Billock, Cunningham & Tsou (2008) 3 APPROVED FOR PUBLIC RELEASEthat have similar second-order statistics must usually be compared on a more laborious point-by-point basis (Julesz & Caelli, 1979; Caelli, 1981). Most natural (and many artificial) images have surprisingly regular 1/fȕ Fourier spatial amplitude spectra (Table 1; see Field & Brady, 1997 and Billock, 2000 for review), a signature which is mimicked by random fractals and which forms the basis for fractal forgeries (Voss, 1985) and digital camouflage. The exponent ȕ (the slope of the Fourier spectra when plotted on log-log coordinates) is a second-order statistic. A growing body of evidence suggests that humans are adapted to this statistical regularity in the environment and that this evolutionary/developmental adaptation forms the basis for neural image enhancement and debluring (Billock, 2000; Billock et al., 2001a,b; Campbell et al., 1978; Hammett & Bex, 1996). A hallmark of random fractal images is the presence of statistically similar features at every spatial scale. The lawful relationship between spatial scales is termed self-similarity and is one of the properties of natural images that give rise to 1/fȕ spectra. This property is what enables random fractals to mimic natural images and backgrounds. For example, a tree branch gives rise to several smaller branches, which give rise to many twigs-a random fractal that distributes and scales its features similarly can emulate foliage and act as camouflage. The ȕ value (or equivalently, fractal dimension) is often used as a mathematical measure of image texture and its perceptual correlates (Cutting & Garvin, 1987; Kumar et al., 1993; Pentland, 1988; Rogowitz & Voss, 1990; Taylor et al., 2005). It follows that some aspects of fractal image discrimination can emulate natural image discrimination (Hansen & Hess, 2006; Thomson & Foster, 1997; Parraga & Tolhurst, 2000; Tolhurst & Tadmor, 2000). Table 1. Second-order statistics of natural images Study Number of images ȕ±1sd Burton & Morehead (1987) 19 1. 05±. 12 Field & Brady (1997) 20 1. 10±0. 14 Parraga (1998) 29 1. 11±0. 13 Ruderman (1994) 45 0. 905 Webster & Miyahara (1997) 48 1. 13 Thomson & Foster (1997) 82 1. 19 Field (1993) 85 1. 10 van Hateren (1992) 117 1. 065±. 18 Tolhurst et al. (1992) 135 1. 20±. 13 Schaaf & Hateren (1996) 276 0. 94±0. 21 Dong & Atick (1995) 320 1. 15 Weighted average 1176 1. 08 If natural backgrounds are fractal-like, camouflage should be designed along similar principles. Newer camouflage schemes like MARPAT (U. S Marines) and CADPAT (Canadian Armed Forces) use a two-scale scheme which is noticeably better at blending into terrain and foliage than the older single-scale schemes. For example, detection times for MARPAT (Fig. 1) camouflaged targets are about 2. 5 times longer than detection of NATO single-scale camouflage