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Feb 21, 2023 320 likes •639 views

Efficient Caustic Rendering with Lightweight Photon Mapping Pascal Grittmann 1,3 Arsne Prard-Gayot 1 Philipp Slusallek 1,2 Jaroslav Krivnek 3,4 1 Saarland University 2 DFKI Saarbrcken 3 Charles University, Prague 4 Render Legion The Idea

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SLIDE 1

Efficient Caustic Rendering with Lightweight Photon Mapping

Pascal Grittmann1,3 Arsène Pérard-Gayot1 Philipp Slusallek1,2 Jaroslav Kr̍ivánek3,4

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

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SLIDE 2

The Idea Behind Guiding

  • Importance sampling of the 𝑀𝑗/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 𝑴𝒋?
  • Many approaches
  • Usually store a representation of 𝑀𝑗 at some point in the scene and

interpolate them

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

them

2

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SLIDE 3

Reduces Variance

  • P. Grittmann et al. – Lightweight Photon Mapping

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(plotted with low pass fjlter)

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SLIDE 4

Photon Mapping Already Does Guiding [Jen96]

  • Heuristic classification of materials as “glossy”
  • Projection of caustic-casters
  • “Caustic map”
  • P. Grittmann et al. – Lightweight Photon Mapping

4

glossy

glossy

diffuse

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SLIDE 5

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 2 4

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

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SLIDE 6

Gaussian Mixture Models – Vorba et al. 2014

  • Fits mixtures of gaussians to the incident radiance/importance at a set
  • f 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)
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SLIDE 7

Vorba GMM – Training Phase

7

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SLIDE 8

Guide Photons According to Visual Importance

  • [PP98] [VKS*14] [SOHK16]
  • Using importance sampling or MCMC
  • P. Grittmann et al. – Lightweight Photon Mapping

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Example Scene Visual importance

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SLIDE 9

Our Method

  • Guide emission based on visual importance
  • Limit to paths with high variance form the path tracer
  • P. Grittmann et al. – Lightweight Photon Mapping

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Example Scene Visual importance

  • f all photons

Our Method: only “useful” photons

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SLIDE 10

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

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SLIDE 11

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

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SLIDE 12

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?

  • P. Grittmann et al. – Lightweight Photon Mapping

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𝑔(𝑦) 𝑞1(𝑦) 𝑞2(𝑦)

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SLIDE 13

The Notion of “Useful” Photons

  • P. Grittmann et al. – Lightweight Photon Mapping

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𝑂𝑛𝑗𝑜 𝑞𝑄𝑁 𝑧 𝜌𝑠2 𝑞𝑄𝑈(𝑧|𝑧𝑙) > 1

“The photon n mappe per can reach a point within 𝑠 with highe her probabil ability ity than n the path h tracer cer, using only 𝑂min light paths” 𝑠 𝑧𝑙 𝑧𝑙−1 𝑧𝑙−2 𝑧0

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SLIDE 14

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!
  • P. Grittmann et al. – Lightweight Photon Mapping

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𝐽 = 𝐽𝑄𝑁 + 𝐽𝑀𝑈 + 𝐽𝑄𝑈 𝐽𝑄𝑁 + 𝐽𝑀𝑈 𝐽𝑄𝑁 + 𝐽𝑀𝑈 + 𝐽𝑄𝑈 > 1% 𝐽𝑄𝑁 + 𝐽𝑀𝑈

Rendered Image PM / LT Contribution (exposure +5) Pixel Classifjcation

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SLIDE 15

Is that Number of Light Paths Optimal?

  • P. Grittmann et al. – Lightweight Photon Mapping

15 0. 0.2

0. 2

2 Ours (0.3 )

ar

time (seconds)

→ Optimal for large scenes with small Caustics

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SLIDE 16

2 Ours (0.7)

till i e

time (seconds)

Is that Number of Light Paths Optimal?

  • P. Grittmann et al. – Lightweight Photon Mapping

16 0. 0.2

0. 2

→ Complex SDS paths require more samples from the path tracer

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SLIDE 17

Ours (0. 3)

  • r 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 effjcient

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SLIDE 18

Results

Impact of the Full Method with Our Test Scenes

  • P. Grittmann et al. – Lightweight Photon Mapping

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SLIDE 19

Photon Densities in the Cornell Box Variations

  • P. Grittmann et al. – Lightweight Photon Mapping

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Reference Photon density – Our Photon density – Guiding with all Photons

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SLIDE 20

Photon Densities in the Cornell Box Variations

  • P. Grittmann et al. – Lightweight Photon Mapping

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Reference Photon density – Our Photon density – Guiding with all Photons

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SLIDE 21

Photon Densities in the Cornell Box Variations

  • P. Grittmann et al. – Lightweight Photon Mapping

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Reference Photon density – Our Photon density – Guiding with all Photons

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SLIDE 22

Photon Densities in the Cornell Box Variations

  • P. Grittmann et al. – Lightweight Photon Mapping

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Reference Photon density – Our Photon density – Guiding with all Photons

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SLIDE 23

The Torus – Simple Example, Directional Light

  • P. Grittmann et al. – Lightweight Photon Mapping

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Path tracer (delta light) Unguided Our Result identical to existing guiding approaches.

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SLIDE 24

Car Scene – Large Exterior Scene, Small Caustics

  • P. Grittmann et al. – Lightweight Photon Mapping

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Equal-time comparison (60 seconds)

00

Time (seconds)

2

RMSE 02

Importance Unguided Ours

Unguided Importance Ours Reference

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SLIDE 25

Car Scene – Large Exterior Scene, Small Caustics

  • P. Grittmann et al. – Lightweight Photon Mapping

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Equal-time comparison (60 seconds)

Unguided Importance Ours Reference

Time (seconds)

2

RMSE 02

Unguided Importance Ours

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SLIDE 26
  • P. Grittmann et al. – Lightweight Photon Mapping
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SLIDE 27
  • P. Grittmann et al. – Lightweight Photon Mapping
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SLIDE 28
  • P. Grittmann et al. – Lightweight Photon Mapping
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SLIDE 29

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

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SLIDE 30

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 Kr̍ivánek

𝑠 𝑧𝑙 𝑧𝑙−1 𝑧𝑙−2 𝑧0

Reference Our Importance driven Reference PM / LT contribution Our pixel classification

Unguided Importance Ours Reference