Abstract

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.

© 2000 Optical Society of America

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