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Optimally Combining Sampling Techniques for Monte Carlo Rendering

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Title: Optimally Combining Sampling Techniques for Monte Carlo Rendering


1
Optimally Combining Sampling Techniques for Monte
Carlo Rendering
  • Eric Veach and Leonidas J. Guibas
  • Computer Science Department Stanford University
  • SIGGRAPH 1995

2
Variance
Sampling the light sources
Sampling the BRDF
3
Multi-sample Model
Weighted combination of all the sample values
An example of wi
ci relative number of samples taken from pi
(balance heuristic)
4
Theorem 1
wi any non-negative functions with
No choice of the wi can improve upon the variance
of the balance heuristic by more than (1/mini ni
1/N)F2
5
Weighting Heuristics
(a) balance
(b) cutoff
(c) power
(d) maximum
6
variance
roughness
7
Combine Sampling
With power heuristic
8
A simple test scene
One area light source and an adjacent diffuse
surface.
(a)
(b)
(c)
(a) Sampling the light source (b) Sampling the
hemisphere according to the projected solid
angle (c) Combination of samples using the power
heuristic
9
Bidirectional Path Tracing
10
Bidirectional Sampling Strategies
  • Standard MC path tracing.
  • Standard MC path tracing with direct lighting.
  • Depositing light on a visible surface (photomap).
  • Depositing light when a photon hits the camera
    lens.

11
(No Transcript)
12
Bidirectional Path Tracing
25 samples per pixel
56 samples per pixel
Standard path tracing using the same amount of
work (same computation time)
Combines samples from all the bidirectional
techniques
13
Conclusion
  • Power heuristic (with beta2) gave the best
    results.
  • These techniques are practical, and the
    additional cost is small less than 10

14
PBRT
PBRT define balance and power heuristic in mc.h
inline float BalanceHeuristic(int nf, float fPdf,
int ng, float gPdf) return (nf fPdf) / (nf
fPdf ng gPdf) inline float
PowerHeuristic(int nf, float fPdf, int ng, float
gPdf) float f nf fPdf, g ng
gPdf return (ff) / (ff gg)
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