No.6 大域照明 Global illumination 担当教員 : 向川康博 田中賢一郎

Transcription

1 Computer Vison July 23, 2018 No.6 大域照明 Global illumination 担当教員 : 向川康博 田中賢一郎

2 Direct and global illuminations Direct illumination Light source Object surface Observer Global (indirect) illumination Light source Object surface Object surface Observer Direct illumination Global illumination Differences in CG (wikipedia) Real global illumination

3 What is global illumination? Rendering images considering global illumination In CG, necessary to render realistic image In CV, necessary to analyze real scene Types of global illumination Inter-reflection ( 相互反射 ) Volume scattering ( 体積散乱 ) Subsurface scattering ( 表面下散乱 ) Inter-reflection Volume scattering Subsurface scattering

4 Inter-reflection ( 相互反射 )

5 Inter-reflection Diffuse inter-reflection Radiosity Describing light passing between object surfaces by finite element method Only direct illumination Direct illumination + ambient illumination Radiosity Specular inter-reflection Expression of caustics ( 集光模様 ) Monte Carlo ray tracing Monte Carlo sampling from ray tracing Photon mapping Two-pass algorithm of distributing and counting photons wiki.povray.org real caustics Photon mapping by POV-Ray

6 Radiosity Compute diffuse inter-reflection components Developed for heat transfer at first Form factor between two patches Bi B i E i i j F ij B j i Reflectance Ei Radiation light intensity (Direct light source) Fij V ( xi, x j ) G( xi, x j ) G( x Visibility Geometric attenuation (Can see each other or not) i, x j ) cosq cosq x i i x j j q i q j xi xj Form factor between two patches [Sillion94]

7 Scene analysis based on Radiosity Reflectance estimation considering diffuse inter-reflection Simple linear solution B i i E i i ( B i Ei) / j F ij j B j F ij B j Superposition of virtual object [ Fournier93 ] [ Drettakis97 ] [ Loscos99 ] [ Loscos00 ]

8 Specular inter-reflection Specular reflection depends on viewing direction The radiance of each patch can not be directly observed Iterative computation of radiance of one-bounce specular reflection specular reflectance Real image Resynthesis Room shape and Camera position (40 places) Yu et al., Inverse Global Illumination: Recovering Reflectance Models of Real Scenes from Photographs, SIGGRAPH'99

9 Specular reflectance Resynthesis under original illumination Superimposition of seven virtual objects

10 Photon mapping (Jensen 1996) Two-pass algorithm to express global illumination 1st pass: Construction of photon map Distribute many photons from light 2nd pass: Rendering Count photons by ray tracing from viewpoint

11 Examples of photon mapping [ Jensen, Global Illumination using Photon Maps, 1996 ] Simple ray tracing Photon mapping

12 Inter-reflection in complex scene simple Diffuse inter-reflection Radiosity based on heat transfer Allowing specular reflection Only one-bounce specular reflection Uniform specular reflection Simple path Light source Diffuse reflection Specular reflection camera Specular inter-reflection Iterative computation to fit input Photon mapping method Photon mapping complex

13 Volume Scattering ( 体積散乱 )

14 Participating media( 関与媒質 ) Consist of small particles Collision with particles Vacuum Participating media SIGGRAPH ASIA 2008 Course Note

15 Light transport in participating media Absorption: Collision with particles Decrease in intensity Out scattering: Scattered to outside Decrease in intensity In scattering: Ray from outside scatters and joins to traveling direction Increase in intensity Absorption Out scattering In scattering

16 Energy decrement Attenuation by absorption dl( x, ) a ( x) L( x, ) ds Attenuation by out scattering dl( x, ) s ( x) L( x, ) ds Summing both attenuations by absorption + out scattering dl( x, ) t ( x) L( x, ) ds L( x, ) ds x Out scattering a (x) : Absorption coefficient [m -1 ] :scattering coefficient [m -1 ] s ( x) ( x) ( x) t (x) a L( x, ) dl( x, ) Absorption s : Extinction coefficient [m -1 ] increment

17 Energy increment Increment by in scattering Integrating rays coming from each direction ' of the spherical surface W surrounding point x dl( x, ) s ( x) p( x, ', ) L( x, ') d ' ds W ds Phase function ' L( x, ') x dl( x, ) x W In scattering Phase function

18 Phase function Expression of scattering bias depends only on the angle q between and ' for most media Henyey-Greenstein function g: scattering anisotropy x ' q p( q ) 1 4 (1 g 2 1 g 2 2g cosq ) g>0 g=0 g<0 Forward scattering Isotropic scattering Back scattering 3 2

19 Subsurface Scattering ( 表面下散乱 )

20 Subsurface scattering in translucent objects Subsurface scattering x x i x o Opaque ( 不透明 ) Translucent ( 半透明 )

21 Translucent objects are not special Typical translucent objects: marble, milk, and skin Most objects except for metal are translucent egg skin milk vegetable candle plastic fruit paper marble soap wood cloth Translucent objects in our daily environment

22 Importance of subsurface scattering in CG Representation of realistic skin Especially necessary for rendering human image Jurassic Park (1993) Dobby of " Harry Potter and the Chamber of Secrets " (2002) (The first movie that computed physically accurate subsurface scattering) Gollum of "Lord of the Rings" ( )

23 Difference in scattering properties

24 Different distribution

25 BSSRDF ( 双方向散乱表面反射分布関数 ) (Bidirectional Scattering Surface Reflectance Distribution Function) How much the incident light at a point x i from a direction (qi,fi) outgoes from a point x r to a direction (qr,fr) The difference with BRDF is that the incident and outgoing exit points are different. Opaque object f BRDF ( x, q,,, i f i q r r f ) x Translucent object f BSSRDF ( x, q, f, x, q, i i i r r r f ) x i x r

26 Single scattering and Multiple scattering Single scattering: Collision with a particle only once inside the medium Observed in optically thin medium such as milky water, fog,... High directivity and uniquely determined light path Multiple scattering: Repeat reflections many times inside the medium Observed in optically dense medium such as skin, marble, milk,... Diffusion approximation

27 Model of single scattering Modeling the sequence of attenuation scattering attenuation f single BSSRDF ( x i, q, f, i i x r, q, f ) r r s p( q) e ( d d2 ) t 1 attenuation: x i x r d 1 d2 e t e t attenuation: q p(q) scattering: p(q ) s

28 Model of multiple scattering Direst tracing Monte Carlo ray tracing, photon mapping High computational cost, since reflections are repeated. Approximated parametric function Diffusion approximation Dipole model (Jensen 2001), multipole model (Donner 2005) Multi-layered model Dipole Multi-layer

29 Dipole Model for BSSRDF (Jensen et al. SIGGRAPH2001) f Decomposition of the BSSRDF Fresnel transmittance: F t (, ) function of relative index of refraction, incident and reflective angles i and o Diffuse BSSRDF: R(d) function of distance d between incident and outgoing points x i and x o including two inherent parameters of the material scattering coefficient: s absorption coefficient: a Diffuse BSSRDF multiple BSSRDF 1 ( xi, qi, fi, xr, qr, fr ) Ft (, qi, fi ) Rd ( xi xr ) Ft (, qr, fr ) Fresnel transmittance at x i Fresnel transmittance at x o i d o x i x o

30 Diffuse BSSRDF in Dipole model Assumption of diffusion approximation A point light source in object In order to satisfy the boundary condition, a negative light source above the incident point R( d) x i z 4 d x o r trdr trdv e e d 1 z d tr Light source that absorbs light Concept of dipole model r d R(d) Light source emitting light t 1 3 v tr v r d 3 v Apple (σ s =2.29,σ a =0.003) Skin (σ s =0.74,σ a =0.032) t Examples of scattering terms d [mm]

31 Rendering example with dipole model BRDF BSSRDF

32 Decomposition of Global Illumination

33 Decomposition of Global Illumination(Nayar 2006) Separation of two components Direct component (diffuse reflection / specular reflection) Global components (inter-reflection, volume scattering, subsurface scattering...) Using a projector as a light source Projecting high frequency pattern (fine grid pattern) Utilizing that the global illumination effect acts as a low-pass filter High frequency pattern

34 Principle of high frequency illumination When not illuminated : Global component /2 When illuminated : Direct component + Global component /2 Separation of two components max = direct global min = 1 2 global - White pixels and black pixels mix - Half is white in the projection pattern direct = max min global = 2 min

35 Decomposition of direct and global components Direct component Global component

36 Decomposition of direct and global components Inter-reflection Volume scattering Subsurface scattering Original scene Direct component Global component

37 Analysis of Light Transport ( 光伝播の解析 )

38 38 Scattering in translucent media How an incident ray repeats scattering and the light propagates in a translucent media? Multiple bounces Complex light field dark bright

39 Different scattering due to optical density Vitamin water Orange juice Milk Single scattering Low-order bounce scattering Multiple scattering (diffusion )

40 Analysis of light transport in scattering media Decomposition of light field for each bounce How an incident ray repeats scattering? = bounce 2-bounce 3-bounce Visualization of the light propagation How the light propagates in the media?

41 Decomposition of light field Light field(l) Describe the intensity distribution of rays passing through each point in the scene T: Recursively expressed by light transport matrix L 0 :Light field emitted from the light source... L 1 = TL 0 L 2 = TL 1 L k+1 = TL k Primary reflection (Single scattering) Secondary reflection High dimensional scattering component expressed recursively L k 1 L k Composition

42 Dimension of Light field Comparison of dimension (s,t) (u,v) 4D: in vacuum 5D: in media 3D: in low height volume Scattering measurement of thick media Translucent liquid in the case (q,f) (x,y,z) Camera In thin plate L(x,y,q) (x,y) (q) Projector

43 55cm Experimental environment Camera (Point Grey Chameleon) diluted milk Case painted with matte black (one side is transparent) Projector (3M MPro110) 12cm 27cm Examples of images

44 Separation of single scattering and Multiple scattering Spatial high-frequency component of illumination Single scattering: preserved Multiple scattering: lost 1-D high-frequency stripe pattern Single scattering: changes by phase shift Multiple scattering: constant Single scattering and Multiple scattering are mixed. Multiple scattering single scattering 1-D high-frequency stripe pattern shift

45 Separation result = + = + High frequency illumination Normal illumination Single scattering Multiple scattering (Including low order bounce scattering) dark bright

46 Analysis of single scattering Pure single scattering exponentially attenuates. The extinction parameter t is estimated by fitting an exponential function fitted exponential function observed intensities 200 fitted exponential function separated single scattering without separation (including Multiple scattering) [mm] with separation (only single scattering) [mm]

47 Analysis of Multiple scattering Forward rendering with assumed parameters vary s and g (symmetric parameter of p(q)) recursive calculation of higher-order light fields... Verification L 1 L 2 L 3 L 4 L 5 single scattering 2 k Higher dimensional scattering component Rendered Multiple scattering L k Separated Multiple scattering

48 Decomposition for each bounce reflection Real intensity Sum of all-bounce components 1-bounce (single scattering) 2-bounce 3-bounce 4-bounce 5-bounce The peak positions move inside as the bounce order becomes higher [mm]

49 Visualization of the light field observed entire 1-bounce 2-bounce 3-bounce 5-bounce 4-bounce 6-bounce light intensities field dark bright

50 Visualization of the light field observed intensity entire light field 1-bounce 2-bounce 3-bounce 4-bounce 5-bounce 6-bounce

51 Summary of global Illumination In our daily environment, there are a lot of volume scattering and subsurface scattering In particular, it is difficult to analyze scattering on inhomogeneous materials Perfect photometric modeling of real scene is extremely difficult candle marble

52 Mini report What is the difference of direct and global components? Explain from the following viewpoints. Optical phenomena ( 光学現象 ) Spatial frequency ( 空間的な周波数 ) Simplicity for modeling ( モデル化の容易さ ) Direct component Global component