Capturing light. Source: A. Efros

Transcription

1 Capturg lght Source: A. Efros

2 Radometr What determes the brghtess of a mage pel? Sesor characterstcs Lght source propertes Eposure Surface shape ad oretato Optcs Surface reflectace propertes Slde b L. Fe-Fe

3 Radometr Radace: eerg carred b a ra Power per ut area perpedcular to the drecto of travel per ut sold agle Uts: Watts per square meter per sterada W m - sr - dω da

4 Sold Agle B aalog wth agle radas the sold agle subteded b a rego at a pot s the area projected o a ut sphere cetered at that pot The sold agle dω subteded b a patch of area da s gve b: dacos dω r dω θ A

5 Radometr Radace L: eerg carred b a ra Power per ut area perpedcular to the drecto of travel per ut sold agle Uts: Watts per square meter per sterada W m - sr - Irradace E: eerg arrvg at a surface E Icdet power per ut area ot foreshorteed Uts: W m - For a surface recevg radace L comg from dω the correspodg rradace s P da L L cosθ dω da cos da θ dωω da θ dacosθ dω

6 Radometr of th leses L: Radace emtted from P toward P E: Irradace fallg o P from the les What s the relatoshp betwee E ad L? Forsth & Poce Sec. 4..3

7 Radometr of th leses da The power δp receved b the les from P s o da δp The radace emtted from the les towards da s The rradace receved at P s z OP cosα z' OP ' cosα Area of the les: π d 4 π d L cosα δω 4 δp π d 4 π d cosα π d 4 E L cos α L z α 4 '/ cosα 4 z' cos Sold agle subteded b the les at P cosαα δω L

8 Radometr of th leses E π d 4 cos α 4 z' L Image rradace s learl related to scee radace Irradace s proportoal to the area of the les ad versel proportoal to the squared dstace betwee the les ad the mage plae The rradace falls off as the agle betwee the vewg ra ad the optcal as creases Forsth & Poce Sec. 4..3

9 Radometr of th leses E π d 4 cos α 4 z ' L Applcato: S B Kag ad R Wess Ca we calbrate a camera usg a S. B. Kag ad R. Wess Ca we calbrate a camera usg a mage of a flat tetureless Lamberta surface? ECCV 000.

10 From lght ras to pel values X E Δt E d π cos 4 α 4 z' L Z f E Δt Camera respose fucto: the mappg f from rradace to pel values Useful f we wat to estmate materal propertes Eables us to create hgh damc rage mages Source: S. Setz P. Debevec

11 From lght ras to pel values X E Δt E d π cos 4 α 4 z' L Z f E Δt Camera respose fucto: the mappg f from rradace to pel values For more fo P. E. Debevec ad J. Malk. Recoverg Hgh Damc Rage Radace Maps from Photographs. I SIGGRAPH 97 August 997 Source: S. Setz P. Debevec

12 The teracto of lght ad surfaces What happes whe a lght ra hts a pot o a object? Some of the lght gets absorbed coverted to other forms of eerg e.g. heat Some gets trasmtted through the object possbl bet through refracto Or scattered sde the object subsurface scatterg Some gets reflected possbl multple drectos at oce Reall complcated thgs ca happe fluorescece Let s cosder the case of reflecto detal Lght comg from a sgle drecto could be reflected all drectos. How ca we descrbe the amout of lght reflected each drecto? Slde b Steve Setz

13 Bdrectoal reflectace dstrbuto fucto BRDF Model of local reflecto that tells how brght a surface appears whe vewed from oe drecto whe lght falls o t from aother whe lght falls o t from aother Defto: rato of the radace the outgog drecto to rradace the cdet drecto φ θ φ θ φ θ φ θ L L e e e e e e surface ormal ω θ φ θ φ φ θ φ φ θ φ θ ρ d L E e e e e e e e e cos Radace leavg a surface a partcular drecto: add cotrbutos from ever comg drecto Ω e e d L ω θ φ θ φ θ φ θ ρ cos

14 BRDF s ca be credbl complcated

15 Dffuse reflecto Lght s reflected equall all drectos Dull matte surfaces lke chalk or late pat Mcrofacets scatter comg lght radoml BRDF s costat Albedo: fracto of cdet rradace reflected b the surface Radost: total power leavg the surface per ut area regardless of drecto

16 Dffuse reflecto: Lambert s law Vewed brghtess does ot deped o vewg drecto but t does deped o drecto of llumato B S ρ d d S B: radost ρ: albedo : ut ormal S: source vector magtude proportoal to test of the source

17 Specular reflecto Radato arrvg alog a source drecto leaves alog the specular drecto source drecto reflected about ormal Some fracto s absorbed some reflected O real surfaces eerg usuall goes to a lobe of drectos Phog model: reflected eerg falls of wth cos δθ Lamberta + specular model: sum of dffuse ad specular term

18 Specular reflecto Movg the lght source Chagg the epoet

19 Photometrc stereo shape from shadg Ca we recostruct the shape of a object based o shadg cues?

20 Photometrc stereo Assume: A Lamberta object A local shadg model each pot o a surface receves lght ol from sources vsble at that pot A set of kow lght source drectos A set of pctures of a object obtaed eactl the same camera/object cofgurato but usg dfferet sources Orthographc projecto Goal: recostruct object shape ad albedo S S S??? Forsth & Poce Sec. 5.4

21 Surface model: Moge patch Forsth & Poce Sec. 5.4

22 Image model Kow: source vectors S j ad pel values I j We also assume that the respose fucto of the camera s a lear scalg b a factor of k Combe the ukow ormal ad albedo ρ to oe vector g ad dthe scalg costat t k ad source vectors S j to aother vector V j: I j k B k ρ S j ρ k S j g V V j Forsth & Poce Sec. 5.4

23 Least squares problem For each pel we obta a lear sstem: I I I V M M V V T T T g 3 3 kow kow ukow Obta least-squares soluto for g Sce s the ut ormal ρ s gve b the magtude of g ad t should be less tha Fall g / ρ Forsth & Poce Sec. 5.4

24 Eample Recovered albedo Recovered ormal feld Forsth & Poce Sec. 5.4

25 Recoverg a surface from ormals Recall the surface s wrtte as If we wrte the estmated vector g as f g Ths meas the ormal has the form: f + f f f + g g g 3 The we obta values for the partal dervatves of the surface: f g g 3 f g g 3 Forsth & Poce Sec. 5.4

26 Recoverg a surface from ormals Itegrablt: for the surface f to est the med secod partal dervatves must be equal: g g 3 g g 3 practce the should at least be smlar We ca ow recover the surface heght at a pot b tegrato alog some path e.g. f 0 f s ds + 0 f tdt + c for robustess ca take tegrals over ma dfferet paths ad average the results Forsth & Poce Sec. 5.4

27 Surface recovered b tegrato Forsth & Poce Sec. 5.4

28 Lmtatos Orthographc camera model Smplstc reflectace ad lghtg model o shadows o terreflectos o mssg data Itegrato s trck

29 Fdg the drecto of the lght source I S + A Full 3D case: z z I I S S Full 3D case: S z z I A S M M M M M I S For pots o the occludg cotour: I I A S M M M M I A P. llus ad J.-O. Ekludh Automatc estmato of the projected lght source drecto CVPR 00

30 Fdg the drecto of the lght source P. llus ad J.-O. Ekludh Automatc estmato of the projected lght source drecto CVPR 00

31 Applcato: Detectg composte photos Real photo Fake photo