Transcript hanrahan.ppt

Reflection from Layered
Surfaces due to Subsurface
Scattering
Pat Hanrahan
Wolfgang Krueger
SIGGRAPH 1993
Andrea Rowan
March 2, 2001
Outline
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Problem description
Previous Work
Reflection / Transmission formulas
Results
Successes / Problems
Related Recent Work
Problem Description
 Light scattering on a subsurface
level
Problem Description
 Realistically model layered materials
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Skin, leaves
Snow, sand, paint, weathered stone
 Model isotropic diffuse exiting radiance,
proportional to surface irradiance
 Subsurface scattering of light
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Enter material  Absorbed/Scattered 
Reflected
Previous Work
 Anisotropic specular reflection on rough
surfaces
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Poulin et al.[24], Cabral et al.[5]
 Reflection/Transmission through clouds
of particles (Saturn’s rings)
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Blinn, 1982 [2]
Description of
Reflection/Transmission
 Reflected Radiance
 Transmission through layered OR thin
materials
Layer 1
d
Li
i
Lr,s
r
Lr,v
r
Layer 2

Layer 3
t
Lri
t
Lt,v
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
Lr,s
i r
Lr,v

L
r
i
Layer 1
d
Layer 2

Layer 3
t
Lri
t
Lt,v
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
Lr,s
i r
Lr,v

L
r
i
Layer 1
d
Layer 2

Layer 3
t
Lri
t
Lt,v
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)
Fresnel coefficients
 Amount of light reflected/transmitted
affected by:
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angle of incidence
each other (R = 1 - T)
material properties
Number of layer crossings
 fr = R fr,s + T fr,v or fr = R fr,s + (1-R) fr,v
 Reflection from subsurface scattering is
high when R is low (R low T high)
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
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
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
Material Properties (cnt’d)
 Materials described macroscopically as
averages of microscopic properties
 Randomness of materials’ properties
addressed with random noise function
Light Transport Theory
 Approximation to Electromagnetic
Scattering Theory
 Change in radiance along a particular
infinitesimal direction ds contains 2
terms:
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Radiance decreases from absorption /
scattering
Light scattered in the direction of ds from all
other directions
Light Transport Theory (cnt’d)
For a detailed explanation of formulas /
integration methods, see:
“Reflection from Layered Surfaces Due to
Subsurface Scattering”
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
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)
Monte Carlo Algorithm
 Approximation of integral techniques
 Send light to random locations, and
estimate average total reflection for
regions
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
Results - Skin
 Fresnel factors (reflection on horizon0)
Results - Skin
 Seeliger’s law - little shading variation
Results - Skin
 Finite layer depth
Results - Skin
 Henyey-Greenstein phase function (g=-.25)
Results - Skin
 Large forward scattering
Results - Skin
 All five factors combined
Results - Skin
 Rendering time - 20s on Silicon Graphics
Personal Iris
Results - Leaves
 Layers of typical leaf:
Waxy Layer
Epidermis
Palisade
Spongy
Epidermis
Results - Leaves
 Reflection largely determined by specular
reflection from waxy stem
 Veins absorb light (cast shadows)
 Leaves are brighter when backlit
Results - Leaves
Successes
 Scientifically-based model
 Framework for range of applications
 Good groundwork for other research (i.e.
weathered stone!)
Problems
 Doesn’t look *that* much better than simple
Lambertian lighting
 Results are not compared to the real world
Related Recent Work
 Stanford University, Elena Vileshin
 Backlit leaves using Hanrahan’s algorithm