0
50
100
150
200
250
020406080100120140160180200
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.80 0.00 [cm] 0.20 0.40 0.60
Shape from Single Scattering for Translucent Objects
Outline
Our proposal is
Implementation
[cm] 0.25 0.00 0.05 0.10 0.15 0.20
0.25 0.00 0.05 0.10 0.15 0.20 [cm]
Estimated scattering parameters
Scattering decomposition [Mukaigawa et al. CVPR2010]
Phase function Represents scattering distribution
2
3
2
2
)cos21(
1
4
1),(
gg
ggp
)(exp),( 21 ddgpsI t
g=0 g>0 g<0 Forward
scattering Backward scattering
Isotropic scattering
Scaling constant
Extinction coefficient
Length of light path
High frequency stripe pattern
Single scattering
Multiple scattering
Projector
Scattering in object
Single scattering (Unique light path)
Multiple scattering (Multiple light path)
= +
Chika Inoshita* Yasuhiro Mukaigawa* Yasuyuki Matsushita** Yasushi Yagi*
*Osaka University **Microsoft Research Asia
Measurement setting
Single Scattering from
Single scattering model
Experimental results
Light path to height
Estimate surface shape h(x, y) from intensity of single scattering I(x, y)
p
out
t
in
t gpyxFFsyxI , ),( ),(
Height is related to
observed intensity Target objects Single scatterings I(x, y)
Estimated heights h(x, y)
I1 I2 I3 I4
I5 I6 I7
I8 I9 I1
0
0 0.2 0.4 0.6 0.8 1 1.2 0
1000
2000
3000
4000
[cm]
I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
Synthesized intensities (Gaussian noise: σ=10) Estimated heights
0 0.2 0.4 0.6 0.8 1 1.2 [cm] -0.1
0
0.1
0.2
[cm]
=0 (Estimation) =10 (Estimation) =20 (Estimation) Ground truth
=0 (initial) =10 (initial) =20 (initial)
Synthetic data and estimated results in 1D
Scaling constant s
Scattering parameter g
Extinction coefficient σt
RSME [cm]
Ground truth - Noise: σ=0
Noise: σ=10
Noise: σ=20
Numerical evaluation
Synthetic data and estimated result in 2D
1500
2500
3500
4500
5500
6500
1500
2500
3500
4500
5500
6500
0
0.9 0.6
0.3 [cm]
0.3
0.1 0
[cm]
0.2
Ground truth Estimated height
Synthesized intensity (Gaussian noise: σ=5)
s
g
σt
Synthesized intensities
Simultaneous estimation of surface shape h(x, y) and scattering parameters s, g, and σt
Estimate initial shape and scattering parameters
Refine shape and parameters
h(x，y) s, g, σt
p=π/2
*ignoring refraction
…
x
d1
d2
dn
Intensities
Real intensities
…
x
d1
d2
dn
Intensities No
Yes
end
same?
Shape
r
it
dyxhx
sin
),(exp
Projector (3M MPro110)
Camera (Point grey Grasshopper2)
Telecentric lens (Edmund optics)
21cm
15cm
Target object
Assumptions - Homogeneous material - Orthographic projection - Planar incident surface
z
(x, y)
y x
I(x, y)
p Scattering point (x’, y’)
r
di
h(x, y)
Camera
Light source
d1
d2
p(g, )
I
