A Robust Wrap Reduction Algorithm for Fringe Projection Profilometry and Applications in Magnetic Resonance Imaging

In this paper, we present an effective algorithm to reduce the number of wraps in a 2D phase signal provided as input. The technique is based on an accurate estimate of the fundamental frequency of a 2D complex signal with the phase given by the input, and the removal of a dependent additive term from the phase map. Unlike existing methods based on the discrete Fourier transform (DFT), the frequency is computed by using noise-robust estimates that are not restricted to integer values. Then, to deal with the problem of a non-integer shift in the frequency domain, an equivalent operation is carried out on the original phase signal. This consists of the subtraction of a tilted plane whose slope is computed from the frequency, followed by a re-wrapping operation. The technique has been exhaustively tested on fringe projection profilometry (FPP) and magnetic resonance imaging (MRI) signals. In addition, the performance of several frequency estimation methods has been compared. The proposed methodology is particularly effective on FPP signals, showing a higher performance than the state-of-the-art wrap reduction approaches. In this context, it contributes to canceling the carrier effect at the same time as it eliminates any potential slope that affects the entire signal. Its effectiveness on other carrier-free phase signals, e.g., MRI, is limited to the case that inherent slopes are present in the phase data.