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

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 non-Gaussian white texture with higher-order spatial correlations at one extreme to Gaussian white noise at the other. The simple construction of a continuum of self-similar ensembles possessing phase correlations provides a tool for investigating human perception of structure in the absence of useful length scales. The fixed-point textures have luminance histogram differences, a direct result of their higher-order 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.