Metropolis Light Transport for Participating Media

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Metropolis Light Transport for Participating
Media
Mark Pauly Thomas Kollig Alexander Keller
ETH Zürich University of Kaiserslautern
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Overview

• Light Transport for Participating Media
• Path Integral Formulation
• Sampling
• Rendering with Metropolis Light Transport
• Results
• Conclusions

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Related Work
MC Methods
FE Methods

• Light Tracing 93
• Pattanaik, Mudur

• Zonal Methods 87
• Rushmeier, Torrance

• Bidirectional Path Tracing 96
• Lafortune, Willems

• Hierarchical Radiosity 93
• Bhate

• Photon Map 98
• Jensen, Christensen

• Spherical Harmonics 84
• Kajiya, von Herzen

• Metropolis Light Transport 97
• Veach, Guibas

• Discrete Ordinates 94
• Languenou, Bouatouch, Chelle

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Light Transport

• Global Balance Equation

In-scattering
Emission
Streaming
Absorption
Out-scattering
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Path Integral Formulation

• Measurement Equation

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• Path Characteristic

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• Path Space

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• Measurement Contribution Function

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Sampling

• Line Integral Computation Ray Marching

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Metropolis Light Transport

• Generate a random walk
  through path space

• For each path deposit a constant amount of energy
  at the corresponding pixel

• Obtain desired image by distributing paths
  according to image contribution

? Metropolis sampling
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• Metropolis Sampling
• Propose a mutation of current path
• Compute acceptance probability
• Choose as new sample if
• ? Samples are correlated
• ? we can exploit coherence

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• Mutation Strategies
• Bidirectional Mutations
• large changes to the current path
• ensures ergodicity
• Perturbations
• high acceptance probability
• changes to image location
• low cost

Scattering Perturbations Propagation
Perturbations
Sensor Perturbations Caustic Perturbations
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• Propagation Perturbation

medium
image plane
light source
eye
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Results
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Results
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Results
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Conclusions

• Participating media are fully integrated
• inhomogeneous media
• multiple, anisotropic scattering
• volume caustics
• color bleeding
• General geometry and reflection models
• Robust
• Complex Scenes
• Difficult Lighting Situations