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
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