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## Efficient Importance Sampling Techniques for the Photon Map

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**Efficient Importance SamplingTechniques for thePhoton 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**importance distribution photon distribution**Bad Importance Distribution - Examples**importance distribution 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 onlydirectcaustics • 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