Local phase coherence and the perception of blur

Humans are able to detect blurring of visual images, but the mechanism by which they do so is not clear. A traditional view is that a blurred image looks "unnatural" because of the reduction in energy (either globally or locally) at high frequencies. In this paper, we propose that the disruption of local phase can provide an alternative explanation for blur perception. We show that precisely localized features such as step edges result in strong local phase coherence structures across scale and space in the complex wavelet transform domain, and blurring causes loss of such phase coherence. We propose a technique for coarse-to-fine phase prediction of wavelet coefficients, and observe that (1) such predictions are highly effective in natural images, (2) phase coherence increases with the strength of image features, and (3) blurring disrupts the phase coherence relationship in images. We thus lay the groundwork for a new theory of perceptual blur estimation, as well as a variety of algorithms for restoration and manipulation of photographic images.