Reflection from Layered Surfaces due to Subsurface Scattering

1. Reflection from Layered Surfaces due to Subsurface Scattering Pat Hanrahan Wolfgang Krueger SIGGRAPH 1993 Andrea Rowan March 2, 2001

2. Outline • Problem description • Previous Work • Reflection / Transmission formulas • Results • Successes / Problems • Related Recent Work

3. Problem Description • Light scattering on a subsurface level

4. Problem Description • Realistically model layered materials • Skin, leaves • Snow, sand, paint, weathered stone • Model isotropic diffuse exiting radiance, proportional to surface irradiance • Subsurface scattering of light • Enter material  Absorbed/Scattered  Reflected

6. Previous Work • Anisotropic specular reflection on rough surfaces • Poulin et al.[24], Cabral et al.[5] • Reflection/Transmission through clouds of particles (Saturn’s rings) • Blinn, 1982 [2]

7. Lr,s Lr,v i r Li r Layer 1 d Layer 2  Layer 3 Lri Lt,v t t Description of Reflection/Transmission • Reflected Radiance • Transmission through layered OR thin materials

8. Lr,s Lr,v i r Li r Layer 1 d Layer 2  Layer 3 Lri Lt,v t t Description of Reflection Lr(r,r) = Lr,s(r,r) + Lr, v(r,r) Lr,s(r,r) = reflected radiance from surface scattering Lr,v(r,r) = reflected radiance due to volume or subsurface scattering

9. Lr,s Lr,v i r Li r Layer 1 d Layer 2  Layer 3 Lri Lt,v t t Description of Transmission Lt(t,t) = Lri(t,t) + Lt, v(t,t) Lri(t,t) = reduced intensity Lt,v(t,t) = transmitted radiance due to volume or subsurface scattering

10. Bidirectional R/T Distribution Function (BRDF, BTDF) fr =Differential reflected radiance (outgoing) Differential incident irradiance (incoming) ft =Differential transmitted radiance (outgoing) Differential incident irradiance (incoming)

11. Fresnel coefficients • Amount of light reflected/transmitted affected by: • angle of incidence • each other (R = 1 - T) • material properties • Number of layer crossings • fr = R fr,s + T fr,vor fr = R fr,s + (1-R) fr,v • Reflection from subsurface scattering is high when R is low (R low T high)

12. Material Properties n - index of refraction a - absorption cross-section s - scattering cross-section s/(s+a) - albedo - fraction of scattered radiation d - depth or thickness

13. Material Properties (cnt’d) p(cos j) - phase function, directional scattering from light on a particle - size of particles - form of particles - orientation of particles - dielectric properties of particles - wavelength of light

14. Material Properties (cnt’d) Henyey-Greenstein formula pHG(cos j) = 1 1-g2 4 (1 + g2 - 2gcosj)3/2 g - mean cosine or phase function (because particles of different sizes have different phase functions) j = angle between incoming/outgoing direction

15. Material Properties (cnt’d) • Materials described macroscopically as averages of microscopic properties • Randomness of materials’ properties addressed with random noise function

16. Light Transport Theory • Approximation to Electromagnetic Scattering Theory • Change in radiance along a particular infinitesimal direction ds contains 2 terms: • Radiance decreases from absorption / scattering • Light scattered in the direction of ds from all other directions

17. Light Transport Theory (cnt’d) For a detailed explanation of formulas / integration methods, see: “Reflection from Layered Surfaces Due to Subsurface Scattering”

18. Light Transport Theory (cnt’d) General conclusions: • Reflection increases as d increases, but transmission due to scattering reaches a max. • Subsurface reflection/transmission can be predominately backward or forward • Angle of incidence becomes more glancing, surface scattering dominates

19. Light Transport Theory (cnt’d) General conclusions: • Reflection goes to zero on horizons (Fresnel effect) • Distributions vary as a function of reflection direction (Lambert’s law predicts constant reflection in all directions)

20. Monte Carlo Algorithm • Approximation of integral techniques • Send light to random locations, and estimate average total reflection for regions

21. Results - Skin • Outer layer of oil • Outer epidermis - randomly sized tissue particles, imbedded pigment particles (melanin) • inner dermis - weakly absorbing, strongly scattering tissue and blood • Significant forward scattering

22. Results - Skin • Fresnel factors (reflection on horizon0)

23. Results - Skin • Seeliger’s law - little shading variation

24. Results - Skin • Finite layer depth

25. Results - Skin • Henyey-Greenstein phase function (g=-.25)

26. Results - Skin • Large forward scattering

27. Results - Skin • All five factors combined

29. Results - Skin • Rendering time - 20s on Silicon Graphics Personal Iris

31. Results - Leaves • Layers of typical leaf: Waxy Layer Epidermis Palisade Spongy Epidermis

32. Results - Leaves • Reflection largely determined by specular reflection from waxy stem • Veins absorb light (cast shadows) • Leaves are brighter when backlit

33. Results - Leaves

34. Successes • Scientifically-based model • Framework for range of applications • Good groundwork for other research (i.e. weathered stone!)

35. Problems • Doesn’t look *that* much better than simple Lambertian lighting • Results are not compared to the real world

36. Related Recent Work • Stanford University, Elena Vileshin • Backlit leaves using Hanrahan’s algorithm