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Portal-MaskedEnvironment Map Sampling
Benedikt Bitterli 1,2 Jan Novák 2 Wojciech Jarosz 2
1 Walt Disney Animation Studios 2 Disney Research Zurich
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Motivation
2
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Motivation
3
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Environment Map Sampling
4
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Environment Map Sampling
shading
point
5
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Environment Map Sampling
8
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Environment Map Sampling
[Ostromoukhov et al.]
[Kollig and Keller]
9
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Environment Map Sampling
occluded
11
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Problem Statement
12
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Visibility Caching
15
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Visibility Caching
[Vorba et al.]
[Georgiev et al.]
[Jensen ‘95]
16
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Portal Sampling
portal
18
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Portal Sampling
20
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Portal Sampling
[Arvo ‘95]
[Ureña et al.]
21
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Portal Sampling
23
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Ours
24
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Environment Map Sampling
25
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Environment Map Sampling
marginal distribution
conditional distributions
26
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Visible Region
27
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Visible Region
28
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Visible Region
29
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
30
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
31
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
32
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
33
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
Visible regions not rectangular in these mappings
34
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Environment Map Parameterizations
Latitude/Longitude Light probe Cube map
Visible regions not rectangular in these mappings
Let’s create one in which they are!
Rectified Coordinates
35
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Rectified Coordinates
36
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Rectified Coordinates
37
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Rectified Coordinates
38
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Rectified Coordinates
39
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Rectified Coordinates
40
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Rectified Coordinates
41
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Rectified Coordinates
Parametrization is aligned with the portal
42
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Rectified Coordinates
Parametrization is aligned with the portal
43
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Rectified Coordinates
Need separate environment map per portal44
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Rectified Coordinates
46
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Rectified Coordinates
47
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Rectified Coordinates
48
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Rectified Coordinates
49
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Rectified Coordinates
50
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Rectified Coordinates
51
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Rectified Coordinates
52
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Rectified Coordinates
53
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Rectified Coordinates
54
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Rectified Coordinates
55
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Rectified Coordinates
56
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Rectified Coordinates
57
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Rectified Coordinates
58
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
59
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Portal-Masked Environment Map Sampling
Challenges:
1) Visible regions have complex shapes
Marginal/conditional decomposition difficult
2) Visible regions different for each shading point
Marginal/conditional cannot be precomputed
60
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Sampling the Visible Region
1) Construct marginal/conditional distribution
2) Invert marginal/conditional distribution
61
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Marginal Distribution
62
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Marginal Distribution
63
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Marginal Distribution
64
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Marginal Distribution
Precompute summed-area table instead [Crow ‘84]
65
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Sampling the Visible Region
1) Construct marginal/conditional distributions
2) Invert marginal/conditional distributions
66
Precompute summed-area table instead [Crow ‘84]
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Inverting the Marginal Distribution
67
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Inverting the Marginal Distribution
68
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Inverting the Marginal Distribution
69
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Inverting the Marginal Distribution
70
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Inverting the Marginal Distribution
71
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Inverting the Marginal Distribution
72
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Sampling the Visible Region
1) Construct marginal/conditional distributions
2) Invert marginal/conditional distributions
73
Precompute summed-area table instead [Crow ‘84]
Use bisection algorithm for logarithmic complexity
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Results
74
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Results
Comparison of:
a) Environment map sampling
b) Portal solid angle sampling [Ureña et al. 2013]
c) Multiple importance sampling of a) and b) [Veach 1998]
d) Ours
at equal sample count (8spp)
All methods combined with 1 BRDF sample using MIS
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77
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78
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79
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80
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Reference
RMSE 81
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Reference
RMSE
Env. Map
0.23
8 spp
82
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Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
8 spp
83
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Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
MIS
0.26
8 spp
84
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Reference
RMSE
Env. Map
0.23
Portal S.Angle
3.31
MIS
0.26
8 spp
Ours
0.16 85
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Reference
RMSE 90
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Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
8 spp
92
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Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
MIS
0.60
8 spp
93
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Reference
RMSE
Env. Map
0.59
Portal S.Angle
0.74
MIS
0.60
Ours
0.34
8 spp
94
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More Results
Please see supplementary material
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By the numbers
Equal time:
• 33% less shadow rays than Env. Map sampling
Equal quality:
• 2x – 8x speedup w.r.t. Env. Map sampling
• 2x – 5x speedup w.r.t. Env Map/Portal MIS
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Area lights with directional profile
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Area lights with directional profile
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Uniform Solid Angle Sampling Ours
10x speedup
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Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
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Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
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Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
102
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Conclusion
Take away from this talk:
• Can importance sample visibility x Env. Map
• Need single (precomputed) SAT per portal
• Easy to implement!
103
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Limitations
104
• Needs a portal to work
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Limitations
105
• Needs a portal to work
• Only considers visibility through a rectangle
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Limitations
106
• Needs a portal to work
• Only considers visibility through a rectangle
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Future Work
Incorporate BRDF:
Combine with product sampling techniques
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[Burke et al.] [Clarberg et al.] [Cline et al.]
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Thanks!
Acknowledgements: • Environment maps: Bernhard Vogl, http://openfootage.net
• Scenes: Jay Hardy, Wayne
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Bonus Slides
109
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Sampling multiple portals
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Sampling multiple portals
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Sampling multiple portals
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Sampling multiple portals
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Scene Sample Allocation