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A Hierarchical Volumetric Shadow Algorithm for Single Scattering Ilya Baran, Jiawen Chen, Jonathan Ragan-Kelley, Frdo Durand, Jaakko Lehtinen Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology

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Volumetric scattering with shadows Photo by Frdo Durand

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Alan Wake by Remedy Entertainment

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Related work Ray marching (brute force) Analytical scattering models Sky lighting, bloom, etc. Doesnt account for visibility Sun et al. [2005]

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Shadow volume methods Max [1986] Analytical integration Wyman and Ramsey [2008] Ray marching along intervals

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Related work Engelhardt and Dachsbacher [2010] Detect discontinuities, subsample and interpolate Performance depends on occluder complexity Epipolar geometry Detected discontinuties Engelhardt and Dachsbacher [2010]

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Overview Incremental integration Approximating single scattering Epipolar rectification ~

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Simplified scenario Orthographic camera Light direction perpendicular to view direction Visibility only

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r d

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7 5 Brute force complexity: O(rd) 1

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7 5 5 1

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1111111 Bit mask Process top down incrementally

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7 1111111 Bit mask

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7 1 1111111

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7 1 1111111

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7 1 1001111

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7 1 5 1001111

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7 1 5 Bit mask algorithm complexity: O(rd) 5 2 2 3 1001111 Bit mask

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Partial sum trees Binary tree Each node stores sum of children 4 22 2011 11001010

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Tree update 4 22 2011 11000010

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4 22 2001 11000010

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4 21 2001 11000010

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3 21 2001 11000010

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Tree query 3 2 1 2001 11000010 = 3

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Complexity 2D Brute force: O(rd) Incremental with bit mask: O(rd) Incremental with tree: O( (r+d) log d ) 3D: s independent slices Brute force: O(srd) Incremental with tree: O( s (r+d) log d )

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Textured lights 0.80.10.50.30.210.8 Light texture 1 0.9 0.8 0.6 0.5 0.4 0.3 Light attenuation

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SVD approximation ~ AUSV T = + + +

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Epipolar rectification Light direction Epipolar slices Eye

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Epipolar coordinates Point light Directional light

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Depth map resampling Camera depth map Light depth map Rectify Corresponding epipolar slice

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9.9 sec (17.1x)169 sec Equal quality comparison: Sibenik Our methodRay marching

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Our methodRay marching Equal quality comparison: Terrain 1.3 sec (41.5x)54 sec

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Equal quality comparisons: Trees Our methodRay marching 2.3 sec (120.4x)277 sec

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GPU Performance on Sibenik

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GPU Performance on Trees

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Limitations and future work Non-homogeneous media All points in volume must be visited SVD will have high rank GPU performance Dynamic data structure: limited parallelism Bandwidth intensive Requires CUDA, not suitable for consoles

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Summary Hierarchical volumetric shadow algorithm with complexity guarantees Significant speedups on CPUs Moderately faster than state-of-the art on GPUs

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GPU Performance on Sibenik