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5D COVARIA NCE TRACING FOR EFFICIENT DEFOCUS AND MOTION BLUR

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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  1. 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

  2. Blur is costly to simulate !

  3. time integration space reconstruction

  4. 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

  5. Previouswork: a priori • First orderanalysis[Ramamoorthiet al. 2007] • Frequencyanalysis[Durand et al. 2005]

  6. Previouswork: a priori • First orderanalysis[Ramamoorthiet al. 2007] • Frequencyanalysis[Durand et al. 2005] Fourier transform zoom

  7. 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!

  8. Our idea: 5D Covariance representation

  9. 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

  10. Contributions • Unified temporal frequencyanalysis • Covariance tracing • Adaptive sampling & reconstruction algorithm

  11. Our algorithm Accumulate 5D Covariance in screenspace

  12. Our algorithm Accumulate 5D Covariance in screenspace angle Estimate 5D samplingdensity time angle time angle time

  13. Our algorithm Accumulate 5D Covariance in screenspace Estimate 5D samplingdensity Estimate 2D reconstruction filters

  14. Our algorithm Accumulate 5D Covariance in screenspace Estimate 5D samplingdensity Estimate 2D reconstruction filters Acquire5D samples Reconstruct image

  15. Accumulate 5D Covariance in screenspace Estimate 5D samplingdensity Estimate 2D reconstruction filters Acquire5D samples Reconstruct image

  16. Covariance tracing • Add information to light paths • Update the covariance along light path • Atomicdecomposition for genericity

  17. Covariance tracing Free transport Free transport

  18. Covariance tracing Free transport Reflection

  19. Covariance tracing Free transport Reflection Free transport

  20. Covariance tracing Free transport Reflection Occlusion Free transport spatial visibility

  21. Covariance tracing Free transport Occlusion Free transport

  22. Covariance tracing Free transport Free transport Reflection

  23. Covariance tracing Free transport Reflection Free transport

  24. Just a chain of operators Free transport Occlusion Curvature Symmetry BRDF Lens

  25. What about motion?

  26. Wecould rewrite all operators… Occlusion withmovingoccluder Curvaturewithmovinggeometry BRDF withmovingreflector Lens withmoving camera

  27. Wewill not rewrite all operators! Occlusion Curvature BRDF Lens Motion Inverse Motion

  28. angle angle Motion operator space space time time Reflectionwithmovingreflector

  29. angle Motion operator space time Reflection Motion

  30. angle angle Motion operator space space time time Inverse Motion Reflection Motion

  31. Accumulate covariance first light path second light path final covariance

  32. Accumulate 5D Covariance in screenspace Estimate 5D samplingdensity Estimate 2D reconstruction filters Acquire5D samples Reconstruct image

  33. 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

  34. Accumulate 5D Covariance in screenspace Estimate 5D samplingdensity Estimate 2D reconstruction filters Acquire 5D samples Reconstruct image

  35. Implementationdetails: occlusion • Occlusion using a voxelizedscene • Use the 3x3 covariance of normals distribution • Evaluateusing ray marching

  36. Results: the helicopter Our algorithm Equal time Monte-Carlo

  37. Results: the snooker defocusblur motion blur BRDF blur Equal-time Monte Carlo Our method

  38. 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

  39. Conclusion • Covariance tracing • Generatebetterlight paths • Simple formulation • Unifiedfrequencyanalysis • Temporal light fields • No specialcase

  40. Future work • Tracing covariance has a cost • Mostly due to the local occlusion query • New operators • Participatingmedia

  41. GROUND IS MOVING!

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