The Importance Of Localized Phase In Vision And Image Representation
Joachim A. Behar, Moshe Porat, Y.Y. Zeevi · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
It is well known that Fourier-phase is sufficient for image representation and reconstruction within a scale factor, under a variety of conditions. For a finite length sequence, i.e., a sampled signal, a finite number of Fourier coefficients suffices to reconstruct the sequence. Several algorithms exist for this purpose. A close form solution involves solving a large set of linear equations. Another approach is an iterative technique which involves repeated transformation between the frequency and the spatial domains. The application of these techniques to image reconstruction from global (Fourier) phase is, however rather limited in practice due to the computational complexity. In this paper we present a new approach to image representation by means of which, similarly to the biological processing at the level of the cortex, the partial information is defined by localized phase. Also, like processing in vision, dc is first extracted from the signal and signaled separately. Computational results and theoretical analysis indicate that image reconstruction from localized phase-only is more efficient than image reconstruction from global (Fourier) phase. It also lends itself to hardware implementation of fast algorithms using highly parallel architecture.