CS635 Spring Department of Computer Science Purdue University

Transcription

1 Light Transport CS635 Spring 2010 Daniel G Aliaga Daniel G. Aliaga Department of Computer Science Purdue University

2 Topics Local and GlobalIllumination Models Helmholtz Reciprocity Dual Photography/Light Transport in Real World

3 Diffuse Lighting Aka A.k.a. Lambertian illumination A fraction of light is radiated in every direction Intensity varies with ihcosine of the angle with ih normal 3

4 Diffuse Lighting I diff = I ρ Light diff ( N L) L N θ 4

5 Specular Lighting Shiny surfaces reflect predominantly in a particular direction, creating highlights Where the highlights appear depends on the viewer s position 5

6 Specular Lighting The most common lighting model was suggested by Phong I spec = ρ spec I Light ( ) n cosφ shiny The n shiny term is an empirical constant to model the rate of falloff The model has no physical basis, but it sort of works 6

7 Example

8 Inter reflections reflections

9 Scattering

10 Scattering Without (subsurface) scattering With (subsurface) scattering

11 Scattering Without (subsurface) scattering With (subsurface) scattering

12 Scattering Scattering through participating media with volume caustics Hu et al. 2010

13 Rendering Equation (l (also known as the light transport transport equation) Illumination can be generalized to I( x, x') = g( x, x') ε ( x, x') + ρ( x, x', x'') I( x', x'') dx'' s I: illumination at first point from second g: geometry term for visibility ε: emitted light from second point to first ρ: reflectivity of light from x to x via x (note: equation is recursive) but it does not model all illumination effects

14 Global Illumination Ray tracing Rays bounce off potentially all objects Good for specular scenes

15 Global Illumination Ray tracing Rays bounce off potentially all objects Good for specular scenes

16 Global Illumination Ray tracing

17 Global Illumination Radiosity All diffuse surfaces are influenced by potentially allother diffuse surfaces Good for diffuse scenes

18 Global Illumination Radiosity

19 Global Illumination Radiosity

20 Global Illumination Radiosity

21 Radiosity All energy emitted or reflected by every surface is accounted for by its reflection or absorption by othersurfaces B i = E i + ρ emitted reflected i i j n B j F j i A A j i using A F = i j i = A j F i j Radiosity equation: B i ρ i 1 j n B j F i j = E i

22 Radiosity Radiosity Radiosity Radiosity All energy emitted or reflected by every All energy emitted or reflected by every surface is accounted for by its reflection or absorption by othersurfaces absorption by other surfaces = n j i j i j i i E F B B 1 ρ n j 1 n E E B B F F F F F F ρ ρ ρ ρ ρ ρ = n n n n n n n n n n E E B B F F F F F F ρ ρ ρ ρ ρ ρ Solve for B, etc

23 Conclusion Modeling illumination is hard Undoing physically observed illumination in order to discover the underlying geometry is even harder Insight: let s sample it and re apply it!

24 Dual Photography Sen et al., SIGGRAPH 2005 (slides courtesy of M. Levoy)

25 Helmholtz Reciprocity camera light scene

26 light Helmholtz Reciprocity camera scene

27 Measuring transport along a set of paths projector photocell scene

28 camera Reversing the paths point light scene

29 Forming a dual photograph dual camera projector dual photocell light scene

30 Forming a dual photograph dual camera dual light image of scene scene

31 Physical demonstration light replaced with projector camera replaced with photocell projector scanned across the scene conventional photograph, dual photograph, with light coming from right as seen from projector s position and as illuminated from photocell s position

32 Related imaging methods time of flight scanner if they return reflectance as well as range but their light source and sensor are typically coaxial il scanning electron microscope Velcro at 35x magnification, Museum of Science, Boston

33 The 4D transport matrix projector photocell camera scene

34 The 4D transport matrix projector camera P C pq x 1 mn x 1 mn x pq T scene

35 The 4D transport matrix mn x pq C = T P mn x 1 pq x 1

36 The 4D transport matrix mn x pq 1 0 C = T mn x 1 pq x 1

37 The 4D transport matrix mn x pq 0 1 C = T mn x 1 pq x 1

38 The 4D transport matrix mn x pq 0 0 C = T mn x 1 pq x 1

39 The 4D transport matrix mn x pq C = T P mn x 1 pq x 1

40 The 4D transport matrix mn x pq C = T P mn x 1 pq x 1 applying Helmholtz lt reciprocity... it pq x mn C = T T P pq x 1 mn x 1

41 Example conventional photograph with light coming from right dual photograph as seen from projector s position

42 Properties of the transport matrix little inter reflection sparse matrix many inter reflectionsreflections dense matrix convex object diagonal matrix concave object full matrix Can we create a dual photograph entirely from diffuse reflections?

43 Dual photography from dff diffuse reflections the camera s view

44 Relighting Paul Debevec s Light Stage 3 subject captured under multiple lights one light at a time, so subject must hold still point lights are used, so can t relight with cast shadows

45 Relighting With Dual Photography

46 Relighting With Dual With Dual Photography

47 Relighting With Dual With Dual Photography

48 The 6D transport matrix

49 The 6D transport matrix

50 The advantage of dual photography capture of a scene as illuminated by different lights cannot be parallelized capture of a scene as viewed by different cameras can be parallelized

51 Measuring the 6D transport matrix projector mirror camerarray scene

52 Relighting with complex illumination projector camera array pq x mn x uv C = T T P scene pq x 1 mn x uv x 1 step 1: measure 6D transport matrix T step 2: capture a 4D light field step 3: relight scene using captured light field

53 Running time the different rays within a projector can in fact be parallelized to some extent this parallelism can be discovered using a coarse to fine adaptive scan can measure a 6D transport matrix in 5 minutes

54 Can we measure an 8D transport projector array matrix? camera array scene