Phase-to-Coordinates Calibration for Fringe Projection Profilometry Using Gaussian Process Regression

In the task of 3-D topography measurement by fringe projection profilometry (FPP), it is crucial to establish mapping from the phase map to the 3-D coordinates, known as 3-D calibration. The traditional methods are prone to select some specific functions to fit the phase-to-coordinates' relationship, which needs to make a compromise between measurement accuracy and efficiency. This article proposes a novel calibration method based on the Gaussian process (GP) regression to solve this problem. In this work, according to the geometric and other systemic constraints, a pixel-dependent semiparameterized calibration model is derived to guarantee the efficiency of computation and data storage. Based on the spatial correlations of the calibration data, the GP regression method is applied to enhance the fitting ability and flexibility of the calibration model without any specific functions and parameters. The GP regression method is also applied to remove random noise from the phase map, which further improves the accuracy of 3-D coordinates. The experimental results of measuring a whiteboard and a double ball bar demonstrate the superiority of the proposed GP-based calibration model in terms of accuracy and robustness when compared with the traditional models.