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 tracing Bidirectionalpath tracing
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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]
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VPL contribution
High values for spiky BRDFs Diverges as || x – y || → 0
x
y)( yxG
)(xs
)(ys
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Clamping
no local light inter-
reflections
clampingreference
splotches(variance)
instant radiosity
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VPL rendering as a bidirectional path sampling technique1. Distribute VPLs
= sample light sub-paths2. Camera ray
= sample camera sub-path3. VPL contribution
= sub-path connection
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VPL rendering as a bidirectional path sampling technique The usual path integral estimator
)()(xpxf
I jj
s
s
eL
eWG
G
G
VPL contribution
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Digression
Sample direction from an existing vertex
)()()( yxGyxpyp
x
yy
x
9
)()()()(yxGyxpyxGyxI s
j
w.r.t
. are
a
w.r.t
. pro
j.
solid
angl
e
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VPL rendering as a bidirectional path sampling technique The usual estimator
)()(xpxf
I jj
s
s
eL
eWG
G
G
VPL contribution
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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
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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
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path tracing
light tracing
VPLs
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All possible bidirectional techniquesvertex on a light sub-path
vertex on en eye subpath
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path tracing
light tracing
VPLs
no single technique importance samples all the terms
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Multiple Importance Sampling (MIS)
f(x)
pa(x) pb(x)
[Veach & Guibas, 95]
2/)]()([)(xpxp
xfIba
Combined estimator:
xaJaroslav Křivánek – Light Transport Simulation with Vertex Connection and Merging
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Multiple Importance Sampling (MIS)
High MIS weight Low MIS weightSingularity cancelled
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Bidirectional path tracing
Use all of the above sampling techniques
Combine using Multiple Importance Sampling
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Naive BPT implementation
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BPT Implementation in practice
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Results
BPT, 25 samples per pixel PT, 56 samples per pixel
Imag
es: E
ric
Veac
h
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LIMITATIONS OF LOCAL PATH SAMPLING
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Insufficient path sampling techniques
Reference solution Bidirectional path tracing22
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Insufficient path sampling techniques Some paths sampled with zero (or very small)
probability
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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
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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]
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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
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Acknowledgements
Czech Science Foundation grant no. P202-13-26189S
Images Ondra “Keymaster” Karlík Eric Tabellion Marcos Fajardo
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THANK YOU!
Time for questions…
Tutorial: Path Integral Methods for Light Transport Simulation
Jaroslav Křivánek – Bidirectional Path Sampling Techniques