EGWR 2000

Metropolis Light Transport for Participating Media

Mark Pauly Thomas KolligAlexander Keller

ETH Zürich University of Kaiserslautern

EGWR 2000

Overview

Light Transport for Participating MediaPath Integral FormulationSamplingRendering with Metropolis Light TransportResultsConclusions

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

EGWR 2000

Light Transport

Global Balance Equation

),()(),()(

),(),,()(),(),(2

0,

xLxxLx

dxLxfxxLxL

sa

S

psVe

Emission In-scattering

Absorption Out-scattering

Streaming

EGWR 2000

Path Integral Formulation

)(),(),(2

)( xdVdxLxWISV

jej

Measurement Equation

)()( xdxfI jj

Path Integral

EGWR 2000

Path Characteristic )(xl

sensor

medium

object

light source

3210 xxxxx

0x

1x2x

3x

0

1

1

1

111011)( bxl

EGWR 2000

Path Space

lxlxxx klk )(: 0

1

12

0

1

:k l

lk

k

Path Space Measure

0: Rlk

lk 0: R

EGWR 2000

Measurement Contribution Function

e L

G

sfpf

)( jeW

G

G

Path Integral

)()( xdxfI jj

)(ˆˆ jeej WGffGLf

EGWR 2000

Sampling

Random Offset Sampling

Line Integral Computation: Ray Marching

Equidistant Sampling

efficient aliasing

Stratified Sampling

anti-aliasing inefficient

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

,,, 210 xxx

Obtain desired image by distributing paths according to image contribution

EGWR 2000

Metropolis SamplingPropose a mutation of current pathCompute acceptance probability

Choose as new sample if

Samples are correlated

we can exploit coherence

y x

)()(

)()(,1min),(

yxTxf

xyTyfxy

y

EGWR 2000

Mutation StrategiesBidirectional 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

EGWR 2000

Propagation Perturbation

image plane

medium

light sourceeye

minDmaxD

D

1

EGWR 2000

Results

EGWR 2000

Results

EGWR 2000

Results

EGWR 2000

ConclusionsParticipating media are fully integrated

inhomogeneous media multiple, anisotropic scattering volume caustics color bleeding

General geometry and reflection modelsRobust

Complex Scenes Difficult Lighting Situations