Understanding the role of phase function in translucent appearance

1. Understanding the role of phase function in translucent appearance Ioannis Gkioulekas1 Shuang Zhao3 Bei Xiao2 KavitaBala3 Todd Zickler1 Edward Adelson2 1Harvard 2MIΤ 3Cornell

2. Translucency is everywhere skin food architecture jewelry

3. Subsurface scattering • outgoing direction • incident direction • isotropic • extinction coefficient σt (λ) • absorption coefficient σa (λ) (λ) • radiative transfer equation • phase function p • Chandrasekhar 1960

4. Phase function is important • thick parts (diffusion) • thin parts

5. Common phase functions • Henyey-Greenstein (HG) lobes • single-parameter family: • average cosine • Henyey and Greenstein 1941

6. What can we represent with HG?    • microcrystalline wax • marble • white jade • Jensen 2001

7. Henyey-Greenstein is not enough • soap • setup • photo • HG • microcrystalline wax

8. Goals ? ? • expanded phase function space • role in translucent appearance

9. Expanded phase function space • von Mises-Fisher (vMF) lobes • Henyey-Greenstein (HG) lobes • single-parameter family: • single-parameter family: • average cosine • second moment

10. Expanded phase function space • soap • setup • photo • HG • vMF • microcrystalline wax

11. Expanded phase function space • von Mises-Fisher (vMF) lobes • Henyey-Greenstein (HG) lobes • single-parameter family: • single-parameter family: • Linear mixtures: • vMF + vMF • HG + HG • HG + vMF

12. Redundant phase function space ≈ ≠ f( ) f( ) ≈

13. Related work • Fleming and Bülthoff 2005, Motoyoshi2010 • 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

14. Our approach • 1. Computational processing • 2. Psychophysical validation • 3. Analysis of results • image-driven analysis • tractable experiment • visualization, perceptual parameterization

15. Scene design • side-lighting • mostly low-order scattering • mostly high-order scattering • thin parts and fine details • thick body and base

16. Expanded phase function space • von Mises-Fisher (vMF) lobes • Henyey-Greenstein (HG) lobes • sample 750+ phase functions • Linear mixtures: • HG + HG • HG + vMF • 3000 machine hours • 750+ HDR images

17. Psychophysics • Hmm, left • Paired-comparison experiments

18. Psychophysics • 750 images = 200 million comparisons

19. Image-driven analysis d( , ) ǁ - ǁ ≈

20. Computational processing ≈ ǁ - ǁ • multidimensional scaling • two-dimensional appearance space • two-dimensional embedding • 750 HDR images

21. Our approach • 1. Computational processing • 2. Psychophysical validation • 3. Analysis of results • image-driven analysis • tractable experiment • visualization, perceptual parameterization

22. Psychophysical validation ǁ - ǁ • clustering • two-dimensional appearance space • 40 representative images

23. Psychophysical validation • 750 phase functions = 200 million comparisons • 40 phase functions = 30,000 comparisons

24. Psychophysical validation • use computational embedding as proxy for psychophysics • generalize to all 750 images ≈ • perceptual embedding • computational embedding • (MDS using image metrics) • (non-metric MDS on psych. data)

25. Our approach • 1. Computational processing • 2. Psychophysical validation • 3. Analysis of results • image-driven analysis • tractable experiment • visualization, perceptual parameterization

26. 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 • more diffused appearance • moving vertically

29. Moving around the space • more glass-like appearance • moving horizontally

30. Moving around the space • we can move anywhere

31. What can we render with… • single forward lobes • forward + isotropic mixtures • forward + backward mixtures

32. What can we render with… • marble ≠ • white jade • best approximation • with HG + isotropic • marble • white jade • with vMF + vMF

33. Editing the phase function • more diffused • move horizontally • move vertically • more glass-like

34. Perceptual parameterization • 0 • HG: • 0.4 • 0.8 • move vertically • g

35. Perceptual parameterization • 0 • HG: • 0.32 • 0.64 • move vertically • g2

36. Perceptual parameterization • 0 • HG: • HG: • 0.32 • 0.4 • 0.64 • 0.8 • move vertically • g • g2

37. 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

38. Three take-home messages • HG is not enough • expanded space • marble • white jade • computation + psychophysics • large-scale perceptual studies • 2D appearance space • uniform parameterization

39. Acknowledgements • Wenzel Jakob • Bonhams • marble • white jade • Funding: • NSF • NIH • Amazon • Dataset of 5000+ images: http://tinyurl.com/s2013-translucency

40. Computational embeddings • 5000+ more HDR images • material variation • shape variation • lighting variation

41. Scene design

42. Psychophysical validation ≈ • perceptual embedding • computational embedding • (MDS using image metrics) • (non-metric MDS on psych. data)

43. Computational metrics • cubic root • L2-norm • L1-norm

44. Perceptual image metrics • material variation • shape variation • lighting variation

45. Embedding stability • perturbation 2 • original • perturbation 1 • perturbation 4 • perturbation 3 • perturbation 5

46. Distance metric • MDS • sample 750+ phase functions • MDS • Davis et al. 2007

47. Non-metric MDS • Learning from relative comparisons • non-metric • MDS • Hmm, left d >d • Wills et al. 2009