Light and shading. Source: A. Efros

Transcription

1 Light ad shadig Source: A. Efros

2 Image formatio What determies the brightess of a image piel? Sesor characteristics Light source properties Eposure Surface shape ad orietatio Optics Surface reflectace properties Slide b L. Fei-Fei

3 Fudametal radiometric relatio L: Radiace emitted from P toward P Eerg carried b a ra Watts per sq. meter per steradia E: Irradiace fallig o P from the les Eerg arrivig at a surface Watts per sq. meter P d α P f z What is the relatioship betwee E ad L? Szeliski..3

4 Fudametal radiometric relatio P d α P E d = π cos 4 α 4 f L f z Image irradiace is liearl related to scee radiace Irradiace is proportioal to the area of the les ad iversel proportioal to the squared distace betwee the les ad the image plae The irradiace falls off as the agle betwee the viewig ra ad the optical ais icreases Szeliski..3

5 Fudametal radiometric relatio E π 4 = d cos 4 f α L S. B. Kag ad R. Weiss Ca we calibrate a camera usig a image of a flat tetureless Lambertia surface? ECCV 000.

6 From light ras to piel values X = E Δt E d = π cos 4 α 4 f L Z = f E Δt Camera respose fuctio: the mappig f from irradiace to piel values Useful if we wat to estimate material properties Eables us to create high damic rage images For more ifo: P. E. Debevec ad J. Malik Recoverig High Damic Rage Radiace Maps from Photographs SIGGRAPH 97

7 The iteractio of light ad surfaces What happes whe a light ra hits a poit o a object? Some of the light gets absorbed coverted to other forms of eerg e.g. heat Some gets trasmitted through the object possibl bet through refractio or scattered iside the object subsurface scatterig Some gets reflected possibl i multiple directios at oce Reall complicated thigs ca happe fluorescece Bidirectioal reflectace distributio fuctio BRDF How bright a surface appears whe viewed from oe directio whe light falls o it from aother Defiitio: ratio of the radiace i the emitted directio to irradiace i the icidet directio Source: Steve Seitz

8 BRDFs ca be icredibl complicated

9 Diffuse reflectio Light is reflected equall i all directios Dull matte surfaces like chalk or late pait Microfacets scatter icomig light radoml Effect is that light is reflected equall i all directios Brightess of the surface depeds o the icidece of illumiatio brighter darker

10 Diffuse reflectio: Lambert s law θ S B = = ρ ρ S S cos θ B: radiosit total power leavig the surface per uit area ρ: albedo fractio of icidet irradiace reflected b the surface : uit ormal S: source vector magitude proportioal to itesit of the source

11 Specular reflectio Radiatio arrivig alog a source directio leaves alog the specular directio source directio reflected about ormal Some fractio is absorbed some reflected O real surfaces eerg usuall goes ito a lobe of directios Phog model: reflected eerg falls of with cos δθ Lambertia + specular model: sum of diffuse ad specular term

12 Specular reflectio Movig the light source Chagig the epoet

13 Role of specularit i computer visio

14 Photometric stereo shape from shadig Ca we recostruct the shape of a object based o shadig cues? Luca della Robbia Catoria 438

15 Photometric stereo Assume: A Lambertia object A local shadig model each poit o a surface receives light ol from sources visible at that poit A set of kow light source directios A set of pictures of a object obtaied i eactl the same camera/object cofiguratio but usig differet sources Orthographic projectio Goal: recostruct object shape ad albedo S S S??? F&P d ed. sec...4

16 Eample Recovered albedo Recovered ormal field Recovered surface model F&P d ed. sec...4

17 Eample Iput Recovered albedo Recovered ormal field Recovered surface model z

18 Image model Kow: source vectors S j ad piel values I j Ukow: surface ormal ad albedo ρ F&P d ed. sec...4

19 j j j j k k I V g S S = = = ρ ρ Image model Kow: source vectors S j ad piel values I j Ukow: surface ormal ad albedo ρ Assume that the respose fuctio of the camera is a liear scalig b a factor of k Lambert s law: F&P d ed. sec...4

20 Least squares problem For each piel set up a liear sstem:! # # # # "# I I! I kow $! & # & # & = # & # %& # " V T V T Obtai least-squares solutio for g which we defied as ρ Sice is the uit ormal ρ is give b the magitude of g Fiall = g / ρ! V T $ & & & g & & % 3 3 kow ukow F&P d ed. sec...4

21 Sthetic eample Recovered albedo Recovered ormal field F&P d ed. sec...4

22 Recall the surface is writte as This meas the ormal has the form: Recoverig a surface from ormals If we write the estimated vector g as The we obtai values for the partial derivatives of the surface: f + + = f f f f = 3 g g g g / / 3 3 g g f g g f = = F&P d ed. sec...4

23 Recoverig a surface from ormals We ca ow recover the surface height at a poit b itegratio alog some path e.g. Itegrabilit: for the surface f to eist the mied secod partial derivatives must be equal: f = f s 0ds f tdt + C g g / g / g 3 3 = for robustess should take itegrals over ma differet paths ad average the results i practice the should at least be similar F&P d ed. sec...4

24 Surface recovered b itegratio F&P d ed. sec...4

25 Limitatios Orthographic camera model Simplistic reflectace ad lightig model o shadows o iterreflectios o missig data Itegratio is trick

26 Assigmet Iput Recovered albedo Recovered ormal field Recovered surface model z

27 Fidig the directio of the light source = z z z z I I I S S S!!!! = I I I S S!!! I = S Full 3D case: For poits o the occludig cotour: P. illius ad J.-O. Ekludh Automatic estimatio of the projected light source directio CVPR 00 S

28 Fidig the directio of the light source P. illius ad J.-O. Ekludh Automatic estimatio of the projected light source directio CVPR 00

29 Applicatio: Detectig composite photos Fake photo Real photo M. K. Johso ad H. Farid Eposig Digital Forgeries b Detectig Icosistecies i Lightig ACM Multimedia ad Securit Workshop 005.