Method with high accuracy for phase retrieval in Fourier FPP based on the modified FCM and variational image decomposition

Phase retrieval with high accuracy remains one of the most challenging problems in Fourier fringe projection profilometry (FPP). The variational image decomposition TV-Hilbert-L2 model has been proved to be a powerful tool for phase retrieval. In this paper, we first propose a modified fuzzy c-means (FCM) clustering algorithm to remove background from fringe projection patterns. In order to further improve the accuracy, we combine the modified FCM and the variational image decomposition TV-Hilbert-L2 model and propose a new method to get the fringe part from the single frame fringe projection pattern. We evaluate the performance of this method via application to two simulated and one experimental fringe projection patterns and comparison with the Fourier transform, morphological operation-based bi-dimensional empirical mode decomposition, and variational image decomposition TV-Hilbert-L2 model. The experiment results show that our method improves the accuracy of phase retrieval for TV-Hilbert-L2 model and can achieve similar accuracy to the phase-shifting method.