The figure illustrates the problem to be solved in order to get a reasonable similarity function. The coefficients of a jet consist of magnitude and phase. Magnitude varies slowly with position.
Phase varies with the corresponding spatial frequency .
A Gabor wavelet responds strongly to edges if the direction is prependicular to its wave vector. But when hitting an edge, the real and the imaginary parts oscillate with the characteristic frequency instead of providing a smooth peak. Thus, the rapid phase variations cause problems. Jets taken from an image few pixels apart from each other have very different coefficients, although they represent almost the same local feature. The magnitudes provide monotonic measures of image properies.