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Ver i ficat i on . From a mathematical perspective, the argument given in the pa-
per for the validity of the separation falls short of a rigorous proof. The authors
point out that the method only estimates the separation of global illumination.
It was therefore important to provide experimental verification of the method.
The authors created several physical test scenes that prominently exhibited inter-
reflection, volumetric scattering, and subsurface scattering. (The scenes shown
in Figures 8.44 and 8.45 are two of these test scenes.) To measure the accuracy
of the separation, they made an approximate direct measurement of the global
component at several points in the scene. This was accomplished by fully il-
luminating the scene except for a small region in the immediate vicinity of the
point to be measured, which is effected by deactivating small squares of pixels in
the projector that illuminate the point. A captured image of the scene so illumi-
nated therefore records only the global component at the point. A general sepa-
ration method can be verified by comparing this directly measured global com-
ponent to the computed global component. The authors experimented with the
size of the deactivated square, and found that measurements taken from squares
of 3
11 stayed within a 10% margin of error. One
exception is a test point on the slab of marble, which exhibits a lot of subsurface
scattering.
The authors ran several other sets of experiments. One set of experiments
varied the light patterns, maintaining the frequency and the overall coverage at
α =
×
3pixelstosquaresof11
×
1
2 . Comparing the results of the separation over all the patterns showed little
variation. Another set of experiments used a fixed-sized 6
6 square with varying
pixel coverages. This tested the validity of the general approach, by comparing
how the value of L g matches the theoretical approximation
×
L g on which the sep-
aration is ultimately based. The results showed that this proportional relationship
is generally valid for 0
α
9. The final experiment varied the frequency
of the checkerboard lighting pattern. For square sizes from 3 to 16 pixels, the
results varied little. However, with larger square sizes the illumination frequency
falls below the frequency of the interreflections, in which case the method does
not apply.
.
1
α
0
.
8.3.4 Extensions of the Separation Method
Depending on the light source, there are cases where capturing images under the
checkerboard illumination pattern is not practical. The test scenes in Figures 8.44
and 8.45 were illuminated in a lab by a digital projector. Large scenes, and out-
door scenes in daylight simply cannot be illuminated in this way. However, high
frequency illumination can be improvised. One way of doing this is to add an
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