Kurtosis and the Phase Structure of Images

Many studies have shown that natural imagery exhibit certain statistical regularities such as scale invariance and non-Gaussian behavior. In particular, it has been shown that the marginal statistics (histograms) of filtered images have distributions with large kurtosis. Furthermore, the joint statistics of two or more filter responses are non-Gaussian often with circular and “diamond” shaped distributions. In this paper, we examine the relationship between the phase angle of a signal and these non-Gaussian statistics. It is shown that both local and global correlations in the phase angle lead to many of the statistical regularities that have been observed in natural images. In addition, the discriminative power of marginal and joint statistical representations is studied. From this study we are able to show that these representations have difficulty differentiating changes in the local correlations of phase angle. Yet, these small changes can manifest as global and visually distinct differences.