SIGGRAPH 2013 slides

Report
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=
∈ −1,1
1
average cosine 1 = cos  =
5
1

−1
cos  cos   cos 
Henyey and Greenstein 1941
What can we represent with HG?
marble
6

white jade


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 = 1
 = 21 / 1 − 2
average cosine 1 = cos  = −11  cos  cos   cos 
second moment 2 = −11  cos  cos  2 cos 
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 = 1
Linear mixtures:
HG + HG
11
 = 21 / 1 − 2
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

ǁd(
19
||

-,
||
)ǁ ≈
Computational processing
ǁ

||
-

||
≈
ǁ
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
ǁ

||
-

||
ǁ
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 − 2
move horizontally
more glass-like
1
2
move vertically
Perceptual parameterization
0
HG: g = 1
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 = 1
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
 1 , 2 =
π
0
Distance metric
π
0
 θ1 , θ2 1 θ1 − 2 θ2
sample 750+
phase functions
2
θ1 θ2
MDS
MDS
Davis et al. 2007
Non-metric MDS
Learning from relative comparisons
1 
min λ  ∗ +
   ,  −   ,  + 
≥0

=1
non-metric
MDS
Hmm, left
d >d
Wills et al. 2009

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