1 temporal radiance caching p. gautron k. bouatouch s. pattanaik

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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