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Reflection from Layered Surfaces due to Subsurface Scattering

Reflection from Layered Surfaces due to Subsurface Scattering. Pat Hanrahan Wolfgang Krueger SIGGRAPH 1993 Andrea Rowan March 2, 2001. Outline. Problem description Previous Work Reflection / Transmission formulas Results Successes / Problems Related Recent Work. Problem Description.

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Reflection from Layered Surfaces due to Subsurface Scattering

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  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

  5. 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]

  6. 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

  7. 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

  8. 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

  9. 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)

  10. 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)

  11. 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

  12. 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

  13. 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

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

  15. 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

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

  17. 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

  18. 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)

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

  20. 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

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

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

  23. Results - Skin • Finite layer depth

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

  25. Results - Skin • Large forward scattering

  26. Results - Skin • All five factors combined

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

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

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

  30. Results - Leaves

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

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

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

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