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Subsurface scattering models
02/26/03
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More subsurface scattering
Sky models
02/26/03
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BSSRDF
Bidirectional surface scattering reflectance distribution function, S
Relates the outgoing radiance at one point to the incident flux at another
BRDF makes the assumption that xi = xo
To get the total radiance leaving a point, integrate over the surface and the incoming directions
S depends on the sub-surface scattering of the material
02/26/03
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Practical Model
Wann Jensen, Marschner, Levoy and Hanrahan, 2001
Handles non-isotropic media
Does not require extensive Monte-Carlo raytracing
Just a modified version of distribution ray-tracing
Approximation based on:
Multiple bounce scattering – diffuse component
Single bounce scattering – directional component
02/26/03
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5. Single Scattering Termo
Assume one one scattering event on the path from incoming to outgoing ray
To get outgoing radiance, integrate along refracted ray xi xo s
02/26/03
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6. Single Scattering Term
S(1) is defined by this formula
02/26/03
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Multiple Scattering
Observation: multiple scattering tends to look diffuse
Each scattering event tends to blur the distribution of radiance, until it looks uniform
For flat, semi-infinite surfaces, the effect of multiple scattering can be approximated with two virtual light sources
One inside the medium
One “negative” light outside the medium
The diffusion approximation
02/26/03
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8. Diffuse Scattering Term (the flavor)
This equation uses the Fresnel, coefficients to scale the incoming radiance, coefficients for transmission and adsorption, and variables for the location of the virtual light sources
02/26/03
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Fitting Parameters
There are 4 material dependent parameters: ’s, a, , 
Seems surprising, but it’s true!
Each parameter, except , depends on wavelength, but just use RGB
Measure by taking a high dynamic range image of a sample piece illuminated by a focused light
High dynamic range imagery will be covered later
02/26/03
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10. Rendering with the BSSRDF
Rendering has to take into account:
Efficient integration of the BSSRDF including importance sampling
Single scattering for arbitrary geometry
Diffuse scattering for arbitrary geometry
Texture on the surface
Use a distribution ray-tracer
Each time you hit a surface point, xo, have to sample incoming points, xi to estimate integral
02/26/03
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Sampling Approaches
For single scattering terms, sample points along the refracted outgoing ray
Cast shadow ray to light to find out incoming radiance
Push this through single scattering equation to get outgoing
Make distant light approximation to ease computations
For diffuse scattering term, sample points around the outgoing point
Then place the virtual lights and evaluate the equation
Must be careful to put virtual lights in appropriate places
For texture, use parameters from xi for diffuse, and combination of xi and xo for single scattering
02/26/03
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Results
02/26/03
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More Results
02/26/03
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Can’t Escape the Bunny
02/26/03
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Sky Illumination
The sky is obviously an important source of illumination
The atmosphere is an important participating medium over large distances (hundreds of meters)
People use atmospheric effects to judge distances (stereo and disparity effects are useless at large distances)
Three models:
CIE model
Perez model
Preetham, Shirley and Smits model
02/26/03
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16. Atmospheric Phenomena
Due to solar illumination and scattering in the atmosphere
Air molecules are modeled by Rayleigh scattering
Optical extinction coefficient varies with -4
What phenomena does this explain?
Scattering due to larger particles is modeled with Mie scattering
Scattering depends less on wavelength, so what color is haze?
Turbidity is a useful measurement: T=(tm+th)/tm
tm is vertical optical thickness of molecular atmosphere
th is vertical optical thickness of haze atmosphere
02/26/03
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Simulation Models
These attempt to simulate the scattering in the atmosphere to produce images
Very expensive for practical use
But work with any atmospheric conditions
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Coordinate System
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CIE Model
Predicts luminance of a point in the sky for a particular sun position on a clear day
What color space do we do sky computations in?
Yz is the luminance of the zenith, which can be found in tables or formulas that incorporate sun position
This formula is used in Radiance, among other systems
02/26/03
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CIE Cloud Model
For completely overcast skies (thick clouds)
02/26/03
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Perez Model
Five parameters:
A: darkening or brightening of the horizon
B: luminance gradient near the horizon
C: relative intensity of the circum-solar region
D: width of the circum-solar region
E: relative backscattered light
02/26/03
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Aerial Perspective
The change in color due to passage of light through the atmosphere
Has been modeling in various ways:
Fog models
Full scattering simulations
Fake ambient illumination
Single scattering integrated along a line from source to viewer
02/26/03
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23. Preetham, Shirley and Smits
Practical model (or so they claim)
Model sun with NASA data and attenuation along path to viewer
Model skylight with Perez model
Run lots of simulation of particle scattering
Fit parameters for Perez model
Also fit chromaticity values
Model aerial perspective with simplifications to scattering integrals
02/26/03
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Results
02/26/03
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Turbidity
02/26/03
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26. Ward’s Model vs Preetham
02/26/03
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