Graphics Reference
In-Depth Information
Image capture
L
i
(
i
= 1, 2, 3) images
Step 1
Calculation of geometry (
K
) and reflectance (
P
)
Calculation of (
K
) and (
P
)
Step 2
L
i
=
L
i
-
PKL
i
(
i
= 1, 2, 3)
Figure 8.36
Recursive calculations to remove the effects of global illumination.
(After [Nayar
et al. 91].)
=
,
,
sources. For definiteness, these are indexed by
i
3. In Step 1, the geometry
of the object and the reflectance are recovered from the current set of images. A
variant of the radiosity method is employed to remove the GI components at each
interaction. The recovered geometry takes the form of a collection of
m
surface
facets, and the radiosity solution is computed using these facets as the surface
patches. The actual facets match the pixels directly: the facet corresponding to
pixel
j
is the subset of the object surface that projects to pixel
j
on the sensor
plane (assuming ideal focus, i.e., the pinhole camera model).
The coordinates of the facet vertices are recovered from the captured images
using photometric stereo, from which the normal vector is derived. Because the
surfaces are assumed to be Lambertian, the BRDF is constant, and the diffuse
reflectance (albedo) of a facet is directly proportional to the cosine of the light di-
rection. The computed normal
1
2
ρ
j
of facet
j
are recorded as part
of the geometry. From these, a “geometry matrix”
K
is constructed, the elements
K
j
,
k
correspond to the form factors between the facets:
K
j
,
k
is the amount of ra-
diant power leaving facet
j
that arrives at facet
k
. The radiosity equation cannot
be applied directly, because none of the facets emit light and the solution would
therefore be trivial (all the patches would be black). Instead, the “emission” term
for each facet is taken to be the direct illumination—it is assumed the the light
source is visible from each facet. Consequently, the surface radiance of patch
i
satisfies
n
j
and reflectance
L
j
+
ρ
j
k
L
j
K
jk
,
L
j
=
(8.10)
where
L
j
denotes the direct (one-bounce) lighting, computed from the source
intensity and the reflectance
ρ
j
of the facet.
In matrix form, Equation (8.10)
becomes
L
1
(
I
−
PK
)
L
=
,
(8.11)
