Fringe Order Correction for Number-Theoretical Phase Unwrapping Method via Maximum Likelihood Principle

The number-theoretical phase unwrapping method has recently been widely applied in fringe projection profilometry. But fringe order errors may occur due to noise or distortion, leading to errors in the unwrapped phase map, and eventually affecting the accuracy of the reconstructed object surface. In this paper, we propose a novel fringe order correction method based on the maximum likelihood principle. The direct cause of fringe order error is the deviation of an intermediate variable which in theory should be an integer, and the ground truth of the integer stays unchanged within a valid neighborhood. By modeling the calculated intermediate variable as an observed sample from the normal distribution of the unknown ground truth integer, we can determine a valid neighborhood relative to the observed pixel. Then the ground truth integer can be calculated by maximizing the likelihood function and then the fringe order error is corrected. The simulation results and experimental comparisons have verified the feasibility, robustness, and superiority of the proposed method in contrast with other fringe order correction methods.