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Analysis of Subsurface Scattering
under Generic Illumination
Y. Mukaigawa K. Suzuki Y. YagiOsaka University, Japan
ICPR2008
Subsurface Scattering Light scattering in translucent media
Opaque
Translucent
Light Camerai o
x
Peers et al. SIGGRAPH2006
BRDF: ),,( oixF
Light Camerai o
oxix
Subsurface scattering
BSSRDF: ),,,( ooii xxS Bidirectional Reflectance
Distribution FunctionBidirectional Scattering SurfaceReflectance Distribution Function
Translucent objects Typical translucent object
marble, milk, and skin Actually, many objects in our living environment are
also translucent.
fruit
vegetablemilk
marblesoap
candleskin
plastic
cloth
paper
eggOne of the reasons that many photometric analyzing
methods do not work well in our living environment is
they cannot treat the subsurface scattering.
Related work BSSRDF measurement using special lighting devices
Projector[Tariq et al. VMV2006]
Fiber optic spectrometer[Weirich et al. SIGGRAPH2006 ]
Laser beam[Goesele et al. SIGGRAPH2004]
Projector[Peers et al. SIGGRAPH2006]
Measurement under strictly controlled illumination
Our goal Analysis of subsurface scattering under generic illumination
Inputs: single image, 3-D shape, illuminationOutputs: reflectance properties
Inverse rendering of translucent object
3-D shape
illumination
reflectanceproperties image
rendering
inverse rendering
Known
Unknown
Dipole Model for BSSRDF Decomposition of the BSSRDF into
Fresnel functions: Ft(, )
Diffuse subsurface reflectance: R(d)
R(d) is the function of the distance d between xi and xo. Including two inherent parameters of the material
scattering coefficient: s absorption coefficient: ai
odxi xo
),( )( ),( ,, ootiit FdRF ),,,( ooii xxS
(Jensen et al. SIGGRAPH2001)
Example of R(d)
Skin( σs=0.74,σa=0.032 )
Apple( σs=2.29,σa=0.003 )0.1
0.01
0.001
0.0001
2 4 6 8 d [mm]
R(d)
Inputs:
1. Estimating R(d) for several distances d.
2. Fitting of the dipole model.
Outputs: two parameters scattering coefficient s.
absorption coefficient a.
Flow of the proposed method
Single image 3-D shape Illumination Camera parameters
+
R(d)
d
estimated R(d)
dipole model fitting
Additional information
Formulation and solution Divide object surfaces into m small patches P1,P2,..., Pm.
Radiance lj of the patch Pj is formulated by
Quantization of the distances djk.
by n discrete distances d'1, d'2,...,d'n. Calculate only R'1, R'2,..., R'n. Linear solution, if n < m.
R(d)
dd'1 d'2 d'3 d'4 d'5
irradiance radiance
Pk Pj
R(djk)
ck ljdjk
m
kkjkj cdRl
1
)(unknownknownknown
Ill-posed problem m2 unknowns > m constraints
Model fitting Dipole model fitting to the estimated R'i Estimation of
scattering coefficient s absorption coefficient a
Discrete estimation R'1, ..., R'n for the quantized distances d'1, ..., d'n
Continuous estimation R(d) for every distance d
n
iii dRR
as 1
2
,)(minarg
R(d)
dd'1 d'2 d'3 d'4 d'5
R'iR(d)
Simulated scene Evaluate how the quantization of the distance affects the
accuracy of the estimated parameters.
Parameter estimation finding the best parameter set
that minimizes the error
Illumination
s=2.19a=0.002=1.3
Rendered image
parameters
s a d (mm)
Min 0.01 0.000 0.05
Max 3.00 0.010 0.50
Step 0.01 0.001 0.05
http://www.debevec.org/Probes/
Range and step of the parameters.
Results of parameter estimation
sampling
Quantization (mm) s a PSNR (dB)
0.05 2.14 0.000 26.5
0.10 2.20 0.007 42.1
0.15 2.19 0.004 30.6
0.20 2.19 0.009 33.5
0.25 2.19 0.005 28.7
0.30 2.32 0.009 29.8
0.35 2.34 0.009 47.9
0.40 2.22 0.009 25.8
0.45 2.18 0.009 20.4
0.50 2.40 0.009 23.4
Ground truth
2.19 0.002
Estimated parameters and the PSNRs
large
small
inaccurate
unstable
0
10
20
30
40
50
0.00 0.10 0.20 0.30 0.40 0.50
quantization (mm)
PSNR(dB)
best
best
Dipole model fitting The parametric model of R(d)
input image
regenerated image( PSNR 47.9dB )
Estimated R(d)
d ( mm )
R(d)
10-1
10-2
10-3
10-4
Ground truth
Estimated model
0 2 4 6 8 10
s=2.19a=0.002
s=2.34a=0.009
Real scene Evaluate the stability 3 materials:
Polypropylene (PP) Polyethylene (PE) Polyoxymethylene (POM)
2 shapes: Cube Pyramid (with base)
2 illuminations: Left and right directions.
In total, 12 images (3x2x2)
Environment for image capture
CameraCamera
Light sourceLight sourceTarget objectTarget object
Target objects
PP PE POM
Estimated parametersa
s0 1 2 3
0002
0004
0006
0008
0010
PP
PE
POM
PP POMPE
Parameters for each material Similar parameters for each
material except for some outliers. s of the cube under right
illumination is always outlier.
Averaged parameters R(d) for each material
Rendered images using estimated parametersd [mm]
R(d)10-1
10-2
10-3
10-4
0 2 4 6 8 10
PPPOM
PE
R(d)
The first step of the inverse renderingfor translucent objects.
Conclusion A new method to analyze subsurface scattering from
a single image taken under generic illumination Linear solution by quantizing the distance between patches. Parameter estimation by fitting dipole model.
Future works improvement of stability and accuracy