A generalized model for relative phases based on bilinear representation of natural image series

Local phase is now known to carry information about image features or object motions. But it is harder to use directly compared with amplitude, so far. In this paper, we propose that the relative local phase, which is a function of scale, position and time, really matters in representing the information of image structures or movements. A unified description of relative phase is given in this paper based on a bilinear representation of natural image series via multi-scale orientated dual tree complex wavelets. Then, the behaviors of nontrivial relative phase, especially for their distribution on multi-scale and multi-subband, are investigated. We propose a new generalized model, which is derived from Mobius transform, to describe various relative phases. Numerical experiments for a large amount of test images show that the new model performs best compared with the von Mises or wrapped Cauchy distribution. Especially for those with asymmetric pdf, our function fits with the histogram quite well while the other two may fail. We thus lay a groundwork for relative phase-based image processing methods, such as classification, deblurring and motion perception. Copyright © 2014 John Wiley & Sons, Ltd.