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ESTIMATORS Jaroslav Kivnek Charles University Render Legion | Chaos - - PowerPoint PPT Presentation

Feb 08, 2024 334 likes •808 views

COMBINING VOLUMETRIC ESTIMATORS Jaroslav Kivnek Charles University Render Legion | Chaos Group UNIFYING POINTS, BEAMS, AND PATHS IN VOLUMETRIC LIGHT TRANSPORT SIMULATION Jaroslav Iliyan Toshiya Petr Kivne k Georgiev Hachisuka V

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COMBINING VOLUMETRIC ESTIMATORS

Jaroslav Křivánek

Charles University – Render Legion | Chaos Group

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UNIFYING POINTS, BEAMS, AND PATHS IN VOLUMETRIC LIGHT TRANSPORT SIMULATION

Jaroslav Křivánek

Charles University in Prague

Petr Vévoda

Charles University in Prague

Toshiya Hachisuka

Aarhus University

Iliyan Georgiev

Light Transportation Ltd.

Martin Šik

Charles University in Prague

Derek Nowrouzezahrai

Univesity of Montreal

Wojciech Jarosz

Disney Research Zurich

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 Robust to: media properties, lighting

Goal: Robust rendering of media

rare dense diffuse lighting focused lighting high scattering low scattering

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Existing volumetric rendering algorithms

 MC path integration

 Path tracing [Kajiya ‘86, Rushmeier and Torrance ‘88]  Bidirectional path tracing [Lafortune and Willems ‘96]

 Photon density estimation

 Volumetric photon mapping [Jensen and Christensen ‘98]  Beam radiance estimate [Jarosz et al. ‘08]  Photon beams [Jarosz et al. ‘11]

 No existing algorithm can handle all cases

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MC methods for volumetric light transport – Combining estimators

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Bidirectional path tracing 1 hour

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MC methods for volumetric light transport – Combining estimators

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Volumetric photon mapping 1 hour

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MC methods for volumetric light transport – Combining estimators

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Beam radiance estimate 1 hour

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MC methods for volumetric light transport – Combining estimators

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Photon beams 1 hour

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UPBP algorithm 1 hour

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Approach: Combine estimators

 Multiple Importance Sampling [Veach and Guibas ‘95]

 Previous work

 Bidirectional path tracing (BPT) [Veach and Guibas ‘95]  Vertex connection and merging (VCM) [Georgiev et al. ‘12]  Unified path sampling (UPS) [Hachisuka et al. ‘12]

 Our algorithm

 “Unified points beams and paths” (UPBP)

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Contributions

 “Does it make sense to combine the estimators?”

 Variance analysis of estimators

 “How can we combine the estimators?”

 Extended multiple importance sampling

 “How do we make the method practical?”

 A combined volume rendering algorithm

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VOLUMETRIC PHOTON DENSITY ESTIMATORS

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photon points [Jarosz et al. ’11a]

QUERY RADIANCE REP.:

photon beams point beam

Beam - Point Point - Point Point - Beam Beam - Point

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 Photon beams  Query beams

 The same story

“Long” vs. “short” beams

[Jarosz et al. ’11b]

“Short” beams

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“Long” beams

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Points “Short” Beams “Long” Beams

×

Bottom line: Many estimators

Points “Short” Beams “Long” Beams

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Why combine points and beams?

 Won’t photon beams always outperform photon points?

from [Jarosz et al. ’11a]

100k photon points reference 5k photon beams

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VARIANCE ANALYSIS

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Variance analysis – Canonical setup

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Variance analysis – Expected value

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transmittance transmittance

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Variance analysis – Estimators

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transmittance “Long” beam “Short” beam Point

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Variance analysis results

dense media rare media kernel width [mean free path] normalized

  • std. dev. (NSD)

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1 4 Short beam – Bl Point – Bl

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Variance analysis results

dense media rare media beams:

 

points:

 

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“HOW TO COMBINE?” EXTENDED MIS

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Our MIS extension

 Extended MIS – accommodate all the different estimators  Compatible with RR interpretation of density estimation

kernels (like VCM [Georgiev et al. ‘12])

 Alternative view: extended path space [Hachisuka et al.

’12, Hachisuka et al. ’17]

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“HOW TO IMPLEMENT IT?” THE COMBINED ALGORITHM

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Estimator choice

Point-Point Point-Beam Beam-Beam Beam-Point

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 “Short” photon beams  “Long” query beams

“Long” vs. “short” beams

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Family of estimators

 + Bidirectional path tracing

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UPBP – Algorithm overview

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MC methods for volumetric light transport – Combining estimators

surface Light tracing

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UPBP – Algorithm overview

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surface Point-Beam Beam-Beam

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UPBP – Algorithm overview

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surface BPT

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UPBP – Algorithm overview

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MC methods for volumetric light transport – Combining estimators

surface Point-Point

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UPBP – Algorithm overview

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surface

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RESULTS

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Full transport

rare, fwd-scattering fog back-scattering back-scattering high albedo

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Medium transport only

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Previous work comparison, 1 hr

Point-Point 3D (≈vol. ph. map.) Point-Beam 2D (=BRE) Beam-Beam 1D (=photon beams) Bidirectional PT

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Previous work comparison, 1 hr

Point-Point 3D Point-Beam 2D Beam-Beam 1D Bidirectional PT

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Point-Point 3D

Weighted contributions

Point-Beam 2D Beam-Beam 1D Bidirectional PT

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UPBP, 1 hr

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UPBP Beam-Beam 1D (photon beams) Beam-Point 2D (BRE)

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Limitations & future work

 Efficiency-based combination  Overhead

 Number of samples from different estimators

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Take-home message

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dense media rare media beams:

 

points:

 

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Source code http://www.smallupbp.com/

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Acknowledgment

 Funding: Czech Science Foundation (16-18964S)

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MC methods for volumetric light transport – Combining estimators