SIGGRAPH 2013 slides
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Understanding the role of phase function in translucent appearance 1 Ioannis Gkioulekas1 Bei Xiao2 Shuang Zhao3 Edward Adelson2 Todd Zickler1 Kavita Bala3 1Harvard 2MIΤ 3Cornell Translucency is everywhere 2 food skin jewelry architecture Subsurface scattering outgoing direction incident direction isotropic extinction coefficient σt (λ) radiative transfer equation 3 absorption coefficient σa(λ) phase function p(λ) Chandrasekhar 1960 Phase function is important thick parts (diffusion) thin parts 4 Common phase functions Henyey-Greenstein (HG) lobes single-parameter family: g= ∈ π−1,1 1 average cosine π1 = cos π = 5 1 π −1 cos π cos π π cos π Henyey and Greenstein 1941 What can we represent with HG? marble 6 ο white jade ο ο microcrystalline wax Jensen 2001 Henyey-Greenstein is not enough soap setup photo microcrystalline wax 7 HG Goals 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: single-parameter family: g = π1 π = 2π1 / 1 − π2 average cosine π1 = cos π = −11 π cos π cos π π cos π second moment π2 = −11 π cos π cos π 2π cos π 9 Expanded phase function space soap setup photo microcrystalline wax 10 HG vMF Expanded phase function space Henyey-Greenstein (HG) lobes von Mises-Fisher (vMF) lobes single-parameter family: single-parameter family: g = π1 Linear mixtures: HG + HG 11 π = 2π1 / 1 − π2 HG + vMF vMF + vMF Redundant phase function space ≈ 12 f( ) ≠≈ f( ) 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 Our approach 14 1. Computational processing 2. Psychophysical validation 3. Analysis of results image-driven analysis tractable experiment visualization, perceptual parameterization Scene design side-lighting mostly loworder scattering thin parts and fine details 15 mostly highorder scattering thick body and base Expanded phase function space 3000 machine von Mises-Fisher (vMF) lobes hours Henyey-Greenstein (HG) lobes sample 750+ phase functions Linear mixtures: HG + HG HG + vMF 750+ HDR images 16 Psychophysics Hmm, left Paired-comparison experiments 17 Psychophysics 750 images = 200 million comparisons 18 Image-driven analysis π Ηd( 19 || π -, || )Η ≈ Computational processing Η π || - π || ≈ Η multidimensional scaling 20 two-dimensional 750 HDR images appearance embedding space Our approach 21 1. Computational processing 2. Psychophysical validation 3. Analysis of results image-driven analysis tractable experiment visualization, perceptual parameterization Psychophysical validation Η π || - π || Η clustering 22 40 representative two-dimensional images 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 perceptual embedding 25 (non-metric MDS on psych. data) ≈ computational embedding (MDS using image metrics) Our approach 26 1. Computational processing 2. Psychophysical validation 3. Analysis of results image-driven analysis tractable experiment visualization, perceptual parameterization 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 27 Moving around the space 28 Moving around the space moving vertically 30 more diffused appearance Moving around the space moving horizontally 32 more glass-like appearance Moving around the space we can move anywhere 33 What can we render with… single forward lobes forward + isotropic mixtures forward + backward mixtures 35 What can we render with… marble ≠ white jade 36 best approximation marble white jade with HG + isotropic with vMF + vMF Editing the phase function 37 1/ 1 − π2 move horizontally more glass-like π1 2 move vertically Perceptual parameterization 0 HG: g = π1 0.4 0.8 38 g move vertically Perceptual parameterization 0 HG: g 2 0.32 0.64 39 g2 move vertically Perceptual parameterization 0 HG: g = π1 HG: g 2 0.32 0.4 0.64 0.8 40 g2 move vertically Discussion • handling other parameters of appearance: σt, σa, 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 • computation + psychophysics • large-scale perceptual studies • 2D appearance space • uniform parameterization 42 marble white jade 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 Scene design 45 Psychophysical validation perceptual embedding 46 (non-metric MDS on psych. data) ≈ computational embedding (MDS using image metrics) Computational metrics cubic root L2-norm L1-norm Perceptual image metrics material variation shape variation lighting variation Embedding stability original perturbation 3 perturbation 1 perturbation 4 perturbation 2 perturbation 5 ππ€ π1 , π2 = π 0 Distance metric π 0 π€ θ1 , θ2 π1 θ1 − π2 θ2 sample 750+ phase functions 2 πθ1 πθ2 MDS MDS Davis et al. 2007 Non-metric MDS Learning from relative comparisons 1 π min λ πΎ ∗ + πΏ ππΎ ππ , ππ − ππΎ ππ , ππ + π πΎ≥0 π π =1 non-metric MDS Hmm, left d >d Wills et al. 2009
