Graphics Reference
In-Depth Information
Q
P
i
A
j
L
P
i
A
j
Q
C
k
A
j
P
i
C
k
C
v
(b)
Figure 8.23
(a) The radiance
L
P
i
A
j
from patch
A
j
to point
P
i
on patch
A
i
is needed in the inverse GI
problem but is not usually available. The radiance
L
C
k
A
j
captured by another camera
C
k
is an approximation. (b) To calculate Δ
S
, the reflectance of patch
A
j
is approximated by
tracing incident light in a cone of directions around the specular directions.
(a)
(After [Yu
et al. 99].)
ular component. The specular reflectance depends on the radiance from all other
patches. These values cannot be measured directly; the radiance
L
P
i
,
A
j
of light
traveling from a particular patch
A
j
to patch
P
i
is only available if there happens
to be an image from a camera placed directly between the patches. This is not
likely, but there might be an image captured from a point that “sees” patch
A
j
from a similar viewing angle (see
Figure 8.23
). Suppose an image from a camera
at a point
C
k
captures the radiance
L
C
k
,
A
j
from patch
A
j
.If
A
j
were Lambertian,
the radiance values
L
P
i
,
A
j
and
L
C
k
,
A
j
would be equal. For a general surface, the
radiance varies by a value denoted by
Δ
S
:
L
P
i
A
j
=
L
C
k
A
j
+
Δ
.
S
The values of
S
are obtained iteratively, with each iteration improving the values.
The algorithm for recovering the specular reflectance starts by assuming
Δ
Δ
0. Incidentally, this does not mean the reflection is necessarily diffuse, it
just means that the radiance values are close enough for an initial approximation.
Assuming
S
=
0, the algorithm uses a nonlinear optimizer to approximate the
BRDF parameters. From these, new values of
Δ
S
=
S
are computed, and the BRDF
parameters are estimated again using the updated
Δ
S
values. The process contin-
ues until a termination condition is reached; the algorithm described in the paper
stops after a fixed number of iterations. The key to the algorithm is the method
used to approximate
Δ
S
is in essence the vari-
ation in the specular component. A simple approximation can be obtained by
reversing the paths: i.e., tracing the rays in the mirror directions of the directions
Δ
S
at each iteration. The value of
Δ
