Billock, Cunningham & Tsou (2008) 11 APPROVED FOR PUBLIC RELEASETo define two-dimensional JNDs we measured discrimination in four directions: both increments and decrements for both spatial ( ȕ) and temporal ( Į) exponents. Not surprisingly, the JNDs in this space are ellipsoidal (they resemble color discrimination JNDs). Interestingly, the interior portion of the resulting two-dimensional discrimination space is remarkably flat, a feature that some psychophysicists have gone to great lengths to obtain in nonlinear mappings of other perceptual systems (e. g., color discrimination). Implications for Future Work It is worth noting that humans can become proficient at naming the spectral exponents of images (or equivalently, fractal dimension, which is a linear transform of the exponent; Cutting & Garvin, 1987; Kumar et al., 1993; Pentland, 1988). A neural ability to estimate the spectral drop-off and exploit it has been speculated on and deserves additional attention (Billock, 2000; Billock et al., 2001b; Campbell et al., 1978; Hammett & Bex, 1996; Rogowitz & Voss, 1990). Taken together with the natural image regularities and perceptual pop-out findings discussed earlier, this suggests that ȕ is a key signature, both for images and for the visual systems that evolved to transduce images. Of particular interest is the finding that, under some conditions (nonlinear systems near threshold), adding noise can facilitate detection and identification of some signals, including images (Repperger et al., 2001; Simonotto et al., 1997; Yang, 1998)-an example of stochastic resonance as an image enhancement mechanism. Dynamic noise is more effective than static (Simonotto et al, 1997). Because other studies of stochastic resonance show that 1/fȕ noise can be more efficient than white noise in inducing stochastic resonance effects (Billock & Tsou, 2007; Hangi et al., 1993; Nozaki et al., 1999), further studies of discrimination in spatiotemporal fractal noise (at various contrast levels) would be warranted and might uncover some practical applications. Implications of Fractal Discrimination for Camouflage and Combat ID Based on this and other work we can enumerate some implications for camouflage and combat ID: (i) Natural images have 1/fȕ spatial amplitude spectra. The most reasonable value of ȕ for general purpose camouflage is around 1. 1. Particular environments will vary in this statistic and in coloration. (ii) Keeping the difference between the ȕtarget and ȕbackground less than 0. 2 generally avoids preattentive popout, but discrimination will still be possible using a point-by-point search. (iii) Using many spatial scales makes camouflage effectiveness almost independent of distance. (iv) For IFF purposes, friendly camouflage schemes should have different ȕs than the unfriendly camouflage patterns, but this may conflict with concealment goals. The best outcome would be for hostile and friendly camouflage statistics to be on opposite sides of the ȕbackground value, with the friendly scheme not easily discriminable from background but discriminable from the hostile. (v) For identification purposes, side-by-side viewing of sensor and reference images is preferable. Sensor operators should be screened for spatial sampling problems (sub-clinical amblyopia) by measuring their contrast sensitivity functions. (vi) It may be possible to break many camouflage schemes by adding filtered noise to the sensor images. This seemingly perverse aspect of stochastic resonance should be exploited if possible. Since stochastic resonance's effectiveness is often dependent on the Fourier spectral qualities of the noise, fractal camouflage may be particularly vulnerable (because the spectral qualities of simple fractals are easily matched by varying one noise parameter). Multi-fractals may be less vulnerable in this regard. It would be ironic if the beautiful mathematical attributes of fractals (which give it so