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of known albedo. The total incident flux, as recorded by the camera, can be
computed by summing the radiant exitance values over all the pixels. Dividing a
pixel value in the original HDR image produces the value of
R
d
at that point.
The next step is to fit values of
σ
s
to this measured
R
d
data. Be-
σ
a
and
cause
R
d
(
depends only on the distance from the illumination point, this can be
done along any line from the illumination point
p
rather than across the entire im-
age. Figure 4.8 contains a plot of the authors' measurements for a slab of marble
along with the plot of the dipole model using the parameter values fit from the
measured data. To further validate the model, the authors ran a Monte Carlo sim-
ulation of multiple scattering using these parameters, the result of which is also
shown in the plot of Figure 4.8. The Monte Carlo simulation, the dipole model,
and the measured results are remarkably close for these particular materials. Ta-
ble 4.1 contains the values of the parameters in red, green, and blue spectral bands.
Notice that scattering dominates absorption.
The authors applied the measurement and verification process to several dif-
ferent materials, including the marble sample, milk, and human skin. Table 4.1
contains the parameter values fit to the measurements. In all of these cases, the
degree of scattering is much larger than the absorption. Subsurface scattering
is likely to be important in such materials, so the authors concluded the model
r
)
10
0
measured data
dipole model
Monte Carlo simulation
10
−1
10
−2
10
−3
10
−4
10
−5
10
−6
0
2
4
6
8
10
12
14
16
18
20
r
(mm)
Figure 4.8
Verification of the dipole model for a marble slab, comparing the dipole-based BSSRDF
model and a Monte Carlo simulation of scattering in the material to measured data. (From
[Jensen et al. 01b] c
2001 ACM, Inc. Included here by permission.)
