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the splitting of illumination into direct and indirect lighting, is frequently used
in global illumination computation. As described in Chapter 1, reasons for this
come from the greater importance of direct lighting, and the greater difficulty of
indirect lighting computation. However, the inverse process of splitting captured
radiance into direct and indirect components remained an unsolved problem. The
method of employing polarizing filters described previously does do a form of
this separation, as the specular reflection comes from direct lighting, but this does
not work for the diffuse reflection (which has a direct and indirect component). It
also requires the use of polarized illumination and capture, which is not always
possible. Had a more general method for image-based separation of direct and
global illumination been available, it might have provided a more accurate way of
acquiring the reflection field.
A flexible method for performing the direct/global split was presented in a
paper entitled “Fast Separation of Direct and Global Components of a Scene
using High Frequency Illumination” by Shree K. Nayar, Gurunandan Krishnan,
Michael D. Grossberg, and Ramesh Raskar. Nayar, an expert in computer vision,
has studied the problem of removing global illumination since the 1990s. The
problem is fundamental in computer vision. A number of image-based methods
described in this topic so far have depended on how the pixel colors change with
variations in lighting and surface orientation. The effects of indirect lighting com-
plicates this substantially. A particularly difficult situation arises when the object
is concave: indirect illumination is more prominent for such objects because of
the orientation of the nearby surfaces (see
Figure 8.38
)
. If the shape recovery as-
sumes all the lighting is direct, the extra interreflection increases the error in the
recovered geometry.
8.3.1 Separation in the Lambertian Case
Nayar along with Katsushi Ikeuchi and Takeo Kanade developed a method that
splits global illumination from direct lighting in the context of recovering geome-
try, which they described in a paper entitled “Shape from Interreflection” [Nayar
et al. 91]. The method solves the separation problem for purely Lambertian sur-
faces. Starting with captured images, which naturally include GI, a preliminary
geometric model is recovered by applying a basic photometric stereo algorithm.
The GI solution for this preliminary model is an approximate solution to the real
model; removing the indirect component from the original images and recovering
the geometry again provides a better geometric model. This process is repeated
until the model converges.
Figure 8.36 contains a flowchart of the iterative algorithm. At the outset, a
collection of images of the object are captured under three separate illumination
