Date post: | 21-Jan-2016 |
Category: |
Documents |
Upload: | jodie-potter |
View: | 216 times |
Download: | 0 times |
On robust Monte Carlo On robust Monte Carlo algorithms for multi-pass global algorithms for multi-pass global
illuminationillumination
Frank Suykens – De Laet
17 September 2002
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
Realistic image synthesisRealistic image synthesis• Goal: Compute images that appear
to an observer as real photographs
Which one is real?
Realistic image synthesisRealistic image synthesis• Applications
– Architecture
– Movie industry
– Lighting design
– Computer games
– Archeology
– Product design
– …
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, size, … (e.g., CAD)
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Diffuse paint, glass, metal, …
BSDF
Materials: BSDFMaterials: BSDF
• Bidirectional scattering distribution function (reflection & transmission)
x
Fraction of incoming radiance L(x ) that is scattered into the direction θ
),( sf
BSDF ComponentsBSDF Components
Diffuse (D) Glossy (G) Specular (S)
Diffuse, glossy and specular: (D|G|S) = X
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, brightness, spotlight, …
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, viewing angle, …
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
• Geometry
• Materials
• Light sources
• Camera/Eye
Compute illuminationCompute illumination• For every pixel: how much light passes through?
Account for all possible paths from light to eye!
Global illumination
Light TransportSimulation
Global illuminationGlobal illumination
• Mathematical basis for light transport
Outgoing radiance L in x in direction θ ?
x
L ??)( xL
Rendering equation
Light TransportSimulation
Rendering equationRendering equation
dfxLxLxL se cos),()()()(
= +Radiance
x
L
Integration over all directions
BSDFUnknown incomingradiance
x
Le
Self emitted radiance
Lr
Reflected (& refracted) radiance
x
Light TransportSimulation
Recursive
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
• Geometry
• Materials
• Light sources
• Camera/Eye
• Global illumination
• Rendering equation
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
Example sceneExample scene
Specular refraction
Caustics
Indirect caustics
Indirect illumination
Many different illumination features:
We want a full global illumination solution!
Algorithms for global Algorithms for global illuminationillumination
• Computation: Numerical integration– Monte Carlo integration
• Algorithms– Image space algorithms
• Stochastic ray tracing• Particle tracing• Bidirectional path tracing
– Object space algorithms• Radiosity
Monte Carlo integrationMonte Carlo integration
• Estimate integrals by random sampling– draw a number of random samples– average their contribution
estimate of integral
• Statistical errors Noise in images• Convergence: More samples, less
noise
Stochastic ray tracingStochastic ray tracing
• Trace paths starting from the eye
9 paths/pixel
L
E
Monte Carlo integration
Particle tracingParticle tracing
• Trace paths starting from the light
9 paths/pixel
L
E
Pattanaik ’92, Dutré ’93
Bidirectional path tracingBidirectional path tracing
• Trace paths starting from the light AND the eye
L
E
Lafortune ’93, Veach ’94
ComparisonComparison
Same computation time (± 5 min.)
Stochastic ray tracing
(9 samples per pixel)
Particle tracing
(9 samples per pixel)
Bidirectional path tracing
(4 samples per pixel)
Radiosity methodsRadiosity methods
• Object space method• Diffuse surfaces only• View independent
Galerkin radiosity
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
Multi-pass methodsMulti-pass methods
• Combine different algorithms
• Separate light transport– Based on BSDF components– Different algorithms different illumination
– Preserve strengths of individual algorithms
• Regular expressions (e.g., LD* , LX*E )– derive path evaluation from regular expression
Radiosity & stochastic ray Radiosity & stochastic ray tracing tracing
LD*(G|S)X*E LX*E
E
D|G|S
LD*
G|S
Full global illuminationbut
drawbacks of stoch. ray tracing
Combine with bidirectional path tracing
1. Radiosity
2. Stochastic ray tracing
Use radiosity solution at end points
Multi-pass configurationMulti-pass configuration
+ +
BPT Use weighting Rad + SR
L(G|S)X*E
LD(G|S)X*E+ LDE
???
Self-emitted light
Direct diffuse
Indirect diffuse
LDD+(G|S)X*E+ LDD+E
• Weighting instead of separation– allow overlapping transport between
different algorithms– weight individual paths
automatic ‘separation’
• Technique– General Monte Carlo variance reduction
technique– Constraints, weighting heuristics
Weighted multi-pass Weighted multi-pass methodsmethods
Results (unweighted)Results (unweighted)
Bidirectional path tracing Radiosity + stoch. ray tracing
LD(G|S)X*E + LDE LD(G|S)X*E + LDE
Results (weighted)Results (weighted)
+
Bidirectional path tracing Radiosity + stoch. ray tracing
LD(G|S)X*E + LDE
Final resultFinal result
BPT only
Radiosity + Stoch. RT
Weighted combination
Radiosity + Stoch. RT and
Bidirectional path tracing
Conclusion: WMPConclusion: WMP
• Multi-pass methods– separation: path evaluation from regular
expression– weighting: each path is weighted
individually automatic ‘separation’
• General technique• Robust combination of bidirectional
path tracing and radiosity
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
Path differentialsPath differentials
• Idea– Many algorithms trace paths– A path is infinitely thin: no neighborhood
information– Knowledge about ‘region of influence’ or
‘footprint ’ would be useful in many applications:• bias-noise trade-off
• Footprint definition• Path differentials
Path footprintPath footprint
• Path = function of random variables– direction sampling, light source sampling, …
),( 21 uux
),,,( 4321 uuuuy
Path footprintPath footprint
• Variables change path perturbation
),( 2211 uuuux
),( 11 uuy
Path footprintPath footprint
• Set of path perturbations footprint
x
y
Path differentialsPath differentials
• Partial derivatives– approximate perturbations– combine into footprint (first order Taylor
approx.)– footprint estimate from a single path!
iu
x
iu
y
ApplicationsApplications
• Path differentials widely applicable– Any Monte Carlo path sampling
algorithm
•Texture filtering•Hierarchical particle tracing radiosity•Importance maps
Application: hierarchical Application: hierarchical radiosityradiosity
• Particle tracing radiosity
L
• Trace light paths
• Each hit contributes to the illumination of the element
In which level should the particle contribute? Path differentials: size
of footprint size of element
Small elements noise
Large elements blurfixed
hierarchical
Application: hierarchical Application: hierarchical radiosityradiosity
Fixed size (large) Fixed size (small)
Path differentials
Application: hierarchical Application: hierarchical radiosityradiosity
Fixed size (large) Fixed size (small)
Path differentials
Conclusion: Path Conclusion: Path differentialsdifferentials
• New, robust technique to compute path footprint
• Handles general BSDFs, complex geometry
• Many applications in global illumination
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
Photon mappingPhoton mapping
• Popular 2-pass global illumination algorithm
Jensen ’96, …
1. Particle tracing
• trace light paths
1. Particle tracing
• trace light paths
• record all hitpoints
Photon mappingPhoton mapping
• Popular 2-pass global illumination algorithm
Set of photons: ‘Photon map’ Jensen ’96, …
Photon mappingPhoton mapping
• Density of photons radiance estimate
Photon hits Radiance estimate
Photon mapping: second Photon mapping: second passpass• Global map: indirect visualization• Caustic map: direct visualization
Global map
Caustic map
Final image
2. Stochastic ray tracing
indirect
direct
Photon Photon mappingmapping
examples examples
Photon mappingPhoton mapping• Advantages
– efficient, full global illumination– robust (photon map independent of
geometrical complexity)
• Difficulties– many photons a lot of memory!– how many photons needed?
Density control
Density controlDensity control
• Only store photons when more photons are needed– choose target density– new photon hit: target density reached?
No store photonYes redistribute photon
power among neighbors
Density controlDensity control• Target density? Importance maps
Path differentials can be used!
Trace ‘importons’ from eye
importance map
Overview Viewpoint
Target densityError analysis
Results: photon map Results: photon map constructionconstruction
Actual density of photon map
Radiance estimate
No density control, 400.000
photons
Density control, 57.000 photons
Results: final imageResults: final image
No density control, 400.000 photons
With density control, 57.000 photons
No visible difference with 1/7th of the photons
Conclusion: Density controlConclusion: Density control
• Fewer photons: memory efficient
• Global & Caustic map
• Important step towards error control
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
ConclusionConclusion• General techniques to construct better,
more robust global illumination methods– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Wide applicability (general scenes, other algorithms)
• Future work:– improved techniques– more applications
• RenderPark: our freely available global illumination software (www.renderpark.be)