• Compared with other self-calibration methods, our proposed method compensates for the error from a single phase map while protecting the edge information. The implementation is simple and easy to deploy in different situations. • The phase registration algorithm based on Gray code guidance is introduced, which pinpoints the boundaries of the Gray code phase order, and two strategies are introduced to select correct phase matching pairs. • We use outlier detection technology to iteratively fit phase matching pairs to eliminate mismatched points, and the fitting relation is used to compensate for the projector nonlinearity point by point. In phase-shifting profilometry, the nonlinearity of the projector is the main error source which undermines the 3D reconstruct accuracy. Most calibration algorithms mainly focus on calibrating the nonlinear responses and compensating for the related errors. However, it requires a tedious pre-calibration process. In this paper, a phase registration algorithm based on Gray code guidance is proposed, Hough transform and majority voting are performed to accurately locate the boundary of Gray code, two strategies are introduced to select correct phase matching pairs. In addition, to eliminate mismatched points and improve the accuracy of the fitting, outlier detection technology is used to iteratively fit phase matching pairs. Finally, the error is compensated point by point using the fitting curve. Experimental and simulation results demonstrate the effectiveness of the proposed method. It has the advantages of simple deployment, no photometric pre-calibration, high accuracy, strong robustness, and can handle the projector's nonlinearity that changes with time. [ABSTRACT FROM AUTHOR]