PC-IFD, because phase is shown to be more informative than magnitude in image processing [@Oppenheim1981]. PC is developed based on the hypothesis that image features are optimally perceived at points where the Fourier series components are maximally in phase, meaning that phases of Fourier series€™ components are similar. This hypothesis was first introduced and verified for Mach bands in [@Morrone1986]. Subsequently, its effectiveness for detecting other features types has been verified in [@Morrone1986; @Venkatesh1990; @Kovesi1996; @Kovesi1999; @Kovesi2003].

It is shown in [@Venkatesh1990] and [@Morrone1987] that the maxima of the local energy occur at the maxima of PC and vice versa. Thus, in practice, the PC measure is often obtained by computing the normalized local energy, [@Morrone1987; @Venkatesh1990; @Kovesi1999; @Kovesi2003]. Moreover, it has been illustrated that the peaks of PC outcome are higher and more distinct when local energy is computed using window-based approaches than the peaks obtained from local energy over the whole signal, [@Kovesi1996]. Consequently, Peter Kovesi proposed a multi-scale PC measurement method based on Gabor wavelets and extended it to solve two dimensions (2D), [@Kovesi1996; @Kovesi1999; @Kovesi2003]. Kovesi further modified the PC formulation to overcome noise and ill-conditioning issues, and introduced a weighting function to penalize PC measures 