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the corresponding pixel values. This completes the construction of the reflectance
field for an arbitrary viewpoint and lighting direction. As previously mentioned,
the reflectance field includes the effects of phenomena such as indirect illumi-
nation and subsurface scattering. It also includes shadowing, but a correction is
necessary for shadows. The authors employ a thresholdingmethod to determine if
a point is in shadow: if the value of a pixel in the synthesized reflectance function
falls below this threshold, the point is assumed to be in shadow.
The method described in the “reflectance field” paper assumes the object is
static. It becomes difficult to calculate reflections using only the information from
the reflectance field in cases where the original object changes shape, or if the
reflections on the original object are partially occluded by another object that was
not there at the time of capture. Reflectance fields also do not capture the change
in reflectance due to a change in position of the object. These limits are overcome
with techniques introduced in the next chapter.
8.2.5 A Reflectance Field for Variable Geometry
A drawback of the reflectance field is that it does not handle any changes in the
shape of the object. One method of acquiring the reflectance of a deforming
object would be to capture a new set of images with a light stage each time the
object changes shape, thereby creating a new reflectance field from those images.
However, this is obviously not an efficient (or practical) method. Even if the
data were available, as it could be if the object were synthetically rendered, some
way of parameterizing the deformation would be needed, and each deformation
parameter adds another variable to the reflectance field function.
The assumption of a static model is particularly troublesome in modeling
facial reflectance, because human faces are constantly changing. An efficient
method of calculating the reflectance field for an animated face was introduced
in the paper “Animatable Facial Reflectance fields” by Tim Hawkins, Andreas
Wenger, Chris Tchou, Andrew Gardner, Fredrik Goransson, and Paul E. De-
bevec [Hawkins et al. 04]. The paper describes a scheme of obtaining the re-
flection for a face after it has changed shape, using the reflectance functions of
the original shape. The method requires a precise model of the face geometry,
which is obtained by placing fiducial marker dots on the subject's face. The au-
thors used 300 dots, and captured light stage image sets for six different camera
positions. The process was repeated for 60 different expressions. The dots in the
image sets were then registered to produce a deformable triangulated model of
the face.
The ultimate goal of the work was to produce a reflectance field model valid
for arbitrary deformations and also arbitrary viewing directions. The underlying
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