Background-extracted extended Kalman filter-based phase shift estimation algorithm for phase shifting profilometry system

•Background is extracted by using 2D-VMD-BEMD algorithm which provides a reliable method under some unfavorable conditions.•A novel 2D-VMD-BEMD EKF-based region-wise phase shift estimation is proposed to address the imprecise phase shift in PSP.•The actual phase step is estimated by the coefficient of the quadratic phase in a selected window.•This method can remove phase shift error induced by the mechanical projector, object motion and be available for N-step PSP.