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

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

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)

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

Bad Importance Distribution - Examples photon distribution

Bad Importance Distribution - Examples photon distribution

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

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

Probabilistic Photon Deposition - Results  Efficiently discards unimportant photons

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

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

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

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

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)

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

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

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

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)

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

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

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

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

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

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