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

2. Overview Light Transport for Participating Media
Path Integral Formulation
Sampling
Rendering with Metropolis Light Transport
Results
Conclusions

3. Related Work FE Methods MC Methods Light Tracing ‘93 Zonal Methods ‘87
Rushmeier, Torrance
Light Tracing ‘93
Pattanaik, Mudur
Hierarchical Radiosity ‘93
Bhate
Bidirectional Path Tracing ‘96
Lafortune, Willems
Spherical Harmonics ‘84
Kajiya, von Herzen
Photon Map ‘98
Jensen, Christensen
Discrete Ordinates ‘94
Languenou, Bouatouch, Chelle
Metropolis Light Transport ‘97
Veach, Guibas

4. Light Transport Global Balance Equation In-scattering Streaming
Emission
Absorption
Out-scattering

5. Path Integral Formulation
Measurement Equation 
Path Integral

6. Path Characteristic
sensor
medium
object
light source 1 1 1 

7. Path Space 
Path Space Measure 

8. Measurement Contribution Function
Path Integral

9. Sampling Line Integral Computation: Ray Marching Equidistant Sampling
 efficient
 aliasing
Stratified Sampling
 anti-aliasing
 inefficient
Random Offset Sampling

10. 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

11. Metropolis Sampling Propose a mutation of current path
Compute acceptance probability
Choose as new sample if
 Samples are correlated
 we can exploit coherence

12. Mutation Strategies Bidirectional Mutations Perturbations
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

13. Propagation Perturbation
medium
image plane
light source
eye

14. Results

15. Results

16. Results

17. 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