Transcript SIGGRAPH 2013 slides
1 Understanding the role of phase function in translucent appearance Ioannis Gkioulekas 1 Edward Adelson 2 1 Harvard Bei Xiao 2 Todd Zickler 1 2 MIΤ Shuang Zhao 3 Kavita Bala 3 3 Cornell
2 Translucency is everywhere food skin jewelry architecture
Subsurface scattering 3 outgoing direction incident direction isotropic radiative transfer equation extinction coefficient σ t (λ) absorption coefficient σ a (λ) phase function p (λ) Chandrasekhar 1960
4 Phase function is important thick parts (diffusion) thin parts
5 Common phase functions Henyey-Greenstein (HG) lobes single-parameter family: g = 𝜇 1 average cosine 𝜇 1 1 = cos 𝜃 = −1 𝑝 cos 𝜃 cos 𝜃 𝑑 cos 𝜃 Henyey and Greenstein 1941
What can we represent with HG?
6 marble white jade microcrystalline wax Jensen 2001
Henyey-Greenstein is not enough soap microcrystalline wax 7 setup photo HG
Goals
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8 expanded phase function space role in translucent appearance
Expanded phase function space Henyey-Greenstein (HG) lobes von Mises-Fisher (vMF) lobes single-parameter family: g = 𝜇 1 single-parameter family: 𝜅 = 2𝜇 1 / 1 − 𝜇 2 9 average cosine second moment 𝜇 1 1 = cos 𝜃 = −1 𝑝 cos 𝜃 cos 𝜃 𝑑 cos 𝜃 𝜇 2 1 = −1 𝑝 cos 𝜃 cos 𝜃 2 𝑑 cos 𝜃
Expanded phase function space soap microcrystalline wax 10 setup photo HG vMF
11 Expanded phase function space Henyey-Greenstein (HG) lobes von Mises-Fisher (vMF) lobes single-parameter family: g = 𝜇 1 Linear mixtures: HG + HG HG + vMF single-parameter family: 𝜅 = 2𝜇 1 / 1 − 𝜇 2 vMF + vMF
12 Redundant phase function space
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• • • Related work Fleming and Bülthoff 2005, Motoyoshi 2010 • • many perceptual cues do not study phase function Pellacini et al. 2000, Wills et al. 2009 • gloss perception • much smaller space Ngan et al. 2006 • • gloss perception navigation of appearance space 13
1. Computational processing Our approach 2. Psychophysical validation 3. Analysis of results 14 image-driven analysis tractable experiment visualization, perceptual parameterization
side-lighting mostly low order scattering thin parts and fine details Scene design mostly high order scattering thick body and base 15
16 Expanded phase function space Henyey-Greenstein (HG) lobes von Mises-Fisher (vMF) lobes hours sample 750+ phase functions Linear mixtures: HG + HG HG + vMF 750+ HDR images
Psychophysics Hmm, left 17 Paired-comparison experiments
Psychophysics 18 750 images = 200 million comparisons
19 Image-driven analysis 𝟑 ||
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20 Computational processing 𝟑 ||
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multidimensional scaling
1. Computational processing Our approach 2. Psychophysical validation 3. Analysis of results 21 image-driven analysis tractable experiment visualization, perceptual parameterization
22 Psychophysical validation 𝟑 ||
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clustering appearance space
Psychophysical validation 750 phase functions = 200 million comparisons 23 40 phase functions = 30,000 comparisons
Psychophysical validation • • use computational embedding as proxy for psychophysics generalize to all 750 images 25 perceptual embedding (non-metric MDS on psych. data)
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computational embedding (MDS using image metrics)
1. Computational processing Our approach 2. Psychophysical validation 3. Analysis of results 26 image-driven analysis tractable experiment visualization, perceptual parameterization
27 What we know so far • • • translucent appearance space two-dimensional perceptual consistent across variations of material, shape, illumination see paper for: 5000+ images, 9 more computational embeddings, 2 more psychophysical experiments including backlighting, analysis and statistics
28 Moving around the space
Moving around the space 30 moving vertically more diffused appearance
Moving around the space 32 moving horizontally more glass-like appearance
Moving around the space 33 we can move anywhere
35 What can we render with… single forward lobes forward + isotropic mixtures forward + backward mixtures
36 marble What can we render with… white jade
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with HG + isotropic white jade with vMF + vMF
Editing the phase function 37 1/ 1 − 𝜇 2 more glass-like 𝜇 1 2 move vertically
38 HG: g = 𝜇 1 Perceptual parameterization 0 0.4
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g move vertically
39 HG: g 2 Perceptual parameterization 0 0.32
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g 2 move vertically
40 HG: g = 𝜇 1 HG: g 2 Perceptual parameterization 0 g 2 move vertically
• Discussion handling other parameters of appearance: σ t , σ a , color • need to (further) scale up methodology • more general or data-driven phase function models • see our SIGGRAPH Asia 2013 paper!
• use in translucency editing and design user interfaces 41
Three take-home messages • • HG is not enough expanded space marble white jade • • computation + psychophysics large-scale perceptual studies • • 2D appearance space uniform parameterization 42
Acknowledgements • • Wenzel Jakob Bonhams • • • Funding: NSF NIH Amazon Dataset of 5000+ images: 43 http://tinyurl.com/s2013-translucency marble white jade
Computational embeddings 5000+ more HDR images material variation shape variation lighting variation
45 Scene design
Psychophysical validation 46 perceptual embedding (non-metric MDS on psych. data)
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computational embedding (MDS using image metrics)
Computational metrics cubic root L 2 -norm L 1 -norm
Perceptual image metrics material variation shape variation lighting variation
Embedding stability original perturbation 1 perturbation 2 perturbation 3 perturbation 4 perturbation 5
Distance metric 𝑑 𝑤 π 0 𝑝 1 , 𝑝 2 π 0 = 𝑤 θ 1 , θ 2 𝑝 1 θ 1 − 𝑝 2 θ 2 2 𝑑θ 1 𝑑θ 2 MDS sample 750+ phase functions MDS Davis et al. 2007
Non-metric MDS Learning from relative comparisons min 𝐾≥0 λ 𝐾 ∗ + 1 𝑆 𝑆 𝑠=1 𝐿 𝑑 𝐾 𝑖 𝑠 , 𝑘 𝑠 − 𝑑 𝐾 𝑖 𝑠 , 𝑗 𝑠 + 𝑏 non-metric MDS Hmm, left d >d Wills et al. 2009