A continuum of non-Gaussian self-similar image ensembles with white power spectra

Abstract-We introduce a scaling procedure that acts on visual textures to produce new textures having the same resolution, display size, and mean contrast power. We derive the form of the scaling fixed-point textures (image ensembles) resulting from repeated application of this scale transformation to the ‘even’ texture with an arbitrary amount of sporadic decorrelation. The result is a continuum of scaling fixed-point or ‘self-similar’ image ensembles, ranging from a strongly nonGaussian white texture with higher-order spatial correlations at one extreme to Gaussian white noise at the other. The simple construction of a continuum of selfsimilar ensembles possessing phase correlations provides a tool for investigating human perception of structure in the absence of useful length scales. The fixedpoint textures have luminance histogram differences, a direct result of their higherorder spatial properties. This suggests that scaling might afford an extension of our understanding of IID (independent identically distributed) texture discrimination (Chubb et al., J. Opt. Soc. Am. A 11, 2350-2374, 1994) to more general texture discrimination tasks in which spatial correlations play a role.