Understanding the role of phase function in translucent appearance

Ioannis Gkioulekas1 Bei Xiao2 Shuang Zhao3

Edward Adelson2 Todd Zickler1 Kavita Bala3

1Harvard 3Cornell2MIΤ

1

Translucency is everywhere

food skin

jewelry architecture

2

Subsurface scattering

radiative transfer equation

Chandrasekhar 1960

phase function pabsorption coefficient σa

extinction coefficient σt

3

isotropic

incident direction

outgoing direction

(λ)(λ)

(λ)

Phase function is important

thick parts (diffusion)

thin parts4

Common phase functions

single-parameter family:

Henyey-Greenstein (HG) lobes

g=𝜇1

5 Henyey and Greenstein 1941

average cosine

g∈ (−1,1 )❑

What can we represent with HG?

microcrystalline wax

6

marble white jade

Jensen 2001

Henyey-Greenstein is not enough

soap

microcrystalline wax

photo HG

setup

7

Goals

8

expanded phase function space role in translucent appearance

??

Expanded phase function space

single-parameter family:

Henyey-Greenstein (HG) lobes

g=𝜇1

9

average cosine second moment

von Mises-Fisher (vMF) lobes

single-parameter family:𝜅=2𝜇1/ (1−𝜇2 )

Expanded phase function space

soap

microcrystalline wax

photo HG

setup

vMF

10

Expanded phase function space

single-parameter family:

Henyey-Greenstein (HG) lobes von Mises-Fisher (vMF) lobes

single-parameter family:

Linear mixtures:HG + HG HG + vMF vMF + vMF

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g=𝜇1 𝜅=2𝜇1/ (1−𝜇2 )

f( ) f( )

Redundant phase function space

≈

≠12

≈

Related work

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• Fleming and Bülthoff 2005, Motoyoshi 2010

• Pellacini et al. 2000, Wills et al. 2009

• many perceptual cues• do not study phase function

• gloss perception• much smaller space

• Ngan et al. 2006 • gloss perception• navigation of appearance space

Our approach1. Computational

processing2. Psychophysical

validation3. Analysis of

results

image-driven analysis tractable experiment visualization, perceptual parameterization

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Scene design

mostly low-order scattering

mostly high-order scattering

side-lighting

thick body and base

thin parts and fine details

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von Mises-Fisher (vMF) lobes

Linear mixtures:HG + HG HG + vMF

Henyey-Greenstein (HG) lobes

Expanded phase function space

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sample 750+ phase functions

3000 machine hours

750+ HDR images

Psychophysics

Paired-comparison experiments

Hmm, left

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Psychophysics

750 images = 200 million comparisons

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d( , ) ǁ - ǁ𝟑√¿∨¿𝟑√¿∨¿

Image-driven analysis

≈

19

two-dimensional appearance spacetwo-dimensional

embedding

Computational processing

750 HDR images

ǁ - ǁ𝟑√¿∨¿𝟑√¿∨¿

multidimensional scaling

20

≈

Our approach1. Computational

processing2. Psychophysical

validation

image-driven analysis tractable experiment

21

3. Analysis of results

visualization, perceptual parameterization

40 representative images

Psychophysical validation

ǁ - ǁ𝟑√¿∨¿𝟑√¿∨¿

clustering

two-dimensional appearance space

22

Psychophysical validation

750 phase functions = 200 million comparisons40 phase functions = 30,000 comparisons23

computational embedding

Psychophysical validation

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≈perceptual embedding

• use computational embedding as proxy for psychophysics

• generalize to all 750 images

(non-metric MDS on psych. data) (MDS using image metrics)

Our approach1. Computational

processing2. Psychophysical

validation

image-driven analysis tractable experiment

26

3. Analysis of results

visualization, perceptual parameterization

What we know so far

translucent appearance space• two-dimensional• perceptual• consistent across variations of

material, shape, illumination

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see paper for: 5000+ images, 9 more computational embeddings, 2 more psychophysical experiments including backlighting, analysis and statistics

Moving around the space

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Moving around the space

moving vertically more diffused appearance30

Moving around the space

moving horizontally more glass-like appearance32

we can move anywhere

Moving around the space

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What can we render with…

single forward lobesforward + isotropic mixturesforward + backward mixtures

35

What can we render with…marble

white jade

marble white jadewith vMF + vMF

best approximationwith HG + isotropic

36

≠

Editing the phase function

move horizontally move vertically37

1/√1−𝜇2𝜇1

2more glass-like

mor

e di

ffuse

d

g

Perceptual parameterization

move vertically0.8

0.4

0

38

HG:

HG:

0.32

Perceptual parameterization

move vertically0.64

g239

0

HG:

Perceptual parameterization

40

move vertically

0

g

0.8

0.40.32

0.64

g2

HG:

Discussion

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• handling other parameters of appearance: σt, σa, color

• more general or data-driven phase function models

• use in translucency editing and design user interfaces

• need to (further) scale up methodology

• see our SIGGRAPH Asia 2013 paper!

Three take-home messages

• HG is not enough• expanded space

• computation + psychophysics• large-scale perceptual studies

• 2D appearance space• uniform parameterization

42

white jademarble

Acknowledgements

• Wenzel Jakob• Bonhams

Funding:• NSF • NIH • Amazon

white jademarble

43 http://tinyurl.com/s2013-translucency

Dataset of 5000+ images:

Computational embeddings

material variation shape variation lighting variation

5000+ more HDR images

Scene design

45

computational embedding

Psychophysical validation

46

≈perceptual embedding(non-metric MDS on psych. data) (MDS using image metrics)

Computational metrics

L1-normL2-normcubic root

Perceptual image metrics

material variation shape variation lighting variation

Embedding stability

original perturbation 1 perturbation 2

perturbation 3 perturbation 4 perturbation 5

Distance metric

MDS

Davis et al. 2007

sample 750+ phase functions

MDS

Non-metric MDS

Wills et al. 2009

Learning from relative comparisons

non-metric MDS

d >d

Hmm, left

min𝐾 ≥ 0

λ‖𝐾‖∗+1𝑆∑

𝑠=1

𝑆

𝐿 (𝑑𝐾 (𝑖𝑠 ,𝑘𝑠 )−𝑑𝐾 (𝑖𝑠 , 𝑗𝑠 )+𝑏)