1. Efficient Importance Sampling Techniques for the Photon Map
Ingo Wald
University of Saarbrücken
Alexander Keller
University of Kaiserslautern

2. Outline Overview: The Photon Map method
New importance sampling techniques for the Photon Map
Probabilistic photon deposition
Automatic caustic generation
Faster direct illumination computation
Summary

3. The Photon Map (Jensen,’95-’98)
Basic idea : Density estimation with a discrete density of photons
2-step algorithm
Photon generation stage
Emit photons on light sources
Random walk (trace photons through scene)
Store interactions (position x, power phi, …)
Rendering : Modified distribution ray tracing
Approximate radiance by density estimation
Query k nearest photons
Density estimation: radiance = sumOfEnergies/coveredArea
Estimate too coarse to be visualized directly  Use only indirectly (final gather)

4. Photon Generation Original algorithm: Pure forward simulation
Visual importance not taken into account
Photon density is high (only) where illumination is high
Problematic whenever photon density doesn’t match importance distribution
High density (high cost) in unimportant regions
Low density (low quality) in important region

5. Bad Importance Distribution - Examples
photon
distribution

6. Bad Importance Distribution - Examples
photon
distribution

7. Importance Driven Photon Maps
Photon generation stage is relatively cheap
Invest more time in photon generation to improve rendering
Goal : Concentrate photons in important regions
 Two approaches :
Guide photons to important regions (Peter, Pietrek, ‘98)
Discard unimportant photons
Guiding photons often problematic
Fails for highly improbable light paths
Generates noise in photon energies ( artifacts)
Our approach: Discard unimportant photons
Probabilistic photon deposition
Similar work : Suykens at al, EGWR 2000

8. Probabilistic Photon Deposition
Initialization stage : Approximate importance
Shoot ‘importons’ from camera into scene
Store in separate importance map
Photon tracing stage
Generate deposition probability P for each new photon
Based on importance of photon location
Approximate importance with density estimation
Stochastically discard unimportant photons
Discard with probability (1-P)
On acceptance : Deposit photon with new energy phi/P
Make sure that P = 1 in important regions
 No noise in photon energies
 Unbiased

9. Probabilistic Photon Deposition - Results
 Efficiently discards unimportant photons

10. Probabilistic Photon Deposition - Results
 Efficiently discards unimportant photons
Comparison at same number of traced photons :
importance
distribution
photons, not
importance driven

11. Probabilistic Photon Deposition - Results
 Efficiently discards unimportant photons
Comparison at same number of traced photons :
importance
distribution
photons, not
importance driven
photons,
importance driven

12. Probabilistic Photon Deposition - Results
Comparison at same number of stored photons :
importance
distribution
photons
old method
photons,
importance driven

13. Probabilistic Photon Deposition - Results
Comparison at same number of stored photons :
importance
distribution
photons
old method
photons,
importance driven
Impact on final image (same number of stored photons)
without importance
importance driven

14. Probabilistic Photon Deposition
Two ways to look at results:
“Emit same number of photons”
Same quality (no important photons are discarded)
Less photons during rendering phase
less storage
“Same number of photons during rendering”
Higher photon tracing cost (often small compared to rendering)
Better quality
all photons are important
higher density in important regions
Often only way to reach required density if total number of photons is limited (available memory)

15. Automatic Caustic Generation
Problem: Caustics need higher photon density
Final gather only works for diffuse indirect illumination
Caustics have to be visualized directly (artifacts)
Higher density required
Jensen: Shoot caustic photons separately
Shoot directly to caustic generating objects
Generates only direct caustics
Our approach : Extend importance driven photon deposition
Trace S times as many photons
Discard non-caustics photons with probability (S-1)/S

16. Automatic Caustic Generation
 Results
Photon generation S (typically 5-20) times as costly (Still often small compared to total rendering time)
Increases caustic density by factor S
Automatically generates indirect caustics

17. Automatic Caustic Generation
 Results
Photon generation S (typically 5-20) times as costly (Still often small compared to total rendering time)
Increases caustic density by factor S
Automatically generates indirect caustics
original caustic density

18. Automatic Caustic Generation
 Results
Photon generation S (typically 5-20) times as costly (Still often small compared to total rendering time)
Increases caustic density by factor S
Automatically generates indirect caustics
original caustic density
higher caustic density (S=20)

19. Direct Illumination Direct illumination calculated separately
Photon Map estimate too coarse
 Monte Carlo sampling of light sources
Send shadow rays to each light source  Very expensive for lots of light sources
Real scenes: Large fraction of lights often occluded  Sampling all sources equally is inefficient
 Importance sampling
Shoot more samples to ‘important’ light sources

20. Importance Driven Direct Illumination
Photon driven direct illumination computation
Estimate light source importances with Photon Map
Rough estimate is enough for importance sampling
Tag direct photons with light source id
Rendering: Estimate contribution from each light source
Based on k nearest direct photons
Select number of shadow rays per light source relative to that light source’s importance
Missing light sources
Light source may ‘by chance’ not contribute a photon
 Artifacts
Highly improbable if query radius is large enough

21. Importance Driven Direct Illumination
 Efficiently excludes unimportant light sources
 Significantly less shadow rays
Better quality at same rendering time

22. Importance Driven Direct Illumination
 Efficiently excludes unimportant light sources
 Significantly less shadow rays
Better quality at same rendering time
Comparison at identical rendering times:
original method
importance driven

23. Summary Presented three new extensions to the Photon Map
Importance driven photon deposition
Makes complex scenes tractable
Automatic caustic generation
Can generate indirect caustics
Importance driven direct illumination
Much faster for lots of light sources with varying importance

24. Questions ?