Graphics Reference
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instead. The images are radiometrically calibrated, so each pixel of the HDR
image contains the value of the radiance coming from the corresponding point on
the object surface. Furthermore, the light source is included in at least one of the
HDR images and so its emissive radiance is also known. A geometric model of
the scene is assumed to be available; methods described in Chapter 5 can be used
to construct the model if it is not already known. At each image pixel, the 3D
coordinates of the light source, the camera position, and corresponding surface
point and surface normal are therefore known. The BRDF value at a surface point
is the outgoing radiance divided by the incident direct irradiance; however, the
outgoing radiance obtained from the HDR image includes
indirect
irradiance due
to global illumination. This has to be removed before the BRDF value can be
computed. Unfortunately, standard methods for doing this requires knowledge
of the BRDF of all the surfaces in the environment. Obtaining the BRDF is, in
essence, an inverse GI problem.
If all the surfaces are Lambertian, the exitant radiance is proportional to the
radiant exitance (radiosity) at the surface. In the radiosity method (see Chapter 2),
the environment is divided into surface patches and the lighting is assumed to be
constant over each patch. The reflectance of each patch can be determined from
the final radiosity solution. The radiant exitance
B
i
from patch
i
satisfies
∑
j
B
j
F
i
,
j
,
=
+
ρ
B
i
E
i
(8.8)
i
where
F
i
,
j
is the
form factor
between patch
i
and patch
j
, and represents the frac-
tion of radiant power leaving patch
i
that hits patch
j
(or vice versa). The
E
i
term
is the emission of the patch, and is zero unless the patch is a light source. In other
words, the radiant exitance
M
i
of patch
i
is proportional to the sum of the radiant
power received from all the other surface patches. The proportionality constant
ρ
i
is the diffuse reflectance (albedo) of patch
i
. Assuming for the moment that
the environment is entirely Lambertian, the small surface region corresponding
to each pixel in the HDR image can be treated as a surface patch. Normally the
radiosity method solves the system of equations formed from Equation (8.8) for
each patch
i
, but the inverse problem is actually much simpler. The exitance
B
i
(or
E
I
) of the patch is obtained from the pixel value. Equation (8.8) therefore has only
one unknown
ρ
i
, and can be solved directly, independent of the other equations.
Of course, real surfaces are not Lambertian. The problem becomes much
more complicated for general surface reflection. The diffuse reflectance term in
Equation (8.8) has to be replaced by a general model (Ward's model) to recover
specular reflectance. The approach used in the paper splits the diffuse component
of the BRDF. Directionality plays an important role in recovering the specular
components. Suppose a camera at
C
v
captures a patch
P
i
that has a notable spec-
