Camera calibration & radiometry
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1 Caera calbrato & radoetr Readg: Chapter 2, ad secto 5.4, Forsth & oce Chapter, Hor Optoal readg: Chapter 4, Forsth & oce Sept. 2, 22 MI 6.8/6.866 rofs. Freea ad Darrell
2 Req: F 2, 5.4, H Opt: F 4 Req: F 6
3 hoto to lear aes
4 oda s class Frst part: how postos the age relate to 3-d postos the world. Secod part: how the testes the age relate srface ad lghtg propertes the world.
5 raslato î ĵ î ĵ O r How does relate to? O +
6 Rotato î ĵ How does relate to? R
7 Fd the rotato atr roect oto the frae s coordate aes. ( O î ĵ
8 Rotato atr ths R ples R where
9 raslato ad rotato Let s wrte as a sgle atr eqato: O R + O R
10 Hoogeos coordates dd a etra coordate ad se a eqalece relato for 3D eqalece relato *(,,, s the sae as (,,, Motato ossble to wrte the acto of a perspecte caera as a atr
11 Hoogeos/o-hoogeos trasforatos for a 3-d pot Fro o-hoogeos to hoogeos coordates: add as the 4 th coordate, e Fro hoogeos to o-hoogeos coordates: dde st 3 coordates b the 4 th, e
12 Hoogeos/o-hoogeos trasforatos for a 2-d pot Fro o-hoogeos to hoogeos coordates: add as the 3 rd coordate, e Fro hoogeos to o-hoogeos coordates: dde st 2 coordates b the 3 rd, e
13 he caera atr, hoogeos coordates f f r preos epresso to HC s HC s for 3D pot are (,,, HC s for pot age are (U,V,W f f HC No-HC
14 he proecto atr for orthographc proecto, hoogeos coordates U V W HC No-HC
15 Caera calbrato Use the caera to tell o thgs abot the world. Relatoshp betwee coordates the world ad coordates the age: geoetrc caera calbrato. (Later we ll dscss relatoshp betwee testes the world ad testes the age: photoetrc caera calbrato.
16 Itrsc paraeters Forsth&oce erspecte proecto f f
17 Itrsc paraeters t pels are soe arbtrar spatal ts α α
18 Itrsc paraeters Mabe pels are ot sqare α β
19 Itrsc paraeters We do t ow the org of or caera pel coordates α β + +
20 Itrsc paraeters Ma be sew betwee caera pel aes α β s( α cot( + +
21 ( K p r r r Itrsc paraeters s( cot( + + β α α s( cot( β α α Usg hoogeos coordates, we ca wrte ths as: or: ( K p r r r
22 Etrsc paraeters: traslato ad rotato of caera frae W C W C W C O R + No-hoogeeos coordates W C C W W W W O R C C C Hoogeeos coordates loc atr for
23 Cobg etrsc ad trsc calbrato paraeters Forsth&oce
24 Other was to wrte the sae eqato W W W M p r r r r r r pel coordates world coordates s the caera coordate sste, bt we ca sole for that, sce, leadg to: r 3
25 Calbrato target
26 Caera calbrato r r r r Fro before, we had these eqatos relatg age postos,,, to pots at 3-d postos ( hoogeeos coordates: ( ( r r So for each featre pot,, we hae:
27 Caera calbrato ( ( r r Stac all these easreets of pots to a bg atr: 3 2 M L L L
28 3 2 M L L L M L L L Showg all the eleets: I ector for: Caera calbrato
29 M L L L Caera calbrato We wat to sole for the t ector (the staced oe that es 2 he egeector of the atr ges s that (see Forsth&oce, 3.
30 Oce o hae the M atr, ca recoer the trsc ad etrsc paraeters as Forsth&oce, sect Caera calbrato
31 oda s class Frst part: how postos the age relate to 3-d postos the world. Secod part: how the testes the age relate srface ad lghtg propertes the world.
32 lght Irradace, E srface Lght power per t area (watts per sqare eter cdet o a srface. he ts tell o what to tegrate oer to fd the eerg pgg o a ge area. E tes pel area, tes eposre te ges the pel test ot (for lear sesor respose
33 lght Radace, L srface ot of lght radated fro a srface to a ge sold agle per t area (watts per sqare eter per sterada. Note: the area s the foreshorteed area, as see fro the drecto that the lght s beg etted. Iforall, radace tells o the brghtess.
34 Sold agle he sold agle sbteded b a coe of ras s the area of a t sphere (cetered at the coe org tersected b the coe. ll possble agles fro a pot coers 4π steradas. hesphere coers 2π steradas, etc.
35 What s the sold agle sbteded b ths patch, area, see fro? Mltpl b cos( to accot for foreshorteg cos( R 2 Dde b R sqared to coert the area to what o d see o a t sphere
36 Iage rradace/scee radace relatoshp he defto of scee radace s costrcted so that age rradace s proportoal to scee radace. Scee radace E π L 4 d f 2 cos 4 ( α Iage rradace Hor, sect..3
37 How the brghtess depeds o the srface propertes: RDF drectoal reflectace dstrbto fcto tells how brght a srface appears whe ewed fro oe drecto whle lght falls o t fro aother.
38 Hor, 986 Coordate sste
39 Hor, 986 RDF f (, φ,, φ e e L( E( e,, φ φ e
40 Helholt recproct codto f (, φ,, φ f (, φ,, e e e e φ Otherwse, olate the 2 d law of therodacs.
41 How does the world ge s the brghtess we obsere at a pot? Sold agle of ths patch: δω s( δ δφ Itegrate all the sorce radace pgg o the srface Let radace per sold agle be: E (, φ he the radace fro ths patch toward the org s: E(, φ s( δ δφ
42 ccotg for eteded lght sorces d d E E φ φ π π π cos( s(, ( 2 / e e e e d d E f L φ φ φ φ φ π π π cos( s(, (,,, (, ( 2 / ccotg for the foreshorteed area of ceter patch relate to llat. he total rradace of the srface s: he total radace reflected fro the srface patch s:
43 Specal case RDF: Laberta reflectace π φ φ,,, ( e e f e e d d L φ φ φ δ δ π φ π π π cos( s( ( (, ( 2 / Radace reflected fro Laberta srface llated b pot sorce: RDF s a costat. hese srfaces loo eqall brght fro all ewg drectos. cos(
44 Show srfaces
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