COMBINING VOLUMETRIC ESTIMATORS Jaroslav Kivnek Charles University Render

COMBINING VOLUMETRIC ESTIMATORS Jaroslav Křivánek Charles University – Render Legion | Chaos Group

UNIFYING POINTS, BEAMS, AND PATHS IN VOLUMETRIC LIGHT TRANSPORT SIMULATION Jaroslav Křivánek Iliyan Georgiev Toshiya Hachisuka Petr Vévoda Charles University in Prague Light Transportation Ltd. Aarhus University Charles University in Prague Martin Šik Derek Nowrouzezahrai Wojciech Jarosz Charles University in Prague Univesity of Montreal Disney Research Zurich

Goal: Robust rendering of media n Robust to: media properties, lighting high scattering dense low scattering rare diffuse lighting focused lighting MC methods for volumetric light transport – Combining estimators 3

Existing volumetric rendering algorithms n MC path integration q q n Photon density estimation q q q n Path tracing [Kajiya ‘ 86, Rushmeier and Torrance ‘ 88] Bidirectional path tracing [Lafortune and Willems ‘ 96] 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 MC methods for volumetric light transport – Combining estimators 4

Bidirectional path tracing 1 hour MC methods for volumetric light transport – Combining estimators 5

Volumetric photon mapping 1 hour MC methods for volumetric light transport – Combining estimators 6

Beam radiance estimate 1 hour MC methods for volumetric light transport – Combining estimators 7

Photon beams 1 hour 8

UPBP algorithm 1 hour MC methods for volumetric light transport – Combining estimators 9

Approach: Combine estimators n Multiple Importance Sampling [Veach and Guibas ‘ 95] n Previous work q q q n 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 q “Unified points beams and paths” (UPBP) MC methods for volumetric light transport – Combining estimators 10

Contributions n “Does it make sense to combine the estimators? ” q n “How can we combine the estimators? ” q n Variance analysis of estimators Extended multiple importance sampling “How do we make the method practical? ” q A combined volume rendering algorithm MC methods for volumetric light transport – Combining estimators 11

VOLUMETRIC PHOTON DENSITY ESTIMATORS

RADIANCE REP. : photon points photon beams Point - Point Beam - Point - Beam - Point QUERY point beam [Jarosz et al. ’ 11 a]

“Long” vs. “short” beams n [Jarosz et al. ’ 11 b] Photon beams surface “Short” beams n “Long” beams Query beams q The same story MC methods for volumetric light transport – Combining estimators 14

Bottom line: Many estimators Points “Short” Beams “Long” Beams Points × “Short” Beams “Long” Beams MC methods for volumetric light transport – Combining estimators 15

Why combine points and beams? n Won’t photon beams always outperform photon points? 100 k photon points reference 5 k photon beams from [Jarosz et al. ’ 11 a] MC methods for volumetric light transport – Combining estimators 16

VARIANCE ANALYSIS

Variance analysis – Canonical setup MC methods for volumetric light transport – Combining estimators 18

Variance analysis – Expected value transmittance MC methods for volumetric light transport – Combining estimators 19

Variance analysis – Estimators “Long” beam “Short” beam transmittance Point MC methods for volumetric light transport – Combining estimators 20

Variance analysis results normalized std. dev. (NSD) rare media dense media Short beam – Bl Point – Bl 0 1 4 kernel width [mean free path] MC methods for volumetric light transport – Combining estimators 21

Variance analysis results beams: points: rare media dense media MC methods for volumetric light transport – Combining estimators 22

“HOW TO COMBINE? ” EXTENDED MIS

Our MIS extension n Extended MIS – accommodate all the different estimators n Compatible with RR interpretation of density estimation kernels (like VCM [Georgiev et al. ‘ 12]) n Alternative view: extended path space [Hachisuka et al. ’ 12, Hachisuka et al. ’ 17] MC methods for volumetric light transport – Combining estimators 24

“HOW TO IMPLEMENT IT? ” THE COMBINED ALGORITHM

Estimator choice Point-Point Beam-Point-Beam-Beam MC methods for volumetric light transport – Combining estimators 26

“Long” vs. “short” beams n n “Short” photon beams “Long” query beams MC methods for volumetric light transport – Combining estimators 27

Family of estimators n + Bidirectional path tracing MC methods for volumetric light transport – Combining estimators 28

UPBP – Algorithm overview Light tracing surface MC methods for volumetric light transport – Combining estimators 29

UPBP – Algorithm overview Beam-Beam Point-Beam surface MC methods for volumetric light transport – Combining estimators 30

UPBP – Algorithm overview BPT surface MC methods for volumetric light transport – Combining estimators 31

UPBP – Algorithm overview Point-Point surface MC methods for volumetric light transport – Combining estimators 32

UPBP – Algorithm overview surface MC methods for volumetric light transport – Combining estimators 33

RESULTS

Full transport rare, fwd-scattering fog back-scattering high albedo back-scattering 35

Medium transport only 36

Previous work comparison, 1 hr Point-Point 3 D (≈vol. ph. map. ) Point-Beam 2 D (=BRE) Beam-Beam 1 D (=photon beams) Bidirectional PT 37

Previous work comparison, 1 hr Point-Point 3 D Point-Beam 2 D Beam-Beam 1 D Bidirectional PT 38

Weighted contributions Point-Point 3 D Point-Beam 2 D Beam-Beam 1 D Bidirectional PT 39

UPBP, 1 hr 40

MC methods for volumetric light transport – Combining estimators 41

Beam-Point 2 D (BRE) UPBP Beam-Beam 1 D (photon beams) MC methods for volumetric light transport – Combining estimators 42

Limitations & future work n Efficiency-based combination n Overhead q Number of samples from different estimators MC methods for volumetric light transport – Combining estimators 43