an important topic in the image-processing field [@Kovesi1996]. It aims at finding image features including lines, edges, Mach bands, corners, and blobs, by using quantitative methods. Many IFD methodologies have been proposed, which can be classified into two broad categories. First, the IFD methods that are based on dimensional metrics. The majority of the published IFD methods lie into this category including dilation-erosion residue operator [@Noble1989], gradient [@Canny1983], weak membrane [@Blake1987], anisotropic diffusion [@Perona1990], and univalue segment assimilating nucleus [@Smith1997] -based methods. The main issue of the dimensional IFD methods is that they are too sensitive to image contrasts and spatial magnifications [@Kovesi1996]. Second, the IFD methods that are based on non-dimensional metrics. Phase congruency (PC) is such a method [@Morrone1986]. References [@Kovesi1996], [@Ziou1998], [@Patel2014], and [@Noble1989] review many of the proposed IFD techniques in details.

The PC-IFD method is important for several reasons [@Kovesi1996; @Kovesi1999; @Kovesi2003]: 1) It is invariant to the image contrast, because it is not based on intensity gradient; 2) No assumption is made in the PC-IFD formulation and computation; 3) It can detect various features; and 4) It uses the image phase information. The latter might be one of the most significant features of the 