The domains in which we have characterized natural illumination statistics — distributions of intensities, power spectra, and distributions of wavelet coefficients — are also used to characterize texture (Heeger & Bergen,
1995; Portilla, Strela, Wainwright, & Simoncelli,
2001). Indeed, we might think of illumination patterns as types of textures. We can test the extent to which a set of statistics captures the perceptually essential characteristics of real-world illumination by applying texture synthesis algorithms to generate novel illuminations whose statistics match those of real-world illuminations. Panel (a) of
Figure 18 shows a sphere rendered under the photographically acquired illumination map of
Figure 7(d). Panels (b), (c), and (d) show identical spheres rendered under synthetic illumination maps. The illumination map of (b) consists of Gaussian noise with a 1/
f2 power spectrum; although the power spectrum resembles that of natural illumination, the resulting sphere does not look realistic at all.
4 The illumination map of (c) was synthesized to have a pixel intensity distribution and marginal wavelet coefficient distributions identical to those of (a), using the texture synthesis technique of Heeger and Bergen (
1995). This sphere looks much more realistic, and human observers are able to recognize that its reflectance properties are similar to those of the sphere in (a) (Fleming, Dror, et al.,
2003). Finally, the illumination map of (d) was created using the texture synthesis technique of Portilla and Simoncelli (
2001), which ensures that not only its pixel intensity distribution and marginal wavelet coefficient distributions but also certain properties of its joint wavelet coefficient distributions match those of (a). This synthetic illumination map captures the presence of edges in the real illumination map, leading to a sphere whose apparent reflectance properties are even more similar to that of (a). This suggests that the statistical properties of natural illumination described in this chapter play an important role in reflectance estimation by the human visual system (as discussed in Fleming, Dror, et al.,
2003). It also suggests that one may be able to produce realistic renderings using properly synthesized illumination.