Large-scale failures of f(-alpha) scaling in natural image spectra

Several studies have demonstrated that the power spectra of natural image ensembles scale as f(-alpha). A stronger claim that has been made is that the power spectra of single natural images typically also scale as f(-alpha). Results are presented that challenge this latter claim. The results are based on a method for estimating large-scale structure in single images that compares aliasing artifacts produced by image windows of different shape. Failures of f(-alpha) scaling are found at large scales in many natural images. These failures cannot be accounted for by f(-alpha) scaling models such as a linear superposition model or a model based on two-dimensional occlusions in the image plane. The results imply that claims about f(-alpha) scaling in single natural images have been exaggerated. The results also offer insight into why such failures of f(-alpha) scaling occur.