Efficient Caustic Rendering with Lightweight Photon Mapping Pascal - PowerPoint PPT Presentation

Efficient Caustic Rendering with Lightweight Photon Mapping Pascal Grittmann 1,3 Arsène Pérard-Gayot 1 Philipp Slusallek 1,2 Jaroslav Kr̍ivánek 3,4 1 Saarland University 2 DFKI Saarbrücken 3 Charles University, Prague 4 Render Legion

The Idea Behind Guiding • Importance sampling of the 𝑀 𝑗 / 𝑋 𝑗 term (path tracing / particle tracing) • Combine with importance sampling of the BSDF • Ideally results in perfect importance sampling of the entire Light Transport Equation (LTE)! • How to importance sample 𝑴 𝒋 ? • Many approaches • Usually store a representation of 𝑀 𝑗 at some point in the scene and interpolate them • Methods differ in what representations they choose and how they obtain them 2

Reduces Variance (plotted with low pass fjlter) P. Grittmann et al. – Lightweight Photon Mapping 3

Photon Mapping Already Does Guiding [Jen96] • Heuristic classification of materials as “glossy” • Projection of caustic-casters • “ Caustic map ” glossy glossy diffuse P. Grittmann et al. – Lightweight Photon Mapping 4

Path Guiding Using the Photon Map • One of the first approaches to guide • Uses nearby photons to construct a histogram of incident radiance • Samples a cell of this histogram and a direction within the cell (uniformly) • Histogram is a grid, each cell maps to a part of the hemisphere 0 0 0 0 0 2 0 0 The red photon has a luminance of 2 The blue one a luminance of 4 0 0 4 0 0 0 0 0 5

Gaussian Mixture Models – Vorba et al. 2014 • Fits mixtures of gaussians to the incident radiance/importance at a set of points in the scene • Project hemisphere onto plane, incident directions as bivariate Gaussians over that plane • Gaussians are easy to sample and easy to update • Long training pass before actual rendering (~15-30 min)

Vorba GMM – Training Phase 7

Guide Photons According to Visual Importance • [PP98] [VKS*14] [SOHK16] • Using importance sampling or MCMC Example Scene Visual importance P. Grittmann et al. – Lightweight Photon Mapping 8

Our Method • Guide emission based on visual importance • Limit to paths with high variance form the path tracer Example Scene Visual importance Our Method: only of all photons “useful” photons P. Grittmann et al. – Lightweight Photon Mapping 9

Our Method Relies Only on Path Probabilities • No (implicit) material classification • Accounts for the (relative) size of the light source P. Grittmann et al. – Lightweight Photon Mapping 10

The Lightweight Photon Mapping Algorithm • Based on VCM / UPS – [GKDS12] [HPJ12] • Goal: More efficient solution for large scenes with a few small caustics • MIS Combination of • Light Tracer • Photon Mapper • Path Tracer P. Grittmann et al. – Lightweight Photon Mapping 11

Motivation / Idea • Existing methods: Try to be unbiased for all estimators • Looses main advantage of MIS! • Why not ignore estimators that we know will contribute little? • A la maximum heuristics or alpha-max heuristics – but only where necessary 𝑔(𝑦) 𝑞 1 (𝑦) 𝑞 2 (𝑦) • Can restricting costly estimators to regions of high variance result in more efficient combined algorithms? P. Grittmann et al. – Lightweight Photon Mapping 12

The Notion of “Useful” Photons “The photon n mappe per can reach a point within 𝑠 𝜌𝑠 2 𝑂 𝑛𝑗𝑜 𝑞 𝑄𝑁 𝑧 > 1 with highe her probabil ability ity than n the path h tracer cer, 𝑞 𝑄𝑈 (𝑧|𝑧 𝑙 ) using only 𝑂 min light paths” 𝑧 𝑙−2 𝑠 𝑧 0 𝑧 𝑙 𝑧 𝑙−1 P. Grittmann et al. – Lightweight Photon Mapping 13

How Many Photons Should We Trace? - One Per Pixel Influenced by Caustics • VCM: One light path per pixel • With guiding: Fewer light paths are needed! 𝐽 𝑄𝑁 + 𝐽 𝑀𝑈 > 1% 𝐽 = 𝐽 𝑄𝑁 + 𝐽 𝑀𝑈 + 𝐽 𝑄𝑈 𝐽 𝑄𝑁 + 𝐽 𝑀𝑈 𝐽 𝑄𝑁 + 𝐽 𝑀𝑈 + 𝐽 𝑄𝑈 Rendered Image PM / LT Contribution Pixel Classifjcation (exposure +5) P. Grittmann et al. – Lightweight Photon Mapping 14

Is that Number of Light Paths Optimal? ar 0. 2 0.2 0. 2 0 0 time (seconds) Ours (0.3 ) → Optimal for large scenes with small Caustics P. Grittmann et al. – Lightweight Photon Mapping 15

Is that Number of Light Paths Optimal? till i e 2 0. 0.2 0. 2 0 0 time (seconds) Ours (0.7) → Complex SDS paths require more samples from the path tracer P. Grittmann et al. – Lightweight Photon Mapping 16

Is that Number of Light Paths Optimal? or s 0. 0.2 0. 2 0 0 time (seconds) Ours (0. 3) → For scenes that are trivial except for the caustics, a higher number would be more effjcient P. Grittmann et al. – Lightweight Photon Mapping 17

Results Impact of the Full Method with Our Test Scenes P. Grittmann et al. – Lightweight Photon Mapping 8

Photon Densities in the Cornell Box Variations Reference Photon density – Guiding with all Photons Photon density – Our P. Grittmann et al. – Lightweight Photon Mapping 19

Photon Densities in the Cornell Box Variations Reference Photon density – Guiding with all Photons Photon density – Our P. Grittmann et al. – Lightweight Photon Mapping 20

Photon Densities in the Cornell Box Variations Reference Photon density – Guiding with all Photons Photon density – Our P. Grittmann et al. – Lightweight Photon Mapping 21

Photon Densities in the Cornell Box Variations Reference Photon density – Guiding with all Photons Photon density – Our P. Grittmann et al. – Lightweight Photon Mapping 22

The Torus – Simple Example, Directional Light Path tracer Unguided Our (delta light) Result identical to existing guiding approaches. P. Grittmann et al. – Lightweight Photon Mapping 23

Car Scene – Large Exterior Scene, Small Caustics Equal-time comparison (60 seconds) 0 RMSE 0 2 2 Unguided Reference Unguided Importance Ours Importance Ours 0 0 0 Time (seconds) P. Grittmann et al. – Lightweight Photon Mapping 24

Car Scene – Large Exterior Scene, Small Caustics Equal-time comparison (60 seconds) 2 RMSE 0 2 Unguided Reference Unguided Importance Ours Importance Ours 0 0 Time (seconds) P. Grittmann et al. – Lightweight Photon Mapping 25

P. Grittmann et al. – Lightweight Photon Mapping

P. Grittmann et al. – Lightweight Photon Mapping

P. Grittmann et al. – Lightweight Photon Mapping

Limitations • Only for caustic-casters directly in front of the light source • Resorts to path tracing for (diffuse) indirect illumination P. Grittmann et al. – Lightweight Photon Mapping 2

Efficient Caustic Rendering with Lightweight Photon Mapping Pascal Grittmann Arsène Pérard-Gayot Philipp Slusallek Jaroslav Kr̍ivánek 𝑧 𝑙−2 𝑠 𝑧 𝑙 𝑧 0 𝑧 𝑙−1 Reference PM / LT contribution Our pixel classification Restrict costly estimators to a subset of the domain → More efficient MIS combination Reference Unguided Importance Ours Reference Importance driven Our 30