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

0.64

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