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The spatial characteristics of letters and their influence on readability and letter identification have been intensely studied during the last decades. There have been few studies, however, on statistical image properties that reflect more global aspects of text, for example properties that may relate to its aesthetic appeal. It has been shown that natural scenes and a large variety of visual artworks possess a scale-invariant Fourier power spectrum that falls off linearly with increasing frequency in log-log plots. We asked whether images of text share this property. As expected, the Fourier spectrum of images of regular typed or handwritten text is highly anisotropic, i.e., the spectral image properties in vertical, horizontal, and oblique orientations differ. Moreover, the spatial frequency spectra of text images are not scale-invariant in any direction. The decline is shallower in the low-frequency part of the spectrum for text than for aesthetic artworks, whereas, in the high-frequency part, it is steeper. These results indicate that, in general, images of regular text contain less global structure (low spatial frequencies) relative to fine detail (high spatial frequencies) than images of aesthetics artworks. Moreover, we studied images of text with artistic claim (ornate print and calligraphy) and ornamental art. For some measures, these images assume average values intermediate between regular text and aesthetic artworks. Finally, to answer the question of whether the statistical properties measured by us are universal amongst humans or are subject to intercultural differences, we compared images from three different cultural backgrounds (Western, East Asian, and Arabic). Results for different categories (regular text, aesthetic writing, ornamental art, and fine art) were similar across cultures.

From regular text to artistic writing and artworks: Fourier statistics of images with low and high aesthetic appeal