Efficient Caustic Rendering with Lightweight Photon Mapping

Pascal Grittmann1,3 Arsène Pérard-Gayot1 Philipp Slusallek1,2 Jaroslav Krivánek3,4

1Saarland University 2DFKI Saarbrücken 3Charles University, Prague 4Render Legion

The Idea Behind Guiding

• Importance sampling of the 𝐿𝑖/𝑊𝑖 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 𝑳𝒊?• Many approaches

• Usually store a representation of 𝐿𝑖 at some point in the scene and interpolate them

• Methods differ in what representations they choose and how they obtain them

2

Reduces Variance

P. Grittmann et al. – Lightweight Photon Mapping 3

(plotted with low pass filter)

Photon Mapping Already Does Guiding [Jen96]

• Heuristic classification of materials as “glossy”• Projection of caustic-casters• “Caustic map”

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glossy

glossy

diffuse

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

5

0 0 0 0

0 2 0 0

0 0 4 0

0 0 0 0

The red photon has a luminance of 2The blue one a luminance of 4

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

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Example Scene Visual importance

Our Method

• Guide emission based on visual importance• Limit to paths with high variance form the path tracer

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Example Scene Visual importanceof all photons

Our Method: only “useful” photons

Our Method Relies Only on Path Probabilities

• No (implicit) material classification• Accounts for the (relative) size of the light source

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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

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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

• Can restricting costly estimators to regions of high variance result in more efficient combined algorithms?

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𝑓(𝑥)

𝑝1(𝑥)

𝑝2(𝑥)

The Notion of “Useful” Photons

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𝑁𝑚𝑖𝑛 𝑝𝑃𝑀 𝑦 𝜋𝑟2

𝑝𝑃𝑇(𝑦|𝑦𝑘)> 1

“The photon mapper can reach a point within 𝑟with higher probability than the path tracer, using only 𝑁min light paths”

𝑟

𝑦𝑘𝑦𝑘−1

𝑦𝑘−2

𝑦0

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!

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𝐼 = 𝐼𝑃𝑀 + 𝐼𝐿𝑇 + 𝐼𝑃𝑇

𝐼𝑃𝑀 + 𝐼𝐿𝑇𝐼𝑃𝑀 + 𝐼𝐿𝑇 + 𝐼𝑃𝑇

> 1%𝐼𝑃𝑀 + 𝐼𝐿𝑇

Rendered Image PM / LT Contribution(exposure +5)

Pixel Classification

Is that Number of Light Paths Optimal?

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0.

0.2

0.

2

0 0

2

Ours (0.3 )

ar

time (seconds)

→ Optimal for large scenes with small Caustics

0 0

2

Ours (0.7)

till i e

time (seconds)

Is that Number of Light Paths Optimal?

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0.

0.2

0.

2

→ Complex SDS paths require more samples from the path tracer

0 0

Ours (0. 3)

or s

time (seconds)

Is that Number of Light Paths Optimal?

P. Grittmann et al. – Lightweight Photon Mapping 17

0.

0.2

0.

2

→ For scenes that are trivial except for the caustics, a higher number would be more efficient

ResultsImpact of the Full Method with Our Test Scenes

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Photon Densities in the Cornell Box Variations

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Reference

Photon density – Our

Photon density – Guiding with all Photons

Photon Densities in the Cornell Box Variations

P. Grittmann et al. – Lightweight Photon Mapping 20

Reference

Photon density – Our

Photon density – Guiding with all Photons

Photon Densities in the Cornell Box Variations

P. Grittmann et al. – Lightweight Photon Mapping 21

Reference

Photon density – Our

Photon density – Guiding with all Photons

Photon Densities in the Cornell Box Variations

P. Grittmann et al. – Lightweight Photon Mapping 22

Reference

Photon density – Our

Photon density – Guiding with all Photons

The Torus – Simple Example, Directional Light

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Path tracer(delta light)

Unguided Our

Result identical to existing guiding approaches.

Car Scene – Large Exterior Scene, Small Caustics

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Equal-time comparison (60 seconds)

00 0

Time (seconds)

2

0

RMSE

02

Importance

Unguided

Ours

Unguided Importance Ours Reference

Car Scene – Large Exterior Scene, Small Caustics

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Equal-time comparison (60 seconds)

Unguided Importance Ours Reference

0 0Time (seconds)

2

RMSE

02

Unguided

Importance

Ours

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

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Efficient Caustic Rendering with Lightweight Photon Mapping

Restrict costly estimators to a subset of the domain

→ More efficient MIS combination

30

Pascal Grittmann Arsène Pérard-Gayot Philipp Slusallek Jaroslav Krivánek

𝑟

𝑦𝑘𝑦𝑘−1

𝑦𝑘−2

𝑦0

Reference

Our

Importancedriven

Reference PM / LT contribution Our pixel classification

Unguided Importance Ours Reference