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

Outline Overview: The Photon Map methodOverview: The Photon Map method New importance sampling techniques for the Photon MapNew importance sampling techniques for the Photon Map –Probabilistic photon deposition –Automatic caustic generation –Faster direct illumination computation SummarySummary

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

Photon Generation Original algorithm: Pure forward simulationOriginal 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 importance distribution photon distribution

Bad Importance Distribution - Examples importance distribution photon distribution

Importance Driven Photon Maps Photon generation stage is relatively cheapPhoton generation stage is relatively cheap  Invest more time in photon generation to improve rendering Goal : Concentrate photons in important regionsGoal : Concentrate photons in important regions  Two approaches : Guide photons to important regions (Peter, Pietrek, ‘98)Guide photons to important regions (Peter, Pietrek, ‘98) Discard unimportant photonsDiscard unimportant photons Guiding photons often problematicGuiding 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 importanceInitialization stage : Approximate importance –Shoot ‘importons’ from camera into scene –Store in separate importance map Photon tracing stagePhoton tracing stage –Generate deposition probability P for each new photon Based on importance of photon locationBased on importance of photon location Approximate importance with density estimationApproximate importance with density estimation –Stochastically discard unimportant photons Discard with probability (1-P)Discard with probability (1-P) On acceptance : Deposit photon with new energy phi/POn 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 importance distribution photons, not importance driven Comparison at same number of traced photons :

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

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

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

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 storageless storage “Same number of photons during rendering” –Higher photon tracing cost (often small compared to rendering) –Better quality all photons are importantall photons are important higher density in important regionshigher 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 densityProblem: 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 separatelyJensen: Shoot caustic photons separately –Shoot directly to caustic generating objects  Generates only direct caustics Our approach : Extend importance driven photon depositionOur 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 densityhigher caustic density (S=20)

Direct Illumination Direct illumination calculated separatelyDirect 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 computationPhoton driven direct illumination computation –Estimate light source importances with Photon Map Rough estimate is enough for importance samplingRough estimate is enough for importance sampling Tag direct photons with light source idTag direct photons with light source id –Rendering: Estimate contribution from each light source Based on k nearest direct photonsBased on k nearest direct photons –Select number of shadow rays per light source relative to that light source’s importance Missing light sourcesMissing 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 timeBetter quality at same rendering time

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

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

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