.AydnALATAN Bdctonal Rflctanc Dtbuton Functon [BRDF] /3 What dtmn cn adanc, L? Amount of lght fall on th ufac at th cn Facton of ncdnt lght that flctd Vwng angl Φ : ola angl Φ : azmuth angl Sufac-cfc coodnat ytm, Φ, Φ Incdnt lght and mttd lght can b dfnd ung azmuth and ola angl 5

6 MTU 584 Lctu Not by A.AydnALATAN Bdctonal Rflctanc Dtbuton Functon [BRDF] /3 Radanc contant along taght ln Pow, lavng atch-: L x,ϑ,ϕ da coϑ da coϑ Pow, avng at atch-: L x,ϑ,ϕ da coϑ da coϑ Th uantt mut b ual to ach oth two adanc a ual MTU 584 Lctu Not by A.AydnALATAN Bdctonal Rflctanc Dtbuton Functon [BRDF] 3/3 dφ dφ BRDF, f., catu th nfomaton how bght a ufac aa whn vwd fom on dcton whl lght fall on t fom anoth f, Φ ;, Φ dl, Φ, d, Φ tdan dl daco dω d, Φ da dl, Φ f, Φ ;, Φ da co dφ dω / da co dφ / da dω Fo many ufac.g. matt, cula, adanc a functon of th dffnc btwn th azmuth angl : Φ - Φ BRDF ha 3 ndndnt vaabl 6

7 MTU 584 Lctu Not by A.AydnALATAN xtndd Lght Souc / Fnd th total adanc on a ufac, ultng fom xtndd lght ouc Aum th aa of an nfntmal atch of th ky gvn a : du dv R n d dφ δ δφ δ Total ow mttd fom th atch towad th ufac, δ : δ Lky, Φn δ δ Φ R co R Pmt adanc Aa old angl Iadanc on th ufac, δ, ultng fom atch on th ky:, Φ P / δ L, Φ n δ δ Φ mt ky co MTU 584 Lctu Not by A.AydnALATAN xtndd Lght Souc / Total adanc on ufac, δ, fom all atch of th ky: π π / Lky, Φ n cod d Φ δ δ δφ Radanc fom ufac, δ, towad,φ ultng fom atch L Φ, Φ f, Φ ;, Φ L ky, Φ n co δ δφ Total adanc fom ufac, δ, towad, Φ : π π / L, Φ f, Φ;, Φ Lky, Φ n cod d Φ 7

8 MTU 584 Lctu Not by A.AydnALATAN Sufac Rflctanc Pot / Lambtan ufac : aa ually bght fom all angl; flct all ncdnt lght;.. BRDF contant Total adatd ow on ufac Total adatd ow fom ufac π π / δ δ co L, Φ n d d Φ π f π / n aa co d f o dffntal old angl f π δ δ δφ du dv R n d dφ MTU 584 Lctu Not by A.AydnALATAN Sufac Rflctanc Pot / Scula ufac : flct all th lght avng fom on dcton to th v dcton f,φ ;,Φ k δ δφ Φ Total adatd ow on ufac Total adatd ow fom ufac, Φ δ π π / δ co kδ δ Φ Φ, Φ n d d Φ aa f, Φ ;, Φ dffntal old angl π π / kδ δ Φ Φ n co d d Φ f, Φ;, Φ δ δ Φ Φ n co 8

9 Snc L Lambt Con Law MTU 584 Lctu Not by A.AydnALATAN Aum a Lambtan ufac llumnatd by a ngl dtant ont ouc dtant lght wav av fom a ngl angl oduc an adanc on a ufac othogonal to th angl,φ What adanc of th ont ouc,,φ? π π /, Φ L co π, Φ n d fo co d Φ > δ, Φ f, Φ;, Φ, Φ n / π co δ Φ Φ n d dφ Sufac Ontaton /3 MTU 584 Lctu Not by A.AydnALATAN Aum a vw-ontd coodnat ytm vouly, coodnat ytm ctd on a hyothtcal ufac z-ax : vwng dcton o otcal ax of cama Dcb th ufac of an objct n tm of t ndcula dtanc zx,y fom om fnc lan aalll to an mag lan fo a cama 9

10 Sufac Ontaton /3 Aum othogahc ojcton MTU 584 Lctu Not by A.AydnALATAN y n z x f -zx,y Sufac ontaton at any ont can b dtmnd by th ontaton of th tangnt lan at that ont Nomal to th tangnt lan nt th ontaton Sufac Ontaton 3/3 MTU 584 Lctu Not by A.AydnALATAN On th ufac, fo a mall chang n x and y, th atal chang n z can b aoxmatd by ung Taylo a z z t δz δx δy δx δy δz { x { y Unt nomal vcto to th tangnt lan gvn by T n,, nˆ n If th objct fa away fom th fnc lan, th angl btwn th ufac nomal and dcton vw,, : co Locaton of lght ouc can alo b cfd ung a mla notaton, -,-, : ung a ufac ndcula to th ay δz x,y z δx δy z δ y y z δ x x

11 Rflctanc Ma / MTU 584 Lctu Not by A.AydnALATAN Rflctanc Ma, R,, hould b dfnd to lat ufac ontaton -,-, to th bghtn by takng nto account ufac flctanc ot and lght dtbuton -,-, Fo a ouc of adanc,, llumnatng a Lambtan ufac, L co fo co > π Th angl btwn llumnatng ay and ufac nomal : co Snc L ootonal to mag adanc, R, can b dfnd a abov o that t lat ufac ontaton to bghtn R, Rflctanc Ma / MTU 584 Lctu Not by A.AydnALATAN Not that f w lot R, a a functon of,, vy ont n -lan gadnt ac coond to a atcula ufac ontaton Fo R,c, contou ma can b ud to undtand th flctanc ma c Fo dffnt valu of c, w hav dffnt contou on whch R, contant Ov th contou, t not obl to fnd th ontaton of a ufac, by only obvng a adanc valu on th mag

12 Shadng n Imag / MTU 584 Lctu Not by A.AydnALATAN Shadng th vaaton n bghtn fo th mag of an objct du to ufac atch wth dffnt ontaton aang n dffnt bghtn Bghtn ootonal to mag adanc, x,y x,y ootonal to cn objct adanc, L L ootonal to R, fo ufac gadnt, Hnc, aft ttng contant of ootonalty to : x, y R, : mag adanc uaton Shadng n Imag / MTU 584 Lctu Not by A.AydnALATAN Cond a h wth Lambtan ufac llumnatd by a ont ouc at th am lac wth vw Snc -,-, R, If th h on z-ax : z z < x y fo x y Sufac gadnt,, and mag bghtn can b obtand a x y z z x y x, y R, z z z z In comut gahc alcaton, n od to obtan x,y uckly,, valu a uantzd and R, valu a tod n a look-u tabl Gvn z, x,y dtmnd unuly. How about th v?

13 3 MTU 584 Lctu Not by A.AydnALATAN Th a unu mang fom ufac ontaton to th adanc, gvn by R,, but nv mang not unu In od to dtmn two unknown, &, w nd to uaton fo ach mag ont two mag takn wth dffnt lghtng Solv th nonlna uaton blow to fnd, Photomtc Sto /,, R R Th can b th zo o val o vn nfnt numb of oluton MTU 584 Lctu Not by A.AydnALATAN In contay to ou aumton, n actc all th ncdnt lght do not adat back fom th ufac, but th ffct can b aly ncooatd nto th mag adanc uaton by a facto Photomtc Sto / {,, < < ρ ρ R y x albdo Fo a ufac wth vayng albdo, both ufac ontaton and albdo can b covd ung 3 mag maumnt,,,,,,3. n and wh ouc locaton lght nt n t t th ρ Th th uaton a combnd to obtan a oluton : S n S wh S n 3 3, ρ ρ

14 MTU 584 Lctu Not by A.AydnALATAN Photomtc to xaml data fom: htt:// 4