Bidirectional Path Sampling Techniques

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Bidirectional Path Sampling Techniques. Jaroslav Křivánek Charles University in Prague http://cgg.mff.cuni.cz/~jaroslav/. Bidirectional path sampling. Bidirectional path tracing. Path tracing. Light tracing. Algorithms = different path sampling techniques.
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Bidirectional Path Sampling TechniquesJaroslav KřivánekCharles University in Praguehttp://cgg.mff.cuni.cz/~jaroslav/Bidirectional path samplingBidirectionalpath tracingPath tracingLight tracingAlgorithms = different path sampling techniquesJaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL RENDERING AS A PATH SAMPLING TECHNIQUEInstant radiosity – VPL rendering [Keller 1997]Distribute VPLsAccumulate VPL contributions Jaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL contributionHigh values for spiky BRDFsDiverges as || x – y||→ 0Jaroslav Křivánek – Bidirectional Path Sampling TechniquesClampinginstant radiosityreferenceclampingsplotches(variance)no local light inter-reflectionsJaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL rendering as a bidirectional path sampling technique
  • Distribute VPLs
  • = sample light sub-paths
  • Camera ray
  • = sample camera sub-path
  • VPL contribution
  • = sub-path connection
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL rendering as a bidirectional path sampling techniqueVPL contributionThe usual path integral estimatorJaroslav Křivánek – Bidirectional Path Sampling TechniquesDigressionw.r.t. proj.solid anglew.r.t. area
  • Sample direction from an existing vertex
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL rendering as a bidirectional path sampling techniqueVPL contributionThe usual estimatorJaroslav Křivánek – Bidirectional Path Sampling TechniquesVPL rendering summary
  • VPL rendering corresponds to a bidirectional path sampling technique
  • Splotches = noise = variance
  • Due to bad path sampling
  • Correlation
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesCombiningpath sampling TechniquesAll possible bidirectional techniquesvertex on a light sub-pathvertex on en eye subpathpath tracingVPLslight tracingJaroslav Křivánek – Bidirectional Path Sampling TechniquesAll possible bidirectional techniquesvertex on a light sub-pathvertex on en eye subpathpath tracingno single technique importance samples all the termsVPLslight tracingJaroslav Křivánek – Bidirectional Path Sampling TechniquesMultiple Importance Sampling (MIS)[Veach& Guibas, 95]Combined estimator:f(x)pa(x)pb(x)xaJaroslav Křivánek – Light Transport Simulation with Vertex Connection and MergingMultiple Importance Sampling (MIS)High MIS weightLow MIS weightSingularity cancelledJaroslav Křivánek – Bidirectional Path Sampling TechniquesBidirectional path tracingUse all of the above sampling techniquesCombine using Multiple Importance SamplingJaroslav Křivánek – Bidirectional Path Sampling TechniquesNaiveBPT implementationJaroslav Křivánek – Bidirectional Path Sampling TechniquesBPT Implementation in practiceJaroslav Křivánek – Bidirectional Path Sampling TechniquesResultsImages: EricVeachBPT, 25 samples per pixelPT, 56 samples per pixelJaroslav Křivánek – Bidirectional Path Sampling TechniquesLimitations of local path samplingInsufficient path sampling techniquesReference solutionBidirectional path tracingInsufficient path sampling techniquesspecular – Sdiffuse – DSome paths sampled with zero (or very small) probabilityJaroslav Křivánek – Bidirectional Path Sampling TechniquesAlternatives 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
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesNearly there…“Path integral” – A historical remark
  • This course [Veach and Guibas 1995], [Veach 1997]
  • Easily derived form the rendering equation [Veach 1997]
  • Feynman path integralformulationofquantummechanics[Feynman and Hibbs 65]
  • Homogeneous materials [Tessendorf 89, 91, 92]
  • Rendering [Premože etal. 03, 04]
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesSummary
  • VPL rendering
  • One bidirectional path sampling technique
  • Not robust
  • Bidirectional path tracing
  • Combines many bidirectional techniques
  • More robust
  • Bad at reflected caustics
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesAcknowledgements
  • Czech Science Foundation
  • grant no. P202-13-26189S
  • Images
  • Ondra “Keymaster” Karlík
  • Eric Tabellion
  • Marcos Fajardo
  • Jaroslav Křivánek – Bidirectional Path Sampling TechniquesThank you!Time for questions…
  • Tutorial: Path Integral Methods for Light Transport Simulation
  • Jaroslav Křivánek– Bidirectional Path Sampling Techniques
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