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Temporal Radiance Caching
P. Gautron K. Bouatouch S. Pattanaik
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Global IlluminationGlobal Illumination
P
Lo(P, ωo) ∫ Li(P, ωi)= * BRDF(ωo, ωi) *cos(θ)dωi
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GI: ComputationGI: Computation
Lo(P, ωo) ∫ Li(P, ωi)= * BRDF(ωo, ωi) *cos(θ)dωi
No analytical solution
Numerical methods
- Radiosity
- Photon mapping- Path tracing- Bidirectional path tracing
- Irradiance & Radiance caching- …
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GI: ComputationGI: Computation
Lo(P, ωo) ∫ Li(P, ωi)= * BRDF(ωo, ωi) *cos(θ)dωi
No analytical solution
Numerical methods
- Radiosity
- Photon mapping
- Path tracing
- Bidirectional path tracing
- Irradiance & Radiance caching- …
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(Ir)Radiance Caching(Ir)Radiance Caching
R
Spatial weighting function
Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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(Ir)Radiance Caching(Ir)Radiance Caching
Spatial gradients
Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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(Ir)Radiance Caching(Ir)Radiance CachingWard et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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(Ir)Radiance Caching(Ir)Radiance Caching
Record Location GI Solution
Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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(I)RC in Dynamic Scenes(I)RC in Dynamic Scenes
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(I)RC in Dynamic Scenes(I)RC in Dynamic Scenes
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(I)RC in Dynamic Scenes(I)RC in Dynamic Scenes
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(I)RC in Dynamic Scenes(I)RC in Dynamic Scenes
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ContributionsContributions
Temporal (ir)radiance interpolation scheme
Temporal weighting function
Temporal gradients
Fast estimate of future indirect lighting
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
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Irradiance Caching: ObservationsIrradiance Caching: Observations
- Indirect lighting is costly
-Indirect lighting changes slowly over a surface
Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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Irradiance Caching: PrincipleIrradiance Caching: Principle
Record Location GI Solution
Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections
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IC Records: Zone of InfluenceIC Records: Zone of Influence
Close objects = Small zone Distant objects = Large zone
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IC: Spatial Weighting FunctionIC: Spatial Weighting Function
Spatial change of indirect lighting depends on
- Local geometry
- Surrounding geometry
nk
n
PPk
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IC: Spatial Weighting FunctionIC: Spatial Weighting Function
nk
n
PPk
Upper bound of the change
change = ||P-Pk||
Rk
+ 1-n.nk
Distance Normals divergence
Mean dist. to the surrounding geometry
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IC: Spatial Weighting FunctionIC: Spatial Weighting Function
nk
n
PPk
wk(P) = 1
||P-Pk||
Rk
+ 1-n.nk
Distance Normals divergence
> 1/a
Mean dist. to the surrounding geometry
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IC: Spatial GradientsIC: Spatial Gradients
No Gradients With Gradients
Estimate of the spatial change wrt.- Distance - Normals divergence
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Radiance CachingRadiance Caching
Extension of irradiance caching to glossy interreflections
Cache directional distribution of light
Hemispherical Harmonics
Krivanek et al. 05: Radiance Caching for Efficient Global Illumination Computation
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Radiance CachingRadiance Caching
Same weighting function as IC
Transl. gradient for each coef.
Rot. gradient replaced by rotation
Krivanek et al. 05: Radiance Caching for Efficient Global Illumination Computation
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(I)RC in Dynamic Scenes(I)RC in Dynamic Scenes
New cache for each frame
High cost
Flickering
Reuse records across frames
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
- Temporal Weighting Function- Estimate of the Future Incoming Lighting- Temporal Gradients
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
- Temporal Weighting Function- Estimate of the Future Incoming Lighting- Temporal Gradients
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Temporal Weighting FunctionTemporal Weighting Function
Estimate the temporal change rate of indirect lighting
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Temporal Weighting FunctionTemporal Weighting Function
Estimate the temporal change rate of indirect lighting
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Temporal Weighting FunctionTemporal Weighting Function
Estimate the temporal change rate of indirect lighting
≈Et-Et+1
δt
∂E∂t
(t0)
= E0( -1)
= Et+1/Et
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Temporal Weighting FunctionTemporal Weighting Function
Inverse of the temporal change rate of indirect lighting
= Et+1/Et
( -1)(t-t0)
1wk
t(t) = > 1/at
Problem : Lifespan is determined when the record is created
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Lifespan ThresholdingLifespan Thresholding
P
At point P and time t:
Static environment
= Et+1/Et = 1
wkt(t) = ∞ for all t
Infinite Lifespan
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Lifespan ThresholdingLifespan Thresholding
P
At point P and time t:
Static environment
= Et+1/Et = 1
wkt(t) = ∞ for all t
Infinite Lifespan
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Lifespan ThresholdingLifespan Thresholding
P
At point P and time t:
Static environment
= Et+1/Et = 1
wkt(t) = ∞ for all t
Infinite LifespanIncorrect
wkt(t) = 0 if t-tk>δtmax
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Record ReplacementRecord Replacement
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Temporal Weighting FunctionTemporal Weighting Function
Determines the lifespan of the records
Lifespan depends on the local change of incoming radiance
If the environment is static, threshold the lifespan to a maximum value
= Et+1/Et
Requires the knowledge of future irradiance
However
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
- Temporal Weighting Function- Estimate of the Future Incoming Lighting- Temporal Gradients
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Future Incoming LightingFuture Incoming Lighting
P P
≈Time t Time t+1
E(P, t) = E(P, t+1) =
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Future Incoming LightingFuture Incoming Lighting
Assumption: Animation is predefined
Future transformation matrices are known
Use reprojection to estimate the future incoming lighting
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ReprojectionReprojection
k
Et
Et+1
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ReprojectionReprojection
t+1t
k
EtOK
Et+1
Hemispheresampling
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ReprojectionReprojection
t+1
? ?
EtOK
Et+1
Reprojection
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ReprojectionReprojection
EtOK
Et+1
t+1
? ?
Depth culling
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ReprojectionReprojection
EtOK
Et+1
Hole filling
t+1
? ?
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ReprojectionReprojection
EtOK
Et+1
t+1
OK
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Future Incoming LightingFuture Incoming Lighting
Simple reprojection
No additional hemisphere sampling
Easy GPU Implementation
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Temporal InterpolationTemporal Interpolation
k
Et =
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Temporal InterpolationTemporal Interpolation
k
Et = Recompute Irradiance
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Temporal Interpolation: GoalTemporal Interpolation: Goal
k
Et =
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
- Temporal Weighting Function- Estimate of the Future Incoming Lighting- Temporal Gradients
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Extrapolated GradientsExtrapolated Gradients
Et computed by hemisphere sampling
Et+1 estimated by reprojection
Δ
textra ≈ Et+1-Et
Δ
t = ∂E / ∂t
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Extrapolated GradientsExtrapolated Gradients
k
Etextra = E0 = Computed
E1 = EstimatedEt
actual =
Etactual-Et
extra =
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Extrapolated GradientsExtrapolated Gradients
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Interpolated Gradients: Pass 1Interpolated Gradients: Pass 1
k
E0 = Computed
Etactual =
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Interpolated Gradients: Pass 2Interpolated Gradients: Pass 2
k
Etinter = E0 = Computed
Et = ComputedEt
actual =
Etactual-Et
inter =
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Interpolated GradientsInterpolated Gradients
Et computed by hemisphere sampling
Et+n computed by hemisphere sampling
Δ
t = ∂E / ∂t
Δ Et+n-Et
ntinter ≈
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Temporal GradientsTemporal Gradients
Extrapolated
1 pass
Possible flickering
Interpolated
2 passes
No flickering
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OutlineOutline
- Introduction
- Irradiance and Radiance Caching
- Temporal Radiance Caching
- Results
- Conclusion
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Flying KiteFlying Kite
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Japanese InteriorJapanese Interior
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Japanese InteriorJapanese Interior
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SpheresSpheres
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ConclusionConclusion
Temporal radiance interpolation scheme
Reuse records across frames
Quality improvement Speedup
Easily integrates within (ir)radiance caching-based renderers
GPU ImplementationWork submitted for publication
Dynamic objects, light sources, viewpoint
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Future WorkFuture Work
Avoid the need of maximum lifespan
Propose an interpolation method adapted to fast changes(temporal details are smoothed out by the gradients)
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On the web:http://www.irisa.fr/siames/Pascal.Gautron/
ORGoogle ‘pascal gautron’
P. Gautron, K. Bouatouch, S. Pattanaik
Temporal Radiance Caching
Technical Report no. 1796, IRISA, Rennes, France