Flexible Nonlinear Error Correction Method Based on Support Vector Regression in Fringe Projection Profilometry

The gamma effect of a projector is the most critical factor affecting 3-D shape measurements. A flexible and efficient error correction algorithm based on machine learning is proposed that facilitates correcting the system nonlinear error without any system nonlinear parameter calibration or knowledge of prior system information. The proposed method is a two-stage framework. The first stage is the projector gamma estimation module. First, the probability density function (PDF) of the wrapped phase with different gamma values is generated by simulation. The corresponding PDF sequence and gamma values are combined into a dataset to train a support vector regression (SVR) model. The trained SVR model can estimate the system gamma value according to the PDF sequence of the actual measured wrapped phases. The second stage is the phase error compensation module. In this stage, we establish the objective function according to the mathematical model and the gamma value estimated in the first part, and then use an iterative algorithm to solve the precise phase. The experimental and simulation results confirm the effectiveness of this method in directly identifying the system gamma value from the wrapped phase without complicated system calibration or any prior system information. The proposed algorithm is suitable for time-varying nonlinear systems.