1. EGWR 2000 Metropolis Light Transport for Participating Media Mark Pauly Thomas KolligAlexander Keller ETH ZürichUniversity of Kaiserslautern

2. EGWR 2000 Overview Light Transport for Participating Media Path Integral Formulation Sampling Rendering with Metropolis Light Transport Results Conclusions

3. EGWR 2000 Related Work MC Methods Bidirectional Path Tracing ‘96 Lafortune, Willems Light Tracing ‘93 Pattanaik, Mudur Photon Map ‘98 Jensen, Christensen Metropolis Light Transport ‘97 Veach, Guibas FE Methods Hierarchical Radiosity ‘93 Bhate Zonal Methods ‘87 Rushmeier, Torrance Spherical Harmonics ‘84 Kajiya, von Herzen Discrete Ordinates ‘94 Languenou, Bouatouch, Chelle

4. EGWR 2000 Light Transport Global Balance Equation Emission In-scattering Absorption Out-scattering Streaming

5. EGWR 2000 Path Integral Formulation Measurement Equation  Path Integral

6. EGWR 2000 Path Characteristic sensor medium object light source 0 1 1 1 

7. EGWR 2000 Path Space  Path Space Measure 

8. EGWR 2000 Measurement Contribution Function Path Integral 

9. EGWR 2000 Sampling Random Offset Sampling Line Integral Computation: Ray Marching Equidistant Sampling  efficient  aliasing Stratified Sampling  anti-aliasing  inefficient

10. EGWR 2000 Metropolis Light Transport Generate a random walk through path space  Metropolis sampling For each path deposit a constant amount of energy at the corresponding pixel Obtain desired image by distributing paths according to image contribution

11. EGWR 2000 Metropolis Sampling Propose a mutation of current path Compute acceptance probability Choose as new sample if  Samples are correlated  we can exploit coherence

12. EGWR 2000 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

13. EGWR 2000 Propagation Perturbation image plane medium light source eye

14. EGWR 2000 Results

15. EGWR 2000 Results

16. EGWR 2000 Results

17. EGWR 2000 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