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Directional Dipole Model for Subsurface Scatteringhachisuka/dirpole_tr...Directional Dipole Model...
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Directional Dipole Model for Subsurface Scattering Toshiya Hachisuka Collaboration with Jeppe Frisvad and Thomas Kjeldsen 1 The slides are based on the tech. report published in August 2013 For the latest results, please refer to the corresponding paper at TOG
Transcript of Directional Dipole Model for Subsurface Scatteringhachisuka/dirpole_tr...Directional Dipole Model...
Directional Dipole Model for Subsurface Scattering
Toshiya Hachisuka
Collaboration with Jeppe Frisvad and Thomas Kjeldsen
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The slides are based on the tech. report published in August 2013For the latest results, please refer to the corresponding paper at TOG
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Bidirectional Reflectance Distribution Function
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Bidirectional Surface Scattering Reflectance Distribution Function
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Bidirectional Surface Scattering Reflectance Distribution Function
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Reference Solution
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Existing BSSRDF Model
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Our BSSRDF Model
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Prev
ious
Mod
el A
Previous Model B
Our
Mod
el Reference
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Previous Models
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Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Dipole
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Dipole
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Dipole
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Dipole
Approximate solution [Reynolds et al. 1976]
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Dipole
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Dipole
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Dipole
Virtual
Real26
Dipole
Diffuse BRDF Dipole BSSRDF
[Jensen et al. 2001]27
Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Multipole
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Multipole
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Multipole
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Multipole
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Multipole
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Multipole
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Multipole
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Multipole
[Donner & Jensen 2005]36
Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Quantized Diffusion
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Quantized Diffusion
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Quantized Diffusion
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Quantized Diffusion
Dipole Quantized Diffusion
[d’Eon & Irving 2011]41
Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Precomputed BSSRDF
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Precomputed BSSRDF
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Precomputed BSSRDF
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Precomputed BSSRDF
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Precomputed BSSRDFAn Empirical BSSRDF Model
Craig Donner⇥ Jason Lawrence† Ravi Ramamoorthi ‡
Toshiya Hachisuka§ Henrik Wann Jensen§ Shree Nayar⇥⇥Columbia University † University of Virginia ‡ UC Berkeley § UC San Diego
Monte Carlo PathTracing (30 hours)
Diffusion Dipole + Single Scattering (10 min) Our Model + Single Scattering (30 min) Single Scattering OnlyFigure 1: Although the appearance of orange juice is dominated by low-order scattering events, it is not accurately predicted by a singlescattering model alone (lower right). Adding the contribution from high-order multiple scattering using the diffusion dipole (left) still failsto capture these effects and produces visible color artifacts. Numerical methods such as Monte Carlo path tracing (upper right) or photonmapping are accurate, but do not provide an explicit model of the BSSRDF and require long rendering times. Our proposed model is compact,efficient to render and can accurately express the complex spatial- and directionally-dependent appearance of these types of materials.
Abstract
We present a new model of the homogeneous BSSRDF based onlarge-scale simulations. Our model captures the appearance ofmaterials that are not accurately represented using existing singlescattering models or multiple isotropic scattering models (e.g. thediffusion approximation). We use an analytic function to modelthe 2D hemispherical distribution of exitant light at a point on thesurface, and a table of parameter values of this function computedat uniformly sampled locations over the remaining dimensions ofthe BSSRDF domain. This analytic function is expressed in ellipticcoordinates and has six parameters which vary smoothly with sur-face position, incident angle, and the underlying optical propertiesof the material (albedo, mean free path length, phase function andthe relative index of refraction). Our model agrees well with mea-sured data, and is compact, requiring only 250MB to represent thefull spatial- and angular-distribution of light across a wide spectrumof materials. In practice, rendering a single material requires onlyabout 100KB to represent the BSSRDF.
1 Introduction
Light propagates into and scatters within all non-metallic materi-als. This subsurface scattering is common in many liquids—suchas orange juice, coffee or milk, and in solids—such as gemstones,leaves, wax, plastics and skin. It gives materials their characteristiccolors, and provides a soft, translucent appearance. Accurate andcompact models of the way light interacts with these materials arenecessary to efficiently render them.
Light scattering in translucent materials is described by the bidi-rectional scattering surface reflectance distribution function S (theBSSRDF [Nicodemus et al. 1977]). The BSSRDF defines the gen-eral transport of light between two points and directions as the ratioof the radiance Lo(⇥xo,⇥⇤o) exiting at position ⇥xo in direction ⇥⇤o tothe radiant flux �i(⇥xi,⇥⇤i) incident at⇥xi from direction ⇥⇤i:
dLo(⇥xo,⇥⇤o)d�i(⇥xi,⇥⇤i)
= S(⇥xi,⇥⇤i;⇥xo,⇥⇤o|⇥s, ⇥a, g, �), (1)
where S depends on the optical properties of the material—the scat-tering and absorption coefficients ⇥s and ⇥a, the relative index ofrefraction � , and g ⇤ [�1 : 1] which parameterizes the anisotropyof the phase function.
1.1 Related Work
Numerical techniques such as Monte Carlo path tracing [Kajiya1986; Jensen et al. 1999] are capable of simulating general BSS-RDFs. However, these methods are expensive, often requiring
An Empirical BSSRDF Model
Craig Donner⇥ Jason Lawrence† Ravi Ramamoorthi ‡
Toshiya Hachisuka§ Henrik Wann Jensen§ Shree Nayar⇥⇥Columbia University † University of Virginia ‡ UC Berkeley § UC San Diego
Monte Carlo PathTracing (30 hours)
Diffusion Dipole + Single Scattering (10 min) Our Model + Single Scattering (30 min) Single Scattering OnlyFigure 1: Although the appearance of orange juice is dominated by low-order scattering events, it is not accurately predicted by a singlescattering model alone (lower right). Adding the contribution from high-order multiple scattering using the diffusion dipole (left) still failsto capture these effects and produces visible color artifacts. Numerical methods such as Monte Carlo path tracing (upper right) or photonmapping are accurate, but do not provide an explicit model of the BSSRDF and require long rendering times. Our proposed model is compact,efficient to render and can accurately express the complex spatial- and directionally-dependent appearance of these types of materials.
Abstract
We present a new model of the homogeneous BSSRDF based onlarge-scale simulations. Our model captures the appearance ofmaterials that are not accurately represented using existing singlescattering models or multiple isotropic scattering models (e.g. thediffusion approximation). We use an analytic function to modelthe 2D hemispherical distribution of exitant light at a point on thesurface, and a table of parameter values of this function computedat uniformly sampled locations over the remaining dimensions ofthe BSSRDF domain. This analytic function is expressed in ellipticcoordinates and has six parameters which vary smoothly with sur-face position, incident angle, and the underlying optical propertiesof the material (albedo, mean free path length, phase function andthe relative index of refraction). Our model agrees well with mea-sured data, and is compact, requiring only 250MB to represent thefull spatial- and angular-distribution of light across a wide spectrumof materials. In practice, rendering a single material requires onlyabout 100KB to represent the BSSRDF.
1 Introduction
Light propagates into and scatters within all non-metallic materi-als. This subsurface scattering is common in many liquids—suchas orange juice, coffee or milk, and in solids—such as gemstones,leaves, wax, plastics and skin. It gives materials their characteristiccolors, and provides a soft, translucent appearance. Accurate andcompact models of the way light interacts with these materials arenecessary to efficiently render them.
Light scattering in translucent materials is described by the bidi-rectional scattering surface reflectance distribution function S (theBSSRDF [Nicodemus et al. 1977]). The BSSRDF defines the gen-eral transport of light between two points and directions as the ratioof the radiance Lo(⇥xo,⇥⇤o) exiting at position ⇥xo in direction ⇥⇤o tothe radiant flux �i(⇥xi,⇥⇤i) incident at⇥xi from direction ⇥⇤i:
dLo(⇥xo,⇥⇤o)d�i(⇥xi,⇥⇤i)
= S(⇥xi,⇥⇤i;⇥xo,⇥⇤o|⇥s, ⇥a, g, �), (1)
where S depends on the optical properties of the material—the scat-tering and absorption coefficients ⇥s and ⇥a, the relative index ofrefraction � , and g ⇤ [�1 : 1] which parameterizes the anisotropyof the phase function.
1.1 Related Work
Numerical techniques such as Monte Carlo path tracing [Kajiya1986; Jensen et al. 1999] are capable of simulating general BSS-RDFs. However, these methods are expensive, often requiring
An Empirical BSSRDF Model
Craig Donner⇥ Jason Lawrence† Ravi Ramamoorthi ‡
Toshiya Hachisuka§ Henrik Wann Jensen§ Shree Nayar⇥⇥Columbia University † University of Virginia ‡ UC Berkeley § UC San Diego
Monte Carlo PathTracing (30 hours)
Diffusion Dipole + Single Scattering (10 min) Our Model + Single Scattering (30 min) Single Scattering OnlyFigure 1: Although the appearance of orange juice is dominated by low-order scattering events, it is not accurately predicted by a singlescattering model alone (lower right). Adding the contribution from high-order multiple scattering using the diffusion dipole (left) still failsto capture these effects and produces visible color artifacts. Numerical methods such as Monte Carlo path tracing (upper right) or photonmapping are accurate, but do not provide an explicit model of the BSSRDF and require long rendering times. Our proposed model is compact,efficient to render and can accurately express the complex spatial- and directionally-dependent appearance of these types of materials.
Abstract
We present a new model of the homogeneous BSSRDF based onlarge-scale simulations. Our model captures the appearance ofmaterials that are not accurately represented using existing singlescattering models or multiple isotropic scattering models (e.g. thediffusion approximation). We use an analytic function to modelthe 2D hemispherical distribution of exitant light at a point on thesurface, and a table of parameter values of this function computedat uniformly sampled locations over the remaining dimensions ofthe BSSRDF domain. This analytic function is expressed in ellipticcoordinates and has six parameters which vary smoothly with sur-face position, incident angle, and the underlying optical propertiesof the material (albedo, mean free path length, phase function andthe relative index of refraction). Our model agrees well with mea-sured data, and is compact, requiring only 250MB to represent thefull spatial- and angular-distribution of light across a wide spectrumof materials. In practice, rendering a single material requires onlyabout 100KB to represent the BSSRDF.
1 Introduction
Light propagates into and scatters within all non-metallic materi-als. This subsurface scattering is common in many liquids—suchas orange juice, coffee or milk, and in solids—such as gemstones,leaves, wax, plastics and skin. It gives materials their characteristiccolors, and provides a soft, translucent appearance. Accurate andcompact models of the way light interacts with these materials arenecessary to efficiently render them.
Light scattering in translucent materials is described by the bidi-rectional scattering surface reflectance distribution function S (theBSSRDF [Nicodemus et al. 1977]). The BSSRDF defines the gen-eral transport of light between two points and directions as the ratioof the radiance Lo(⇥xo,⇥⇤o) exiting at position ⇥xo in direction ⇥⇤o tothe radiant flux �i(⇥xi,⇥⇤i) incident at⇥xi from direction ⇥⇤i:
dLo(⇥xo,⇥⇤o)d�i(⇥xi,⇥⇤i)
= S(⇥xi,⇥⇤i;⇥xo,⇥⇤o|⇥s, ⇥a, g, �), (1)
where S depends on the optical properties of the material—the scat-tering and absorption coefficients ⇥s and ⇥a, the relative index ofrefraction � , and g ⇤ [�1 : 1] which parameterizes the anisotropyof the phase function.
1.1 Related Work
Numerical techniques such as Monte Carlo path tracing [Kajiya1986; Jensen et al. 1999] are capable of simulating general BSS-RDFs. However, these methods are expensive, often requiring
Reference(30 hours)
Dipole(10 min)
Precomputed(30 min)
[Donner et al. 2009]47
Previous Models
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Photon Diffusion
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Photon Diffusion
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Photon Diffusion
[Donner & Jensen 2007]51
Photon Beam Diffusion
[Habel et al. 2013]52
Photon Diffusion
Dipole Photon Diffusion
[Donner & Jensen 2007]53
Previous Models• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Previous Models
• Ignores incoming light direction
• Requires no precomputation
• Provides fully analytical function
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Previous Models
• Considers incoming light direction
• Requires precomputation
• Provides fully analytical function
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Previous Models
• Considers incoming light direction
• Requires no precomputation
• Relies on numerical integration
• Dipole [Jensen et al. 2001]
• Multipole [Donner & Jensen 2005]
• Quantized diffusion [d’Eon & Irving 2011]
• Precomputed BSSRDF [Donner et al. 2009] [Yan et al. 2012]
• Photon diffusion [Donner & Jensen 2007] [Habel et al. 2013]
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Contributions
• First BSSRDF which...
• Considers incoming light direction
• Requires no precomputation
• Provides fully analytical function
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Dip
ole
Quantized
Our
Mod
el Reference
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Idea
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Directional solution [Menon et al. 2005]
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Mirror direction&
Offset location
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Virtual
Real
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Original Dipole
Virtual
Real68
Virtual
Real
Directional Dipole
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Two Challenges
• Mirroring sources is unstable
• Singularity at the real source
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Two Challenges
• Mirroring sources is unstable
• Singularity at the real source
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Mirroring plane
Unstable Mirroring
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Mirroring plane
Unstable Mirroring
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Modified Mirroring Plane
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Modified Mirroring Plane
Modified mirroring plane
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Modified Mirroring Plane
Modified mirroring plane
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Two Challenges
• Mirroring sources is unstable
• Singularity at the real source
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Singularity
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Singularity
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Singularity
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Singularity
O(r�3)
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Distance Correction
• Inspired by the correction technique in computational physics [Elliot 86]
r0 =p
r2 + z02
corrected distance distance correction factor
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Results
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Simple Test Cases
• Various measured materials
• Comparisons with Monte Carlo simulation
• Highly directional lighting
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Simple Test Cases
0
0͘1
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apple choc�milk marble potato skin1 soy�milk grapefruit whole�milk
RMSEstandard�dipolebetter�dipolequantizedour�model
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Directional Effect
• Incident angle: 30°
Quantized Ours86
Directional Effect
• Incident angle: 45°
Quantized Ours87
Directional Effect
• Incident angle: 60°
Quantized Ours88
Grapefruits BunnyD
ipol
eQ
uantizedO
urs
Reference
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Image Based Lighting
Quantized Ours90
Image Based Lighting
Quantized Ours91
Image Based Lighting
Quantized Ours92
Failure Case• Low albedo materials (e.g., Cranberry juice)
Dipole Ours93
Conclusions
• First BSSRDF which...
• Considers incoming light direction
• Requires no precomputation
• Provides fully analytical solution
• Far more accurate than previous models
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• First BSSRDF which...
• Considers incoming light direction
• Requires no precomputation
• Provides fully analytical solution
http://cs.au.dk/~toshiya/dirpole_tr.pdf
Thank You
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