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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
11
g=𝜇1 𝜅=2𝜇1/ (1−𝜇2 )
f( ) f( )
Redundant phase function space
≈
≠12
≈
Related work
13
• 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
14
Scene design
mostly low-order scattering
mostly high-order scattering
side-lighting
thick body and base
thin parts and fine details
15
von Mises-Fisher (vMF) lobes
Linear mixtures:HG + HG HG + vMF
Henyey-Greenstein (HG) lobes
Expanded phase function space
16
sample 750+ phase functions
3000 machine hours
750+ HDR images
Psychophysics
Paired-comparison experiments
Hmm, left
17
Psychophysics
750 images = 200 million comparisons
18
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
25
≈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
27
see paper for: 5000+ images, 9 more computational embeddings, 2 more psychophysical experiments including backlighting, analysis and statistics
Moving around the space
28
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
33
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
41
• 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)
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