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

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

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

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

Path Integral Formulation Measurement Equation  Path Integral

Path Characteristic sensor medium object light source 1 1 1 

Path Space  Path Space Measure 

Measurement Contribution Function  Path Integral

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

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

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

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

Propagation Perturbation medium image plane light source eye

Results

Results

Results

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