P RINCIPLED K ERNEL P REDICTION FOR S PATIALLY V ARYING BSSRDF S - - PowerPoint PPT Presentation

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P RINCIPLED K ERNEL P REDICTION FOR S PATIALLY V ARYING BSSRDF S Oskar Elek and Jaroslav K ivnek This project has received funding from the European Unions Horizon 2020 research and innovation programme under the Charles University, Prague

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      

PRINCIPLED KERNEL PREDICTION

FOR SPATIALLY VARYING BSSRDFS

Oskar Elek and Jaroslav Křivánek Charles University, Prague

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642841.

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Topic

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Prediction of spatially varying BSSRDF kernels from optical parameters

Scattering albedo texture (here 2.5D) Local approaches Parameter aggregation Ours Path tracing reference

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Topic

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Not tackling SV-BSSRDF acquisition / compression / editing

[Peers et al. @ SIGGRAPH 2006] [Song et al. @ SIGGRAPH 2009]

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BSSRDF and SV-BSSRDF

Uses and challenges

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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SLIDE 5

BSSRDF: Background

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

𝑇 𝒚𝑗, 𝒚𝑓 = “scattering kernel”

Statistical estimate of point-to-point volumetric light transport

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SLIDE 6

BSSRDF: Background

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

[Donner et al. @ SIGGRAPH 2005] [Frisvad et al. @ ACM ToG 2014] [Jensen et al. @ SIGGRAPH 2001]

Great for (quasi-)homogeneous materials with well localized light transport…

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BSSRDF: Background

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

[Elek, Sumin et al. @ SIGGRAPH Asia 2017]

…but not so great when the transport scale exceeds the feature scale

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SV-BSSRDF: Kernel Shape

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Albedo Albedo Point response (“kernel”) Point response (“kernel”)

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SLIDE 9

SV-BSSRDF: Kernel Shape

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Albedo Albedo Point response (“kernel”) Point response (“kernel”)

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SV-BSSRDF: Kernel Shape

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Two key ideas:

  • 1. Data-driven parameter aggregation
  • 2. Decomposition of transport into local and global

𝑔

𝐻

𝑔

𝑀

𝑔

𝑀

Albedo Point response (“kernel”)

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SLIDE 11

Methodology

Step-by-step walkthrough

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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SLIDE 12

Method Outline

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Preprocessing:

i.

Derive a basis (homogeneous) BSSRDF

ii.

For each (𝒚𝑗, 𝒚𝑓) estimate the transport path distribution connecting them

iii.

Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime:

1)

Use standard MC to select 𝒚𝑓

2)

For given (𝒚𝑗, 𝒚𝑓) 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

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Method Outline

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

𝑇 ≅ 𝐵𝑗 ∙ 𝑓−𝑠∙𝐶𝑗

𝑗

BSSRDF kernel:

Also see [Christensen and Burley @ SIGGRAPH Talks 2015] normalized radial distance different albedos

0 MFP 10 MFP

Preprocessing:

i.

Derive a basis (homogeneous) BSSRDF

ii.

For each (𝒚𝑗, 𝒚𝑓) estimate the transport path distribution connecting them

iii.

Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime:

1)

Use standard MC to select 𝒚𝑓

2)

For given (𝒚𝑗, 𝒚𝑓) 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

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SLIDE 14

Method Outline

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

Distribution of unweighted sub-surface paths Line: [d’Eon and Irving @ SIGGRAPH 2011] Ellipse: [Sone et al. @ EG Shorts 2017]

Preprocessing:

i.

Derive a basis (homogeneous) BSSRDF

ii.

For each (𝒚𝑗, 𝒚𝑓) estimate the transport path distribution connecting them

iii.

Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime:

1)

Use standard MC to select 𝒚𝑓

2)

For given (𝒚𝑗, 𝒚𝑓) 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

14

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SLIDE 15

Method Outline

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

𝐿 = 𝑙𝐻

Aggregation kernel:

𝛽𝑢 = 𝐿(𝒚)

‘Transport’ albedo:

Preprocessing:

i.

Derive a basis (homogeneous) BSSRDF

ii.

For each (𝒚𝑗, 𝒚𝑓) estimate the transport path distribution connecting them

iii.

Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime:

1)

Use standard MC to select 𝒚𝑓

2)

For given (𝒚𝑗, 𝒚𝑓) 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

15

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SLIDE 16

Method Outline

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

𝑔

𝐻

𝑔

𝑀

𝑔

𝑀

𝑇𝑊 = 𝑔

𝑀(𝒚𝑗) ∙ 𝑔 𝐻(𝒚𝑗, 𝒚𝑓) ∙ 𝑔 𝑀(𝒚𝑓)

= 𝛽𝑗 𝛽𝑢 ∙ 𝑇(𝛽𝑢) ∙ 𝛽𝑓 𝛽𝑢 𝑇𝑊 = 𝑇(𝛽𝑗) ∙ 𝑇(𝛽𝑓)

Factorization:

[Song et al. @ SIGGRAPH 2009]

𝑇𝑊 = 𝑇(𝛽𝑢)

[Sone et al. @ EG Shorts 2017]

Aggregation:

Preprocessing:

i.

Derive a basis (homogeneous) BSSRDF

ii.

For each (𝒚𝑗, 𝒚𝑓) estimate the transport path distribution connecting them

iii.

Fit a generic parametric model to the distribution (e.g. Gaussian mixture) Runtime:

1)

Use standard MC to select 𝒚𝑓

2)

For given (𝒚𝑗, 𝒚𝑓) 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 2) to compute the global component

16

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SLIDE 17

Evaluation

Overall quality and detail preservation

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Evaluation: Simple Structures

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Evaluation: Complex Structures

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Evaluation: Color Features

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Evaluation: Feature Preservation

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Discussion

What follows?

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Future Work

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

  • Principled aggregation kernel
  • Currently only a manual fit

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Future Work

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

  • Principled aggregation kernel
  • Spatial variation of all material parameters
  • Currently only scattering albedo

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[Hasan et al. @ SIGGRAPH 2010]

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SLIDE 25

𝑔

𝐻

𝑔

𝑀

𝑔

𝑀

𝑇𝑊 = 𝑔

𝑀(𝒚𝑗) ∙ 𝑔 𝐻(𝒚𝑗, 𝒚𝑓) ∙ 𝑔 𝑀(𝒚𝑓)

Future Work

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

  • Principled aggregation kernel
  • Spatial variation of all material parameters
  • Importance sampling
  • Currently only uniform sampling of incident illumination

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Future Work

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

  • 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]

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      

PRINCIPLED KERNEL PREDICTION

FOR SPATIALLY VARYING BSSRDFS

Oskar Elek and Jaroslav Křivánek Charles University, Prague

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642841.

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Extra Slides

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Basis BSSRDF

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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Full Results

OSKAR ELEK AND JAROSLAV KRIVANEK: PRINCIPLED KERNEL PREDICTION FOR SPATIALLY VARYING BSSRDFS

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