In the above equations, E i [ n , m ] is the input image, n and m are the spatial variables, F F T 2 is the two-dimensional fast Fourier transform, and u and v are spatial frequency variables. The function K ~ ~ ( u , v ) is the warped phase kernel and the function L ~ ~ ( u , v ) is a localization kernel implemented in frequency domain. PST operator is defined as the phase of the Warped Stretch Transform output as follows