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Figure 8.39 Matrix T accounts for the effects of global illumination. (After [Seitz et al. 05].)
pulse scatter function is captured for each separately lit pixel, and each image is
arranged into a column vector, they collectively form the columns of a square ma-
trix T . In the absence of indirect lighting, each impulse scatter function has only
one nonzero value, which corresponds to the single lit pixel in the image. In this
case, the collective matrix T is a diagonal matrix. Conversely, a diagonal matrix
T implies there is no indirect lighting. Consequently, the process of removing the
indirect component amounts to converting the impulse scattering function matrix
T to a diagonal matrix. This casts the separation of direct lighting as the process
of diagonalizing the matrix T . In the case of a purely Lambertian surface, the
diagonal matrix is proportional to the reflectance matrix P in Equation (8.11) and
diagonalization corresponds to the operation of removing the effects of indirect
illumination in the 1991 paper. Figure 8.39 illustrates the idea.
8.3.3 A New Concept for Separation
The main result of the 2005 paper by Seitz et al., the existence of a matrix to
remove the effects of indirect illumination regardless of the characteristics of the
reflection of the object, certainly has theoretical importance. However, in order
to apply the method in practice, the impulse scattering images would have to be
physically obtained. While not impossible, it would require a precisely controlled
collimated light source, and a huge number of captured images. Subsequent re-
search concentrated on ways to reduce the number of images, and also on finding
more practical capture methods. The 2006 paper “Fast Separation of Direct and
Global Components of a Scene using High Frequency Illumination” by Nayar
et al. mentioned above was a major advance on both fronts. This paper was also
considered a landmark work in the nascent field of computational photography.
In computer vision, the main purpose of separating direct lighting from global
illumination had been to improve the accuracy of geometry reconstruction. In
contrast, Nayar's goal was to develop a method for re-rendering a captured im-
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