A frequency-based window width optimized two-dimensional S-Transform profilometry

A new scheme is proposed to as a frequency-based window width optimized two-dimensional S-Transform profilometry, in which parameters p_u and p_v are introduced to control the width of a two-dimensional Gaussian window. Unlike the standard two-dimensional S-transform using the Gaussian window with window width proportional to the reciprocal local frequency of the tested signal, the size of window width for the optimized two-dimensional S-Transform varies with the ^{p_u th} (^{p_v th}) power of the reciprocal local frequency f_x (f_y) in x (y) direction. The paper gives a detailed theoretical analysis of optimized two-dimensional S-Transform in fringe analysis as well as the characteristics of the modified Gauss window. Simulations are applied to evaluate the proposed scheme, the results show that the new scheme has better noise reduction ability and can extract phase distribution more precise in comparison with the standard two-dimensional S-transform even though the surface of the measured object varies sharply. Finally, the proposed scheme is demonstrated on three-dimensional surface reconstruction for a complex plastic cat mask to show its effectiveness.