Phase congruency

Abstract: In the Fourier representation of signals, spectral magnitude and phase tend to play different roles and in some situations many of the important features of a signal are preserved if only the phase is retained. Furthermore, under a variety of conditions, such as when a signal is of finite length, phase information alone is sufficient to completely reconstruct a signal to within a scale factor. In this paper, we review and discuss these observations and results in a number of different contexts and applications. Specifically, the intelligibility of phase-only reconstruction for images, speech, and crystallographic structures are illustrated. Several approaches to justifying the relative importance of phase through statistical arguments are presented, along with a number of informal arguments suggesting reasons for the importance of phase. Specific conditions under which a sequence can be exactly reconstructed from phase are reviewed, both for one-dimensional and multi-dimensional sequences, and algorithms for both approximate and exact reconstruction of signals from phase information are presented. A number of applications of the observations and results in this paper are suggested.

Abstract: This paper presents a simple and biologically plausible model of how mammalian visual systems could detect and identify features in an image. We suggest that the points in a waveform that have unique perceptual significance as 'lines' and 'edges' are the points where the Fourier components of the waveform come into phase with each other. At these points 'local energy' is maximal. Local energy is defined as the square root of the sum of the squared response of sets of matched filters, of identical amplitude spectrum but differing in phase spectrum by 90 degrees: one filter type has an even-symmetric line-spread function, the other an odd-symmetric line-spread function. For a line the main contribution to the local energy peak is in the output of the even-symmetric filters, whereas for edges it is in the output of the odd-symmetric filters. If both filter types respond at the peak of local energy, both edges and lines are seen, either simultaneously or alternating in time. The model was tested with a series of images, and shown to predict well the position of perceived features and the organization of the images.

Abstract: Multimodal medical image fusion, as a powerful tool for the clinical applications, has developed with the advent of various imaging modalities in medical imaging. The main motivation is to capture most relevant information from sources into a single output, which plays an important role in medical diagnosis. In this paper, a novel fusion framework is proposed for multimodal medical images based on non-subsampled contourlet transform (NSCT). The source medical images are first transformed by NSCT followed by combining low- and high-frequency components. Two different fusion rules based on phase congruency and directive contrast are proposed and used to fuse low- and high-frequency coefficients. Finally, the fused image is constructed by the inverse NSCT with all composite coefficients. Experimental results and comparative study show that the proposed fusion framework provides an effective way to enable more accurate analysis of multimodality images. Further, the applicability of the proposed framework is carried out by the three clinical examples of persons affected with Alzheimer, subacute stroke and recurrent tumor.