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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 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
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!
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
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