Graphics Reference
In-Depth Information
(a) (b) (c)
Figure 8.38
The effect global illumination has on reconstructed geometry of a concave Lambertian
object. (a) A cross section of the object. (b) Reconstructing the object assuming all il-
lumination is direct produces a pseudo shape that is incorrectly curved and more shallow
than the real object. (c) Repeatedly removing the indirect lighting from the reconstructed
geometry converges to the true shape. (After [Nayar et al. 91].)
of the true shape and albedo not only feasible but also robust—there is a single
mapping from the pseudo shape to the actual shape, so a convergent iterative
algorithm must find the actual shape. Figure 8.38(c) illustrates the convergence.
8.3.2 Separation in Non-Lambertian Environments
In a paper entitled “A Theory of Inverse Light Transport,” Steven M. Seitz, Ya-
suyuki Matsushita, and Kiriakos N. Kutulakos present a method of extracting the
effects due to direct illumination by multiplying the captured image with a matrix
in a single pass [Seitz et al. 05]. By analyzing the light transport based on the
rendering equation, it was proved in this paper that such a matrix exists regardless
of the reflectance characteristics of the object. Furthermore, the 1991 paper by
Nayar et al. depends on a precise geometric model of the object; the matrix in the
2005 paper can be created without such a model.
The method employs the remarkably simple idea of lighting an object with a
precise beam of light so narrow that it hits only “one pixel” of the object. That
is, given a camera position, the beam illuminates only the small area of the object
captured by a single pixel in the image. In this scenario, the object is assumed
to be contained in an entirely dark environment in which the light beam is the
only source of light. If the object is convex and exhibits no appreciable subsur-
face scattering, all the light reflects away from the object so there is no indirect
illumination. A captured image therefore has only one nonzero pixel, the pixel
corresponding to the illuminated point. Conversely, if such an image of an ar-
bitrary object has only one nonzero pixel, then there is no measurable indirect
light. The authors call such an image an
impulse scattering function
.
15
If an im-
15
The name “impulse” refers to the idea that the narrow light beam is essentially a Dirac δ illumi-
nation function; “impulse function” is another name for the Dirac δ often used in signal processing
literature.
