Improved Radiance Gradient Computation

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Improved Radiance Gradient Computation

• Jaroslav Krivánek
• Pascal Gautron
• Kadi Bouatouch
• Sumanta Pattanaik

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Indirect lighting on glossy surfaces
With indirect
Without indirect
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Indirect lighting on glossy surfaces
With indirect
Without indirect
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Problem to solve

• Illumination integral evaluation at each visible
  point

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Brute Force Approach

• Monte Carlo gathering
• For each visible point
• Slow convergence rate

Cast hundreds of rays
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Slow Monte Carlo Convergence - Example

• 40 samples per pixel

Acknowledgement Jason Lawrence,
http//www.cs.princeton.edu/gfx/proj/brdf/
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Slow Monte Carlo Convergence - Example

• 100 samples per pixel

Acknowledgement Jason Lawrence,
http//www.cs.princeton.edu/gfx/proj/brdf/
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Slow Monte Carlo Convergence - Example

• 300 samples per pixel

Acknowledgement Jason Lawrence,
http//www.cs.princeton.edu/gfx/proj/brdf/
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Slow Monte Carlo Convergence - Example

• 600 samples per pixel

Acknowledgement Jason Lawrence,
http//www.cs.princeton.edu/gfx/proj/brdf/
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Slow Monte Carlo Convergence Example

• 1200 samples per pixel

Acknowledgement Jason Lawrence,
http//www.cs.princeton.edu/gfx/proj/brdf/
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Observation

• Indirect lighting on rough glossy surfaces is
  rather smooth abrupt changes are rare

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Radiance Caching Approach

• Sparse sampling of indirect illumination
• Interpolation
• Based on gradients

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Radiance Caching
Radiance Cache
Scene
Store in cache
P1
Sample hemisphere
Project to hemispherical harmonics
Lo? x BRDF(P1) x cos ? d?
Lo(P2)? x BRDF(P2) x cos ? d?
Lo(P1)
Lo(P2)
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Problem
Reality
With radiance caching
Wrong extrapolation
Li(P1) Li(P2)
Li(P1) ! Li(P2)
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Wrong Extrapolation

• How does Li(P) change with P?
• ( Li(P) incoming radiance at P )
• First approximation RADIANCE GRADIENT
• Our contribution
• New radiance gradient computation

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Wrong Extrapolation
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Corrected with the New Gradients
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Radiance Gradients Problem Definition
Prerequisites

• Incoming radiance Li(P) representation
• Li(P) is defined over a hemisphere
• Represented using hemispherical harmonics
• Li(P) represented by a set of coefficients

Basis functions
Coefficients
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Radiance Gradients Problem Definition
Prerequisites

• Coefficients computed with Monte Carlo quadrature
• Uniform hemisphere sampling
• Stratification

Sum over all strata
Multiplied by thebasis function
Incoming radiance from the sampled direction
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Radiance Gradients Problem Definition

• Coefficients hemisphere sampling
• Gradients from the same hemisphere sampling
• Something like

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Previous Work - Polygonal emitters

• Arvo 1994
• Irradiance Jacobian due to partially occluded
  polygonal emitters of constant radiosity
• Holzschuch and Sillion 1995
• Polygonal emitters of arbitrary radiosity

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Previous Work - Hemisphere sampling

• Ward and Heckbert 1992 Irradiance gradients
• Specifically for irradiance
• Cosine-proportional, uniformly weighted samples
  over the hemisphere
• We extend this to uniformly distributed,
  arbitrarily weighted samples
• Krivánek et al. 2005, Annen 2004
• Radiance gradient
• Works mostly fine, except when there is occlusion
  in the sampled environment
• We improve quality of this

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Gradient Computation

• Compute contribution from each hemisphere cell
• Sum it all together

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Gradient Computation for One Cell
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Gradient Computation for One Cell
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Gradient Computation for One Cell

• Wall movement gt cell area changes
• Cell area change gt solid angle changes
• Solid angle change gt incoming radiance changes

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Putting it all together

• Sum incoming radiance changes from all cells
• Use the basis functions H as a weighting factor
• Basis functions do not change with displacement

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Results
Old gradients
New gradients - smooth
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Results
New gradients
Old gradients
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Results
Old gradients
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Results
New gradients
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Gradients for GPU-based irradiance and radiance
caching

• Hemisphere sampling GPU rasterization
• Camera position hemisphere center
• Very non-uniform density of samples over the
  hemisphere
• The same gradient derivation still holds (and
  WORKS!).

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Gradients for GPU-based irradiance and radiance
caching

• Irradiance caching video
• Offline irradiance caching video
• Radiance caching video castle, walt disney hall

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Conclusion

• New translational gradient computation
• Use information from hemisphere sampling
• Based on the Irradiance Gradients by Ward and
  Heckbert
• Generalized to support
• Arbitrary distribution of radiance samples over
  the hemisphere
• Arbitrary weighting of radiance samples

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Thank you
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