5d covaria nce tracing for efficient defocus and motion blur
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5D COVARIA NCE TRACING FOR EFFICIENT DEFOCUS AND MOTION BLUR PowerPoint PPT Presentation


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5D COVARIA NCE TRACING FOR EFFICIENT DEFOCUS AND MOTION BLUR. Laurent Belcour 1 Cyril Soler 2 Kartic Subr 3 Nicolas Holzschuch 2 Frédo Durand 4. 1 Grenoble Université, 2 Inria , 3 UC London, 4 MIT CSAIL. Blur is costly to simulate !. t ime integration. space reconstruction.

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5D COVARIA NCE TRACING FOR EFFICIENT DEFOCUS AND MOTION BLUR

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5D COVARIANCE TRACINGFOR EFFICIENT DEFOCUS AND MOTION BLUR

Laurent Belcour1 Cyril Soler2Kartic Subr3 Nicolas Holzschuch2Frédo Durand4

1 Grenoble Université, 2 Inria, 3 UC London, 4 MIT CSAIL


Blur is costly to simulate !


time

integration

space

reconstruction


Previousworks: a posteriori

  • Image spacemethods

    • [Mitchell 1987], [Overbeck et al. 2009],

    • [Sen et al. 2011], [Rousselle et al. 2011]

  • Integrationspace

    • [Hachisukaet al. 2008]

  • Reconstruction

    • [Lehtinenet al. 2011], [Lehtinenet al. 2012]

  • Easy to plug

  • Requirealready dense sampling

  • Rely on point samples


Previouswork: a priori

  • First orderanalysis[Ramamoorthiet al. 2007]

  • Frequencyanalysis[Durand et al. 2005]


Previouswork: a priori

  • First orderanalysis[Ramamoorthiet al. 2007]

  • Frequencyanalysis[Durand et al. 2005]

Fourier transform

zoom


Previouswork: a priori

Predict full spectrum

Predictbounds

Compact & efficient

Special cases formula

  • Anisotropic information

  • Unwieldy

  • [Soler et al. 2009]

  • [Egan et al. 2009], [Bagheret al. 2013], [Mehaet al. 2012]

None canworkwith full global illumination!


Our idea: 5D Covariance representation


5D Covariance representation

  • Use second moments

    • 5x5 matrix

    • Equivalent to Gaussianapprox.

  • Formulate all interactions

    • Analytical matrix operators

    • Gaussianapprox. for reflection

  • Nice properties

    • Symmetry

    • Additivity

angle (2D)

space (2D)

time


Contributions

  • Unified temporal frequencyanalysis

  • Covariance tracing

  • Adaptive sampling & reconstruction algorithm


Our algorithm

Accumulate 5D Covariance

in screenspace


Our algorithm

Accumulate 5D Covariance

in screenspace

angle

Estimate 5D

samplingdensity

time

angle

time

angle

time


Our algorithm

Accumulate 5D Covariance

in screenspace

Estimate 5D

samplingdensity

Estimate 2D reconstruction filters


Our algorithm

Accumulate 5D Covariance

in screenspace

Estimate 5D

samplingdensity

Estimate 2D reconstruction filters

Acquire5D samples

Reconstruct image


Accumulate 5D Covariance

in screenspace

Estimate 5D

samplingdensity

Estimate 2D reconstruction filters

Acquire5D samples

Reconstruct image


Covariance tracing

  • Add information to light paths

  • Update the covariance along light path

  • Atomicdecomposition for genericity


Covariance tracing

Free transport

Free transport


Covariance tracing

Free transport

Reflection


Covariance tracing

Free transport

Reflection

Free transport


Covariance tracing

Free transport

Reflection

Occlusion

Free transport

spatial visibility


Covariance tracing

Free transport

Occlusion

Free transport


Covariance tracing

Free transport

Free transport

Reflection


Covariance tracing

Free transport

Reflection

Free transport


Just a chain of operators

Free transport

Occlusion

Curvature

Symmetry

BRDF

Lens


What about motion?


Wecould rewrite all operators…

Occlusion

withmovingoccluder

Curvaturewithmovinggeometry

BRDF withmovingreflector

Lens withmoving camera


Wewill not rewrite all operators!

Occlusion

Curvature

BRDF

Lens

Motion

Inverse Motion


angle

angle

Motion operator

space

space

time

time

Reflectionwithmovingreflector


angle

Motion operator

space

time

Reflection

Motion


angle

angle

Motion operator

space

space

time

time

Inverse Motion

Reflection

Motion


Accumulate covariance

first light path

second light path

final covariance


Accumulate 5D Covariance

in screenspace

Estimate 5D

samplingdensity

Estimate 2D reconstruction filters

Acquire5D samples

Reconstruct image


Using covariance information

  • How canweextractbandwidth ?

    • Using the volume

    • Determinant of the covariance

  • How canweestimate the filter ?

    • Frequencyanalysis of integration [Durand 2011]

    • Slicing the equivalentGaussian

space

space

time


Accumulate 5D Covariance

in screenspace

Estimate 5D

samplingdensity

Estimate 2D reconstruction filters

Acquire 5D samples

Reconstruct image


Implementationdetails: occlusion

  • Occlusion using a voxelizedscene

  • Use the 3x3 covariance of normals distribution

  • Evaluateusing ray marching


Results: the helicopter

Our algorithm

Equal time Monte-Carlo


Results: the snooker

defocusblur

motion blur

BRDF blur

Equal-time Monte Carlo

Our method


Results: the snooker

  • Our method: 25min

  • Eq. quality Monte Carlo: 2h25min

    • 200 light fieldsamples per pixel

  • Covariance tracing: 2min 36s

    • 10 covariance per pixel

  • Reconstruction: 16s


Conclusion

  • Covariance tracing

    • Generatebetterlight paths

    • Simple formulation

  • Unifiedfrequencyanalysis

    • Temporal light fields

    • No specialcase


Future work

  • Tracing covariance has a cost

    • Mostly due to the local occlusion query

  • New operators

    • Participatingmedia


GROUND IS MOVING!


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