COMBINING VOLUMETRIC ESTIMATORS
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1 COMBINING VOLUMETRIC ESTIMATORS Jaroslav Křivánek Charles University Render Legion Chaos Group
2 UNIFYING POINTS, BEAMS, AND PATHS IN VOLUMETRIC LIGHT TRANSPORT SIMULATION Jaroslav Křivánek Charles University in Prague Iliyan Georgiev Light Transportation Ltd. Toshiya Hachisuka Aarhus University Petr Vévoda Charles University in Prague Martin Šik Charles University in Prague Derek Nowrouzezahrai Univesity of Montreal Wojciech Jarosz Disney Research Zurich
3 Goal: Robust rendering of media Robust to: media properties, lighting high scattering low scattering dense rare diffuse lighting focused lighting MC methods for volumetric light transport Combining estimators 3
4 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 MC methods for volumetric light transport Combining estimators 4
5 Bidirectional path tracing 1 hour MC methods for volumetric light transport Combining estimators 5
6 Volumetric photon mapping 1 hour MC methods for volumetric light transport Combining estimators 6
7 Beam radiance estimate 1 hour MC methods for volumetric light transport Combining estimators 7
8 Photon beams 1 hour 8
9 UPBP algorithm 1 hour MC methods for volumetric light transport Combining estimators 9
10 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) MC methods for volumetric light transport Combining estimators 10
11 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 MC methods for volumetric light transport Combining estimators 11
12 VOLUMETRIC PHOTON DENSITY ESTIMATORS
13 RADIANCE REP.: photon points photon beams QUERY point Point - Point Beam - Point beam Point - Beam Beam - Point [Jarosz et al. 11a]
14 Long vs. short beams [Jarosz et al. 11b] Photon beams Short beams Long beams surface Query beams The same story MC methods for volumetric light transport Combining estimators 14
15 Bottom line: Many estimators Points Points Short Beams Short Beams Long Beams Long Beams MC methods for volumetric light transport Combining estimators 15
16 Why combine points and beams? Won t photon beams always outperform photon points? 100k photon points reference 5k photon beams from [Jarosz et al. 11a] MC methods for volumetric light transport Combining estimators 16
17 VARIANCE ANALYSIS
18 Variance analysis Canonical setup MC methods for volumetric light transport Combining estimators 18
19 transmittance Variance analysis Expected value transmittance MC methods for volumetric light transport Combining estimators 19
20 transmittance Variance analysis Estimators Long beam Short beam Point MC methods for volumetric light transport Combining estimators 20
21 normalized std. dev. (NSD) Variance analysis results rare media dense media Short beam B l kernel width [mean free path] Point B l MC methods for volumetric light transport Combining estimators 21
22 Variance analysis results rare media dense media beams: points: MC methods for volumetric light transport Combining estimators 22
23 HOW TO COMBINE? EXTENDED MIS
24 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] MC methods for volumetric light transport Combining estimators 24
25 HOW TO IMPLEMENT IT? THE COMBINED ALGORITHM
26 Estimator choice Point-Point Beam-Point Point-Beam Beam-Beam MC methods for volumetric light transport Combining estimators 26
27 Long vs. short beams Short photon beams Long query beams MC methods for volumetric light transport Combining estimators 27
28 Family of estimators + Bidirectional path tracing MC methods for volumetric light transport Combining estimators 28
29 UPBP Algorithm overview Light tracing surface MC methods for volumetric light transport Combining estimators 29
30 UPBP Algorithm overview Beam-Beam Point-Beam surface MC methods for volumetric light transport Combining estimators 30
31 UPBP Algorithm overview BPT surface MC methods for volumetric light transport Combining estimators 31
32 UPBP Algorithm overview Point-Point surface MC methods for volumetric light transport Combining estimators 32
33 UPBP Algorithm overview surface MC methods for volumetric light transport Combining estimators 33
34 RESULTS
35 Full transport rare, fwd-scattering fog back-scattering high albedo back-scattering 35
36 Medium transport only 36
37 Previous work comparison, 1 hr Point-Point 3D ( vol. ph. map.) Point-Beam 2D (=BRE) Beam-Beam 1D (=photon beams) Bidirectional PT 37
38 Previous work comparison, 1 hr Point-Point 3D Point-Beam 2D Beam-Beam 1D Bidirectional PT 38
39 Weighted contributions Point-Point 3D Point-Beam 2D Beam-Beam 1D Bidirectional PT 39
40 UPBP, 1 hr 40
41 MC methods for volumetric light transport Combining estimators 41
42 Beam-Point 2D (BRE) UPBP Beam-Beam 1D (photon beams) MC methods for volumetric light transport Combining estimators 42
43 Limitations & future work Efficiency-based combination Overhead Number of samples from different estimators MC methods for volumetric light transport Combining estimators 43
44 Take-home message rare media dense media beams: points: MC methods for volumetric light transport Combining estimators 44
45 Source code MC methods for volumetric light transport Combining estimators 45
46 Acknowledgment Funding: Czech Science Foundation ( S) MC methods for volumetric light transport Combining estimators 46
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