BSSRDF: Bidirectional Surface Scattering Reflectance Distribution Functions

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BSSRDF Bidirectional Surface Scattering
ReflectanceDistribution Functions
Based on "A Practical Model for Subsurface
Light Transport" Henrik Wann Jensen, Steve
Marschner, Marc Levoy and Pat Hanrahan

• Jared M. Dunne
• C95 Adv. Graphics
• Feb. 7, 2002

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What is BSSRDF?

• Bidirectional surface scattering reflectance
  distribution function
• In other words An equation that determines how
  incident light reflects and scatters from a
  surface
• Also, simulates how light reflects off of and
  throughout a surface

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Example Skin
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BRDF

• Bidirectional reflectance distribution function
• Simplification of BSSRDF
• Assumes that light entering a material leaves it
  at the same point
• Usually tries to approximate surface scattering
  in some way

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BSSRDF v. BRDF

• BSSRDF allows simulation of light transport
• Light can enter a material at one point and be
  reflected at another point.
• BSSRDF ? Translucence, Color Bleeding
• BRDF ? Opague, Hard-looking
• But BSSRDF is EXPENSIVE

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BSSRDF v. BRDF
BSSRDF
BRDF
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Example
BRDF
BSSRDF
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The Theory

• Outgoing radiance at point x0 is computed by
  integrating incident radiance at points xi over
  the surrounding area and incoming directions wi.

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Hendrik Wann Jensen et al

• Basic Idea Break into two parts
• Diffuse the radiance at a given point due to
  light transport within the media, via an
  approximation of the scatting
• Single Scattering the first order scattering
  from a surface BRDF reflection light refracted
  through the material

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Diffuse vs. Single Scatter
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The Diffusion Approximation

• In highly scattering media (like milk), light
  scatters many times (often several hundred)
• Causes a lot more calculations, more expensive
  (if you use full BSSRDF)

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Diff. Approx. (cont.) Sd

• It is observed that in such materials the
  scattering becomes isotropic (in all directions)
  even with a highly focused light distribution.
• So the following two-term approximation is used

radiant fluence
vector irradiance
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Single Scattering Term S(1)

• The light which refracts directly through or
  reflects off of the material
• Directional component of incident light
• Jensen (et al) extend a BRDF model (Hanrahan and
  Krueger) to achieve this scatter

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Putting the two together

• So Jensens model of BSSRDF becomes
• Or
• BSSRDF Diffuse Approximation
  Single Scatter Term

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Light propagation

• sa Absorption Coefficient
• ss Scattering Coefficient
• st Extinction Coefficient sa ss
• These are used in the volume rendering equation,
  which describes how light moves through a medium

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Getting the Coefficients
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Got Milk?
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Marble bust
1.3 Million Triangles BRDF 2 minutes BSSRDF lt5
minutes Monte Carlo 1250 minutes
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Stanford Bunny
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Future Plans of Hendrik Wann Jensen

• In an interview of Jensen by CGarchitect.comI
  would like to combine the BSSRDF with photon
  mapping, and also work on making these algorithms
  generally available and easy to use for complex
  models.

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FinalRender

• First Render Engine to support BSSRDF
• More Info http//trinity3d.comhttp//trinity3d.
  com/productinfo/FinalRender/finalrender.shtml