P RINCIPLED K ERNEL P REDICTION FOR S PATIALLY V ARYING BSSRDF S Oskar Elek and Jaroslav K řivánek This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Charles University, Prague Marie Sklodowska-Curie grant agreement No 642841.
Topic Prediction of spatially varying BSSRDF kernels from optical parameters Scattering albedo Local approaches Parameter Ours Path tracing texture (here 2.5D) aggregation reference 2 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Topic Not tackling SV-BSSRDF acquisition / compression / editing [Peers et al. @ SIGGRAPH 2006] [Song et al. @ SIGGRAPH 2009] 3 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
BSSRDF and SV-BSSRDF Uses and challenges OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
BSSRDF: Background 𝑇 𝒚 𝑗 , 𝒚 𝑓 = “scattering kernel” Statistical estimate of point-to-point volumetric light transport 5 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
BSSRDF: Background Great for (quasi-)homogeneous materials with well localized light transport … [Jensen et al. @ SIGGRAPH 2001] [Donner et al. @ SIGGRAPH 2005] [Frisvad et al. @ ACM ToG 2014] 6 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
BSSRDF: Background …but not so great when the transport scale exceeds the feature scale [Elek, Sumin et al. @ SIGGRAPH Asia 2017] 7 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
SV-BSSRDF: Kernel Shape Albedo Albedo Point response (“kernel”) Point response (“kernel”) 8 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
SV-BSSRDF: Kernel Shape Albedo Albedo Point response (“kernel”) Point response (“kernel”) 9 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
SV-BSSRDF: Kernel Shape Albedo Two key ideas: 1. Data-driven parameter aggregation 2. Decomposition of transport into local and global 𝑔 𝑔 𝑀 𝑀 𝑔 𝐻 Point response (“kernel”) 10 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Methodology Step-by-step walkthrough OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Method Outline Preprocessing: i. Derive a basis (homogeneous) BSSRDF ii. For each (𝒚 𝑗 , 𝒚 𝑓 ) estimate the transport path distribution connecting them iii. Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime: Use standard MC to select 𝒚 𝑓 1) 2) For given (𝒚 𝑗 , 𝒚 𝑓 ) aggregate the material properties using the kernel from iii. 3) Separate the transport kernel into the local and global components 4) Use point-evaluated properties to compute the local components 5) Use the aggregate properties from 3) to compute the global component 12 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Method Outline Preprocessing: i. Derive a basis (homogeneous) BSSRDF ii. For each (𝒚 𝑗 , 𝒚 𝑓 ) estimate the transport different albedos path distribution connecting them iii. Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime: Use standard MC to select 𝒚 𝑓 1) 2) For given (𝒚 𝑗 , 𝒚 𝑓 ) aggregate the material 0 MFP 10 MFP properties using the kernel from iii. normalized radial distance 3) Separate the transport kernel into the local and global components BSSRDF kernel: 4) Use point-evaluated properties to 𝑇 ≅ 𝐵 𝑗 ∙ 𝑓 −𝑠∙𝐶 𝑗 compute the local components 𝑗 5) Use the aggregate properties from 3) to compute the global component Also see [Christensen and Burley @ SIGGRAPH Talks 2015] 13 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Method Outline Preprocessing: i. Derive a basis (homogeneous) BSSRDF ii. For each (𝒚 𝑗 , 𝒚 𝑓 ) estimate the transport path distribution connecting them iii. Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime: Use standard MC to select 𝒚 𝑓 1) Distribution of unweighted sub-surface paths 2) For given (𝒚 𝑗 , 𝒚 𝑓 ) aggregate the material properties using the kernel from iii. 3) Separate the transport kernel into the local and global components 4) Use point-evaluated properties to compute the local components 5) Use the aggregate properties from 3) to Line: [d’Eon and Irving Ellipse: [Sone et al. @ SIGGRAPH 2011] @ EG Shorts 2017] compute the global component 14 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Method Outline Preprocessing: i. Derive a basis (homogeneous) BSSRDF ii. For each (𝒚 𝑗 , 𝒚 𝑓 ) estimate the transport path distribution connecting them iii. Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime: Use standard MC to select 𝒚 𝑓 1) 2) For given (𝒚 𝑗 , 𝒚 𝑓 ) aggregate the material properties using the kernel from iii. 3) Separate the transport kernel into the local and global components 4) Use point-evaluated properties to Aggregation kernel: ‘Transport’ albedo: compute the local components 𝐿 = 𝑙 𝐻 𝛽 𝑢 = 𝐿(𝒚) 5) Use the aggregate properties from 3) to compute the global component 15 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Method Outline Preprocessing: i. Derive a basis (homogeneous) BSSRDF ii. For each (𝒚 𝑗 , 𝒚 𝑓 ) estimate the transport path distribution connecting them iii. Fit a generic parametric model to the 𝑔 𝑔 𝑀 𝑀 distribution (e.g. Gaussian mixture) 𝑔 𝐻 Runtime: 𝑇 𝑊 = 𝑔 𝑀 (𝒚 𝑗 ) ∙ 𝑔 𝐻 (𝒚 𝑗 , 𝒚 𝑓 ) ∙ 𝑔 𝑀 (𝒚 𝑓 ) Use standard MC to select 𝒚 𝑓 1) = 𝛽 𝑗 ∙ 𝑇(𝛽 𝑢 ) ∙ 𝛽 𝑓 2) For given (𝒚 𝑗 , 𝒚 𝑓 ) aggregate the material 𝛽 𝑢 𝛽 𝑢 properties using the kernel from iii. 3) Separate the transport kernel into the local and global components 4) Use point-evaluated properties to compute the local components Factorization: Aggregation: 5) Use the aggregate properties from 2) to 𝑇 𝑊 = 𝑇(𝛽 𝑢 ) 𝑇 𝑊 = 𝑇(𝛽 𝑗 ) ∙ 𝑇(𝛽 𝑓 ) compute the global component [Song et al. @ SIGGRAPH 2009] [Sone et al. @ EG Shorts 2017] OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS 16
Evaluation Overall quality and detail preservation OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Evaluation: Simple Structures 18 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Evaluation: Complex Structures 19 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Evaluation: Color Features 20 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Evaluation: Feature Preservation 21 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Discussion What follows? OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Future Work • Principled aggregation kernel • Currently only a manual fit 23 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Future Work • Principled aggregation kernel • Spatial variation of all material parameters • Currently only scattering albedo [Hasan et al. @ SIGGRAPH 2010] 24 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Future Work • Principled aggregation kernel • Spatial variation of all material parameters • Importance sampling • Currently only uniform sampling of incident illumination 𝑔 𝑔 𝑀 𝑀 𝑔 𝐻 𝑇 𝑊 = 𝑔 𝑀 (𝒚 𝑗 ) ∙ 𝑔 𝐻 (𝒚 𝑗 , 𝒚 𝑓 ) ∙ 𝑔 𝑀 (𝒚 𝑓 ) 25 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Future Work • Principled aggregation kernel • Spatial variation of all material parameters • Importance sampling • General 3D geometry and parameter distributions • Current solution limited to 2.5D objects [Frisvad et al. @ ACM ToG 2014] 26 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
P RINCIPLED K ERNEL P REDICTION FOR S PATIALLY V ARYING BSSRDF S Oskar Elek and Jaroslav K řivánek This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Charles University, Prague Marie Sklodowska-Curie grant agreement No 642841.
Extra Slides OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
Basis BSSRDF 29 OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS
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