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![Page 1: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/1.jpg)
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
![Page 2: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/2.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 3: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/3.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 4: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/4.jpg)
Realistic image synthesisRealistic image synthesis• Goal: Compute images that appear
to an observer as real photographs
Which one is real?
![Page 5: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/5.jpg)
Realistic image synthesisRealistic image synthesis• Applications
– Architecture
– Movie industry
– Lighting design
– Computer games
– Archeology
– Product design
– …
![Page 6: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/6.jpg)
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
![Page 7: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/7.jpg)
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, size, … (e.g., CAD)
![Page 8: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/8.jpg)
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Diffuse paint, glass, metal, …
BSDF
![Page 9: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/9.jpg)
Materials: BSDFMaterials: BSDF
• Bidirectional scattering distribution function (reflection & transmission)
x
Fraction of incoming radiance L(x ) that is scattered into the direction θ
),( sf
![Page 10: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/10.jpg)
BSDF ComponentsBSDF Components
Diffuse (D) Glossy (G) Specular (S)
Diffuse, glossy and specular: (D|G|S) = X
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Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, brightness, spotlight, …
![Page 12: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/12.jpg)
Scene descriptionScene description
• Geometry• Materials• Light sources• Camera / Eye
Position, viewing angle, …
![Page 13: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/13.jpg)
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
• Geometry
• Materials
• Light sources
• Camera/Eye
![Page 14: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/14.jpg)
Compute illuminationCompute illumination• For every pixel: how much light passes through?
Account for all possible paths from light to eye!
Global illumination
Light TransportSimulation
![Page 15: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/15.jpg)
Global illuminationGlobal illumination
• Mathematical basis for light transport
Outgoing radiance L in x in direction θ ?
x
L ??)( xL
Rendering equation
Light TransportSimulation
![Page 16: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/16.jpg)
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
![Page 17: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/17.jpg)
Realistic image synthesisRealistic image synthesis
Scene description
Light TransportSimulation
Compute illumination
Image
• Geometry
• Materials
• Light sources
• Camera/Eye
• Global illumination
• Rendering equation
![Page 18: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/18.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 19: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/19.jpg)
Example sceneExample scene
Specular refraction
Caustics
Indirect caustics
Indirect illumination
Many different illumination features:
We want a full global illumination solution!
![Page 20: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/20.jpg)
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
![Page 21: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/21.jpg)
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
![Page 22: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/22.jpg)
Stochastic ray tracingStochastic ray tracing
• Trace paths starting from the eye
9 paths/pixel
L
E
Monte Carlo integration
![Page 23: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/23.jpg)
Particle tracingParticle tracing
• Trace paths starting from the light
9 paths/pixel
L
E
Pattanaik ’92, Dutré ’93
![Page 24: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/24.jpg)
Bidirectional path tracingBidirectional path tracing
• Trace paths starting from the light AND the eye
L
E
Lafortune ’93, Veach ’94
![Page 25: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/25.jpg)
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)
![Page 26: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/26.jpg)
Radiosity methodsRadiosity methods
• Object space method• Diffuse surfaces only• View independent
Galerkin radiosity
![Page 27: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/27.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 28: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/28.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 29: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/29.jpg)
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
![Page 30: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/30.jpg)
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
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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
![Page 32: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/32.jpg)
• 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
![Page 33: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/33.jpg)
Results (unweighted)Results (unweighted)
Bidirectional path tracing Radiosity + stoch. ray tracing
LD(G|S)X*E + LDE LD(G|S)X*E + LDE
![Page 34: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/34.jpg)
Results (weighted)Results (weighted)
+
Bidirectional path tracing Radiosity + stoch. ray tracing
LD(G|S)X*E + LDE
![Page 35: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/35.jpg)
Final resultFinal result
BPT only
Radiosity + Stoch. RT
Weighted combination
Radiosity + Stoch. RT and
Bidirectional path tracing
![Page 36: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/36.jpg)
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
![Page 37: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/37.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 38: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/38.jpg)
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
![Page 39: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/39.jpg)
Path footprintPath footprint
• Path = function of random variables– direction sampling, light source sampling, …
),( 21 uux
),,,( 4321 uuuuy
![Page 40: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/40.jpg)
Path footprintPath footprint
• Variables change path perturbation
),( 2211 uuuux
),( 11 uuy
![Page 41: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/41.jpg)
Path footprintPath footprint
• Set of path perturbations footprint
x
y
![Page 42: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/42.jpg)
Path differentialsPath differentials
• Partial derivatives– approximate perturbations– combine into footprint (first order Taylor
approx.)– footprint estimate from a single path!
iu
x
iu
y
![Page 43: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/43.jpg)
ApplicationsApplications
• Path differentials widely applicable– Any Monte Carlo path sampling
algorithm
•Texture filtering•Hierarchical particle tracing radiosity•Importance maps
![Page 44: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/44.jpg)
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
![Page 45: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/45.jpg)
Application: hierarchical Application: hierarchical radiosityradiosity
Fixed size (large) Fixed size (small)
Path differentials
![Page 46: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/46.jpg)
Application: hierarchical Application: hierarchical radiosityradiosity
Fixed size (large) Fixed size (small)
Path differentials
![Page 47: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/47.jpg)
Conclusion: Path Conclusion: Path differentialsdifferentials
• New, robust technique to compute path footprint
• Handles general BSDFs, complex geometry
• Many applications in global illumination
![Page 48: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/48.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 49: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/49.jpg)
Photon mappingPhoton mapping
• Popular 2-pass global illumination algorithm
Jensen ’96, …
1. Particle tracing
• trace light paths
![Page 50: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/50.jpg)
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, …
![Page 51: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/51.jpg)
Photon mappingPhoton mapping
• Density of photons radiance estimate
Photon hits Radiance estimate
![Page 52: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/52.jpg)
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
![Page 53: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/53.jpg)
Photon Photon mappingmapping
examples examples
![Page 54: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/54.jpg)
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
![Page 55: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/55.jpg)
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
![Page 56: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/56.jpg)
Density controlDensity control• Target density? Importance maps
Path differentials can be used!
Trace ‘importons’ from eye
importance map
Overview Viewpoint
Target densityError analysis
![Page 57: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/57.jpg)
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
![Page 58: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/58.jpg)
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
![Page 59: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/59.jpg)
Conclusion: Density controlConclusion: Density control
• Fewer photons: memory efficient
• Global & Caustic map
• Important step towards error control
![Page 60: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/60.jpg)
OverviewOverview
• Introduction– Realistic image synthesis– Global illumination
• Algorithms for global illumination• Contributions
– Weighted multi-pass methods– Path differentials– Density control for photon maps
• Conclusion
![Page 61: On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002.](https://reader035.fdocuments.net/reader035/viewer/2022062500/5697bfc01a28abf838ca3f00/html5/thumbnails/61.jpg)
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)