Bidirectional Path Sampling Techniques
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BIDIRECTIONAL PATH SAMPLING TECHNIQUES
Jaroslav KřivánekCharles University in Prague
http://cgg.mff.cuni.cz/~jaroslav/
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Bidirectional path sampling
Algorithms = different path sampling techniques
Path tracing Light tracingBidirectionalpath tracing
2Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL RENDERING
AS A PATH SAMPLING TECHNIQUE
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Instant radiosity – VPL rendering
1. Distribute VPLs2. Accumulate VPL contributions
[Keller 1997]
4Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL contribution
High values for spiky BRDFs Diverges as || x – y || → 0
x
y
)( yxG
)(xs
)(ys
5Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Clamping
no local light inter-
reflections
clampingreference
splotches(variance)
instant radiosity
6Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL rendering as a bidirectional path sampling technique
1. Distribute VPLs = sample light sub-paths
2. Camera ray = sample camera sub-path
3. VPL contribution = sub-path connection
7Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL rendering as a bidirectional path sampling technique
The usual path integral estimator
)(
)(
xp
xfI jj
s
s
eL
eWG
G
G
VPL contribution
8Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Digression
Sample direction from an existing vertex
)()()( yxGyxpyp
x
yy
x
9
)()(
)()(
yxGyxp
yxGyxI sj
w.r.
t. ar
ea
w.r.
t. pr
oj.
solid
ang
le
Course: Recent Advances in Light Transport SimulationJaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL rendering as a bidirectional path sampling technique
The usual estimator
)(
)(
xp
xfI jj
s
s
eL
eWG
G
G
VPL contribution
10
Course: Recent Advances in Light Transport SimulationJaroslav Křivánek – Bidirectional Path Sampling Techniques
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VPL rendering summary
VPL rendering corresponds to a bidirectional path sampling technique
Splotches = noise = variance Due to bad path sampling Correlation
11Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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COMBININGPATH SAMPLING
TECHNIQUES
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All possible bidirectional techniquesvertex on a light sub-path
vertex on en eye subpath
13
path tracing
light tracing
VPLs
Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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All possible bidirectional techniquesvertex on a light sub-path
vertex on en eye subpath
14
path tracing
light tracing
VPLs
no single technique importance samples all the terms
Course: Recent Advances in Light Transport SimulationJaroslav Křivánek – Bidirectional Path Sampling Techniques
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Multiple Importance Sampling (MIS)
f(x)
pa(x)pb(x)
[Veach & Guibas, 95]
15
2/)]()([
)(
xpxp
xfI
ba Combined
estimator:
xaCourse: Recent Advances in Light Transport SimulationJaroslav Křivánek – Bidirectional Path Sampling Techniques
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Multiple Importance Sampling (MIS)
High MIS weight Low MIS weight
Singularity cancelled
16Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Bidirectional path tracing
Use all of the above sampling techniques
Combine using Multiple Importance Sampling
17Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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BPT Implementation
18Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Results
BPT, 25 samples per pixel PT, 56 samples per pixel
Imag
es:
Eri
c V
each
19Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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LIMITATIONS OF LOCAL PATH SAMPLING
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Insufficient path sampling techniques
Reference solution Bidirectional path tracing21
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Insufficient path sampling techniques
Some paths sampled with zero (or very small) probability
22Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
diffuse – D
specular – S
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Alternatives to local path sampling
Global path sampling – Metropolis light transport Initial proposal still relies on local sampling
Leave path integral framework Density estimation – photon mapping
Unify path integral framework and density estimation Vertex Connection & Merging
23Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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NEARLY THERE…
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“Path integral” – A historical remark
This course [Veach and Guibas 1995], [Veach 1997] Easily derived form the rendering equation [Veach
1997]
Feynman path integral formulation of quantum mechanics [Feynman and Hibbs 65]
Homogeneous materials [Tessendorf 89, 91, 92]
Rendering [Premože et al. 03, 04]
25Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Summary
VPL rendering One bidirectional path sampling technique Not robust
Bidirectional path tracing Combines many bidirectional techniques More robust Bad at reflected caustics
26Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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Acknowledgements
Czech Science Foundation grant no. P202-13-26189S
Images Ondra “Keymaster” Karlík Eric Tabellion Marcos Fajardo
27Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques
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THANK YOU!
Time for questions…
Course: Recent Advances in Light Transport Simulation
Jaroslav Křivánek - Path Integral Formulation of Light Transport